Pith. sign in

REVIEW 3 major objections 4 minor 138 references

Eigenstate Preparation on Quantum Computers

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This thesis argues that maximizing the Rodeo algorithm's success probability, rather than minimizing energy, prepares eigenstates with higher fidelity on shallow quantum circuits and also reaches excited states.

desk verdict Genuinely new VRA algorithm with clean math, but its central scalability claim currently rests on noiseless simulations with an idealized energy target; the hardware demos are real. read the letter →

arxiv 2412.15081 v1 pith:EHRZUIZP submitted 2024-12-19 quant-ph

Joey Bonitati This is my paper · ORCID
classification quant-ph PACS 03.67.Lx03.67.-a
keywords eigenstatepreparationRodeoalgorithmvariationalquantumeigensolverQAOAadiabaticevolutionoptimalcontrolsimulationNISQ
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Solving eigenvalue problems—finding the eigenstates and energies of a Hamiltonian—is the bottleneck for quantum simulation of nuclei and molecules. This thesis proposes a practical route through three quantum algorithms: adiabatic evolution with optimal control, the Rodeo algorithm, and the Variational Rodeo Algorithm (VRA). The central claim is that VRA, which uses the Rodeo success probability as its cost function, prepares eigenstates more faithfully than energy minimization when the variational circuit is too shallow to reach the exact ground state, and that it can target excited states by shifting the Rodeo energy window. If correct, this gives near-term quantum computers a concrete way to turn low-depth circuits into high-fidelity eigenstates, a prerequisite for simulating nuclear structure and reactions.

What carries the argument

The central object is the Rodeo success probability used as a variational cost function (Equation 5.13). The circuit is: prepare a parameterized ansatz, then for each of $M$ Rodeo cycles apply a Hadamard to an ancilla, perform a controlled time evolution $e^{-iH_{\text{obj}}t}$, apply a phase rotation $e^{iEt}$, apply another Hadamard, and measure the ancilla. The probability that all ancilla measurements give $|0\rangle$ is $$\sum_n |c_n|^2\left[\frac{1+$e^{{-(E_n-E)^2\sigma^2/2}}$}{2}\right]^M,$$ which exponentially suppresses eigenstates whose energies lie outside a window around $E$. Maximizing this probability is the mechanism that steers the parameterized circuit toward a chosen eigenstate, and it is what distinguishes VRA from energy-minimization approaches.

What would settle it

Run VRA on a real noisy device for a random 6-qubit Hamiltonian, using only an estimated energy (for example from a prior VQE calculation) as the Rodeo target, and compare the measured ground-state overlap and success probability against QAOA energy minimization with equal circuit depth. If the VRA advantage disappears under device noise, or if the optimized parameters fail to increase the measured Rodeo success probability relative to the simulated value predicted by Equation 5.13, the central claim is not borne out on hardware.

Watch

Extended reading notes

Core claim

The paper's central proposal is the Variational Rodeo Algorithm: append a Rodeo circuit to a parameterized state-preparation ansatz (here QAOA) and classically optimize the ansatz parameters to maximize the probability that every Rodeo ancilla measurement returns $|0\rangle$, i.e. to minimize $1-P_N$. For a state $|\psi\rangle=\sum_n c_n|E_n\rangle$ of the object Hamiltonian and a Rodeo energy parameter $E$, the success probability is $$P_\psi=\sum_n |c_n|^2\left[\frac{1+$e^{{-(E_n-E)^2\sigma^2/2}}$}{2}\right]^M.$$ Because each eigenstate's contribution is damped by a Gaussian factor centered at $E$, maximizing this probability concentrates the state on the eigenstate with eigenvalue closest to $E$. In noiseless simulations on random 6- and 10-qubit Hamiltonians, the paper finds that this cost function drives the QAOA output toward the targeted eigenstate—including excited states—and that for shallow circuits (12–20 parameters) it reaches higher ground-state overlap than energy minimization. The same simulations show that using VRA as a fine-tuning step after energy minimization improves overlap in cases where the variational principle is not in effect. The paper also demonstrates the two building blocks: adiabatic evolution with optimal-control custom gates reaches roughly 95% fidelity in emulations against about 60–85% on cloud processors, and the Rodeo algorithm recovers single-qubit eigenvalues to 0.08% relative error on hardware.

Load-bearing premise

The claim that VRA is an effective eigenstate-preparation method rests on the assumption that the noiseless success probability of the Rodeo circuit is a faithful stand-in for real-device performance, since all VRA results come from exact classical simulations and the ground-state tests supply the exact ground-state energy as input.

Editorial extensions

If this is right

  • VRA turns an arbitrary parameterized ansatz into an eigenstate filter: by choosing the Rodeo energy $E$, the same circuit can be steered to the ground state or to a specific excited state.
  • For shallow QAOA circuits, optimizing the Rodeo success probability yields higher ground-state overlap than energy minimization, so VRA can replace or follow VQE/QAOA optimization.
  • The success probability is estimated by counting ancilla measurement outcomes, avoiding the need for full Hamiltonian expectation-value estimation in the optimization loop.
  • Rodeo's exponential suppression of off-target eigenstates means the added cost of the Rodeo tail grows only logarithmically with the desired eigenstate purity, making the hybrid approach compatible with NISQ-era circuit depths.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the same cost function could be applied to any parameterized ansatz beyond QAOA, such as hardware-efficient circuits, as long as controlled time evolution under $H_{\text{obj}}$ is available; the paper only tests QAOA.
  • Editorial inference: because the Rodeo success probability is a binary-measurement count rather than a signed energy expectation, it may be more robust to certain systematic errors; this is testable by comparing gradient noise under a depolarizing noise model.
  • Editorial inference: VRA's ability to target excited states, combined with the Hellmann-Feynman technique demonstrated for the Rodeo algorithm, could enable spectrum and observable calculations without orthogonality-constrained excited-state variational methods.
  • Editorial inference: the noiseless-proxy assumption will be the first thing to break as system size grows: the exact energy input $E_0$ used in the tests must in practice be replaced by an estimate, and error in that estimate should degrade the overlap advantage.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This thesis (arXiv:2412.15081) develops and tests three quantum algorithms for eigenstate preparation: adiabatic evolution with optimal control (Chapter 3), the Rodeo Algorithm (RA, Chapter 4), and the novel Variational Rodeo Algorithm (VRA, Chapter 5). The RA section derives the success probability for N cycles with Gaussian-sampled time parameters, demonstrates eigenvalue scans and eigenstate preparation on a single-qubit Hamiltonian on IBM Casablanca hardware (achieving 0.08% relative energy error with measurement-error mitigation), and argues for an exponential advantage over phase estimation and adiabatic evolution. The VRA section proposes maximizing the RA success probability as a variational cost function for QAOA parameters, derives the gradient structure of three cost functions, and reports noiseless classical simulations on random 6- and 10-qubit Hamiltonians showing that VRA prepares ground and excited states with higher fidelity than energy minimization for low-depth QAOA circuits.

Significance. The strengths of the manuscript are the clean analytic derivations: the RA success probability (Eqs. 4.5–4.10) and the VRA cost-function gradients (Section 5.2) are carefully derived from the initial-state overlap without assuming knowledge of the target eigenstate. The hardware demonstration of RA (Section 4.2.2) is a concrete, reproducible experiment with measurement-error mitigation, and the 0.08% eigenvalue error is a useful benchmark. The VRA idea is a plausible and interesting extension that directly addresses RA's dependence on initial-state overlap, and the comparison of energy minimization versus overlap maximization is informative. However, the central claim that VRA 'allows for better scalability' is currently supported only by noiseless simulations with the exact ground-state energy injected into the cost function; the numerical evidence does not yet cover the operational conditions of a near-term device.

major comments (3)
  1. [Section 5.3.2, Eq. (5.13)] The VRA ground-state comparison sets the target energy E in Eq. (5.13) to the exact ground-state energy E0, a quantity that is not known in practice for the systems that motivate the algorithm. Because the abstract claims better scalability under realistic conditions, this oracle-like input is load-bearing; the manuscript does not test how VRA performs when E is only known approximately, which would require energy scanning or a broader energy filter and could substantially reduce the reported success probabilities.
  2. [Section 5.3 (including 5.3.1 and 5.3.2)] All VRA results are obtained by classically computing exact final states and evaluating the noiseless expectation value P_N from Eq. (5.13); no noisy circuit simulation, finite-shot sampling, or hardware experiment is presented for VRA. Since the VRA circuit appends the RA controlled time evolutions and an ancilla register to the QAOA ansatz, the circuit depth is at least double that of QAOA alone, so the noiseless advantage shown in Figures 5.3 and 5.4 could vanish or reverse under gate errors, decoherence, and the post-selection cost of conditioning on all ancilla successes. A benchmark with a standard noise model and finite shots is needed to support the claim that VRA allows better scalability on near-term devices.
  3. [Section 4.1.1, Eqs. (4.9)–(4.11)] The claimed exponential speedup of RA over phase estimation and adiabatic evolution for eigenstate preparation is based purely on scaling in the residual error Δ, omitting the total coherent evolution time per preparation, which grows with the number of cycles N and the standard deviation σ of the time parameters. The complexity comparison should include these resources, along with the cost of implementing the controlled time evolution (e.g., Trotterization), before concluding that RA is exponentially more efficient for large systems; this is a load-bearing point for the motivation of VRA.
minor comments (4)
  1. [Section 3.3.1.1, Eq. (3.14)] The notation "||c|^2_exp>" in the confusion-matrix equation is malformed; it should read "|c^2_exp>" or similar, with the superscript applied to the probability vector.
  2. [Section 5.2, Eq. (5.13)] The definition of P_ψ uses M for the number of cycles, while the surrounding text and figures (e.g., Figure 5.3) use N; unify the notation to avoid confusion.
  3. [Section 4.2.2.3] The phrase "ascanwith" appears to be a typo; it should read "a scan with".
  4. [Chapter 3, Figures 3.2 and 3.3] The captions state that the figures are reused from [31] but do not specify the source or permission; for an arXiv posting, this is acceptable but should be clarified if the manuscript is submitted elsewhere.

Circularity Check

2 steps flagged · score 4.0 of 10

VRA's cost function is a direct overlap proxy, so the eigenstate-preparation outcome is partly definitional; the comparison with energy minimization retains independent content.

  1. self definitional [Section 5.2.3, Eq. (5.13); Section 5.3.2, Simulation Method 2]
    "Before performing optimizations, we directly solve for the eigenvectors |E_k⟩ of H_obj and use the ground-state energy E0 as the target energy parameter in Equation 5.13 for P_N along with a σ value of 10. ... We note that the plots produced by VRA for ground state overlap and P_N are similar because, in this example, the RA parameters E = E0 and σ = 10 make it so that the energy filter of the RA is smaller than the energy gap to the first excited state."

    With E = E0 and σ large relative to the gap, the Gaussian weight in Eq. (5.13) is approximately 1 for the ground state and approximately 0 for all other eigenstates, so P_N reduces essentially to the ground-state overlap |c_0|^2. Thus VRA's cost function is a direct, reweighted estimate of the very quantity used to report success. Optimizing this cost and then reporting high ground-state overlap or high RA success probability is a tautology: the optimizer is maximizing the metric being measured. The claimed advantage over energy minimization is not fully circular because it depends on the optimization landscape, but the eigenstate-preparation result is built into the objective.

  2. self definitional [Section 5.3.1, Simulation Method 1 (Figure 5.2)]
    "Since VRA aims to maximize the success probability of the Rodeo algorithm, the cost function to minimize is defined as 1−P_N. ... for each value of E used in the VRA cost functions, a red dot is placed at the y coordinate corresponding to the eigenstate that had the highest overlap, which was the one with the eigenvalue closest to E in every case."

    The claimed demonstration of excited-state preparation is forced by the cost function's definition. Equation (5.13) weights each eigenstate by a Gaussian centered at E, so the eigenstate nearest E automatically receives the largest weight and, after optimization, the largest overlap. Observing that VRA selects the eigenstate closest to E is therefore a restatement of the objective rather than an independent finding about the algorithm's excited-state capability.

full rationale

The Rodeo Algorithm analysis in Chapter 4 (Eqs. 4.1-4.10) is a self-contained state-vector derivation: the success-probability formula is computed from the circuit and initial-state overlaps, not assumed from the target eigenstate, so that part is not circular. The load-bearing circularity is in Chapter 5: VRA chooses the RA success probability P_N (Eq. 5.13) as its cost function, and P_N is by construction a weighted sum of eigenstate overlaps. When the numerical benchmark supplies E = E0 exactly and σ is large relative to the gap, P_N becomes essentially the ground-state overlap |c_0|^2, as the paper itself notes. Reporting high P_N and high overlap after optimizing this cost is therefore a direct consequence of the objective. The excited-state 'demonstration' is similarly forced because Eq. (5.13) assigns the largest weight to the eigenstate closest to E. However, the comparison of VRA with energy minimization (Figure 5.3) is not fully circular: that maximizing overlap can beat minimizing energy for low-depth QAOA is a landscape result with independent content. No load-bearing self-citation was found: citations [30,105] underpin the RA, but the thesis re-derives the relevant formulas. The absence of a noise model and the use of the exact E0 oracle are real scalability concerns, but they are not circularity. Score 4 reflects partial, not complete, circularity because the central VRA-versus-VQE claim retains independent numerical content.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central new result of the thesis, the Variational Rodeo Algorithm, rests on the Rodeo success probability formula (Eq. 5.13), which is derived from the Born rule and Gaussian averaging. The numerical evidence for VRA is obtained from noiseless statevector simulation, and the key ground-state comparison uses the exact ground-state energy as input. No new physical entities are introduced.

free parameters (7)
  • transmon anharmonicity alpha = 200 MHz
    Chosen model parameter for the two-transmon Hamiltonian in Section 3.3.2; the optimal-control emulation results depend on it.
  • transmon coupling strength g = 3 MHz
    Chosen model parameter for capacitive crosstalk in Section 3.3.2; affects the gate optimization and emulation.
  • pulse penalty cutoff epsilon_cut = 30 MHz
    Hyperparameter in the GRAPE objective function (Eq. 3.28) that limits pulse amplitudes; chosen for all optimizations.
  • pulse penalty constants n and chi = n=3, chi=1e-3
    Hyperparameters in Eq. 3.28 governing the penalty term for large pulse amplitudes.
  • RA time parameter standard deviation sigma = varies across demonstrations (2, 5, 7, 10, 12)
    Standard deviation of Gaussian sampling for time evolutions; controls the energy filter width and is chosen by hand for each experiment.
  • number of RA cycles N = varies (3, 4, 6, 9)
    Number of rodeo cycles; larger N gives better filtering but deeper circuits; chosen per experiment.
  • QAOA parameter count = 12, 16, 20
    Number of tunable parameters in the QAOA ansatz used in VRA simulations (Section 5.3).
assumptions (6)
  • standard math The adiabatic theorem guarantees that a system initialized in an eigenstate remains in the instantaneous eigenstate for sufficiently slow evolution with a spectral gap.
    Used throughout Chapter 3 to justify eigenstate preparation via slow Hamiltonian interpolation.
  • standard math Born rule and projective measurement statistics.
    Used to derive success probabilities for the Rodeo Algorithm in Equations 4.5 through 4.9.
  • standard math Unitary time evolution and the Trotter-Suzuki decomposition.
    Used to discretize adiabatic evolution (Eq. 3.12) and to implement controlled time evolution in the Rodeo Algorithm.
  • standard math The Gaussian averaging identity that yields the exponential suppression in Eq. 4.10.
    Derived in Section 4.1.1 and used as the basis for RA complexity claims and the VRA cost function.
  • standard math The variational principle for energy expectation values.
    Used in Section 5.2.1 to establish the baseline energy-minimization cost function.
  • domain assumption Random Hermitian Hamiltonians with no degenerate eigenstates are representative test cases for variational algorithms.
    Section 5.3 uses randomly generated Hamiltonians to benchmark VRA against QAOA; the generality of the conclusions depends on this representativeness.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Eigenstate Preparation on Quantum Computers." pith.science (2026). https://pith.science/paper/EHRZUIZP

@misc{pith2026241215081,
  author       = {Pith},
  title        = {Pith review of: Eigenstate Preparation on Quantum Computers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHRZUIZP}},
  note         = {Machine review of arXiv:2412.15081}
}
read the original abstract

This thesis investigates quantum algorithms for eigenstate preparation, with a focus on solving eigenvalue problems such as the Schrodinger equation by utilizing near-term quantum computing devices. These problems are ubiquitous in several scientific fields, but more accurate solutions are specifically needed as a prerequisite for many quantum simulation tasks. To address this, we establish three methods in detail: quantum adiabatic evolution with optimal control, the Rodeo Algorithm, and the Variational Rodeo Algorithm. The first method explored is adiabatic evolution, a technique that prepares quantum states by simulating a quantum system that evolves slowly over time. The adiabatic theorem can be used to ensure that the system remains in an eigenstate throughout the process, but its implementation can often be infeasible on current quantum computing hardware. We employ a unique approach using optimal control to create custom gate operations for superconducting qubits and demonstrate the algorithm on a two-qubit IBM cloud quantum computing device. We then explore an alternative to adiabatic evolution, the Rodeo Algorithm, which offers a different approach to eigenstate preparation by using a controlled quantum evolution that selectively filters out undesired components in the wave function stored on a quantum register. We show results suggesting that this method can be effective in preparing eigenstates, but its practicality is predicated on the preparation of an initial state that has significant overlap with the desired eigenstate. To address this, we introduce the novel Variational Rodeo Algorithm, which replaces the initialization step with dynamic optimization of quantum circuit parameters to increase the success probability of the Rodeo Algorithm. The added flexibility compensates for instances in which the original algorithm can be unsuccessful, allowing for better scalability.

Figures

Figures reproduced from arXiv: 2412.15081 by the authors.

Figure 2
Figure 2. The Bloch sphere representing the state of a single qubit as coordinates on a sphere [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 2
Figure 2. A basic quantum circuit diagram for creating a Bell state. The initial state on the left is [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗
Figure 2.1
Figure 2.1. 2. The gates in these diagrams are applied sequentially from left to right on the quantum [PITH_FULL_IMAGE:figures/full_fig_p026_2_1.png] view at source ↗
Figures from the paper (22 more)
Figure 2
Figure 2. Figure 2: A circuit diagram for a Controlled-U gate. [PITH_FULL_IMAGE:figures/full_fig_p029_2.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) of the fidelity between the device state and the ground state [PITH_FULL_IMAGE:figures/full_fig_p059_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) Decomposition of the first short-time propagator in [PITH_FULL_IMAGE:figures/full_fig_p061_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) Schematic depiction of [PITH_FULL_IMAGE:figures/full_fig_p063_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) First 100 ns of control pulses with lengths [PITH_FULL_IMAGE:figures/full_fig_p068_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) Adiabatic evolution of [PITH_FULL_IMAGE:figures/full_fig_p071_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) Combination of simultaneous U3 gates [circuit [PITH_FULL_IMAGE:figures/full_fig_p074_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) A comparison of the emulated outputs of the adiabatic [PITH_FULL_IMAGE:figures/full_fig_p076_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) Mean error in measured occupation probabilities as a [PITH_FULL_IMAGE:figures/full_fig_p077_3.png]
Figure 3
Figure 3. Figure 3: (Figure reused from [31]) Evolution of [PITH_FULL_IMAGE:figures/full_fig_p078_3.png]
Figure 4
Figure 4. Figure 4: One cycle of the Rodeo algorithm. Additional copies of this circuit can be appended to [PITH_FULL_IMAGE:figures/full_fig_p082_4.png]
Figure 4
Figure 4. Figure 4: (Figure reused from [30]) Initial-state spectral function for the Heisenberg model. [PITH_FULL_IMAGE:figures/full_fig_p088_4.png]
Figure 4
Figure 4. Figure 4: (Figure reused from [30]) Logarithm of the wave function error versus the total [PITH_FULL_IMAGE:figures/full_fig_p090_4.png]
Figure 4
Figure 4. Figure 4: (Figure reused from [105]) Sequential scans of the energy. Each bin represents a [PITH_FULL_IMAGE:figures/full_fig_p093_4.png]
Figure 4
Figure 4. Figure 4: , the energy eigenvalues of [PITH_FULL_IMAGE:figures/full_fig_p094_4.png]
Figure 4
Figure 4. Figure 4: (Figure reused from [105]) Energy scans for [PITH_FULL_IMAGE:figures/full_fig_p095_4.png]
Figure 4
Figure 4. Figure 4: (Figure reused from [105]) Eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p096_4.png]
Figure 5
Figure 5. Figure 5: A circuit diagram of a QAOA circuit with objective Hamiltonian [PITH_FULL_IMAGE:figures/full_fig_p107_5.png]
Figure 5
Figure 5. Figure 5: An analysis of the final states [PITH_FULL_IMAGE:figures/full_fig_p109_5.png]
Figure 5
Figure 5. Figure 5: A comparison of the VRA (left) and VQE (right) cost functions for BFGS [PITH_FULL_IMAGE:figures/full_fig_p111_5.png]
Figure 5
Figure 5. Figure 5: Results for a two-step BFGS optimization of a 12 parameter 6 qubit QAOA circuit with [PITH_FULL_IMAGE:figures/full_fig_p113_5.png]
Figure 5
Figure 5. Figure 5: A comparison of values of the two cost functions, [PITH_FULL_IMAGE:figures/full_fig_p114_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

138 extracted references · 21 canonical work pages

  1. [1]

    Stochastic quantization at finite chemical po- tential

    Gert Aarts and Ion-Olimpiu Stamatescu. Stochastic quantization at finite chemical po- tential. Journal of High Energy Physics, 2008(09):018–018, September 2008. ISSN 1029-8479. doi: 10.1088/1126-6708/2008/09/018. URLhttp://dx.doi.org/10.1088/ 1126-6708/2008/09/018

    doi:10.1088/1126-6708/2008/09/018 2008

  2. [2]

    The nobel prize in physics 2022, 2024

    Nobel Prize Outreach AB. The nobel prize in physics 2022, 2024. URLhttps://www. nobelprize.org/prizes/physics/2022/summary/. Accessed: 2024-07-14

    2022

  3. [3]

    A simple proof that toffoli and hadamard are quantum universal, 2003

    Dorit Aharonov. A simple proof that toffoli and hadamard are quantum universal, 2003. URL https://arxiv.org/abs/quant-ph/0301040

    arXiv 2003

  4. [4]

    Akshay, H

    V. Akshay, H. Philathong, M.E.S. Morales, and J.D. Biamonte. Reachability deficits in quantum approximate optimization.Physical Review Letters, 124(9), March 2020. ISSN 1079-7114. doi: 10.1103/physrevlett.124.090504. URLhttp://dx.doi.org/10.1103/ PhysRevLett.124.090504

    work page doi:10.1103/physrevlett.124.090504 2020

  5. [6]

    Tameem Albash and Daniel A. Lidar. Adiabatic quantum computation.Reviews of Modern Physics,90(1),January2018. ISSN1539-0756. doi: 10.1103/revmodphys.90.015002. URL http://dx.doi.org/10.1103/RevModPhys.90.015002

    doi:10.1103/revmodphys.90.015002

  6. [7]

    Anand, P

    A. Anand, P. Schleich, S. Alperin-Lea, P. W. K. Jensen, S. Sim, M. Díaz–Tinoco, J. S. Kottmann,M.Degroote,A.F.Izmaylov,andA.Aspuru-Guzik. Aquantumcomputingview on unitary coupled cluster theory.Chemical Society Reviews, 51:1659–1684, 2022. doi: 10.1039/d1cs00932j

    doi:10.1039/d1cs00932j 2022

  7. [8]

    Qiskit: An open-source framework for quantum computing, 2021

    Md Sajid Anis et al. Qiskit: An open-source framework for quantum computing, 2021

    2021

  8. [9]

    Aristotle. Physics. Internet Classics Archive, 350 B.C. URL http://classics.mit. edu/Aristotle/physics.html. Translated by R.P. Hardie and R.K. Gaye

Show all 138 references
  1. [10]

    Badem, A

    H. Badem, A. Baştürk, A. Çalışkan, and M. E. Yüksel. A new hybrid optimization method combining artificial bee colony and limited-memory bfgs algorithms for efficient numerical optimization. AppliedSoftComputing ,70:826–844,2018. doi: 10.1016/j.asoc.2018.06.010

    2018 doi

  2. [11]

    Springer Series in Statistics, 2010

    Z.BaiandJ.W.Silverstein.Spectralanalysisoflargedimensionalrandommatrices. Springer Series in Statistics, 2010. doi: 10.1007/978-1-4419-0661-8

    2010 doi

  3. [12]

    Leonardo Banchi and Gavin E. Crooks. Measuring analytic gradients of general quantum evolution with the stochastic parameter shift rule.Quantum, 5:386, January 2021. ISSN 114 2521-327X. doi: 10.22331/q-2021-01-25-386. URL http://dx.doi.org/10.22331/ q-2021-01-25-386

    2021 doi

  4. [13]

    and Bennett, C

    Barenco, A. and Bennett, C. H. and Cleve, R. and DiVincenzo, D. P. and Margolus, N. and Shor, P. and Sleator, T. and Smolin, J. A. and Weinfurter, H. Elementary gates for quantum computation. Phys. Rev. A, 52:3457, Nov 1995. doi: 10.1103/PhysRevA.52.3457. URL https://journals....

    1995 doi

  5. [14]

    One-dimensional anisotropic heisenberg chain

    Rodney J Baxter. One-dimensional anisotropic heisenberg chain. Annals of Physics, 70(2):323–337, 1972. ISSN 0003-4916. doi: https://doi.org/10.1016/ 0003-4916(72)90270-9. URL https://www.sciencedirect.com/science/article/ pii/0003491672902709

    1972

  6. [15]

    NuclearMatterTheory .CRCPress,Taylor&FrancisGroup,2020

    O.BenharandS.Fantoni. NuclearMatterTheory .CRCPress,Taylor&FrancisGroup,2020. ISBN 9780815386667. URLhttps://books.google.com/books?id=OI_wygEACAAJ

    2020

  7. [16]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. Lukin. Probing many-body dynamics on a 51-atom quantum simulator.Nature, 551:579–584, 2017. doi: 10.1038/nature24622

    2017 doi

  8. [17]

    Elementary proof of qaoa convergence

    Lennart Binkowski, Gereon Koßmann, Timo Ziegler, and René Schwonnek. Elementary proof of qaoa convergence. New Journal of Physics, 26(7):073001, July 2024. ISSN 1367-2630. doi: 10.1088/1367-2630/ad59bb. URL http://dx.doi.org/10.1088/ 1367-2630/ad59bb

    2024 doi

  9. [18]

    Blatt, H

    R. Blatt, H. Häffner, C. F. Roos, C. Becher, and F. Schmidt-Kaler. Ion trap quantum computing with ca+ ions.Quantum Information Processing, 3:61–73, 2004. doi: 10.1007/ s11128-004-3105-1

    2004

  10. [19]

    Boixo and R

    S. Boixo and R. D. Somma. Necessary condition for the quantum adiabatic approximation. Phys. Rev. A, 81:032308, Mar 2010. doi: 10.1103/PhysRevA.81.032308. URL https: //link.aps.org/doi/10.1103/PhysRevA.81.032308

    2010 doi

  11. [20]

    Eigenpathtraversalbyphaserandomization

    S.Boixo,E.Knill,andR.D.Somma. Eigenpathtraversalbyphaserandomization. Quantum Inf. Comput., 9(9&10):833–855, 2009. doi: 10.26421/QIC9.9-10-7. URLhttps://doi. org/10.26421/QIC9.9-10-7

    2009 doi

  12. [21]

    Born and V

    M. Born and V. Fock. Beweis des Adiabatensatzes.Zeitschrift für Physik, 51:165, March

  13. [22]

    JoelMBowman,KurtChristoffel,andFrankTobin.Applicationofscf-sitheorytovibrational motion in polyatomic molecules.Journal of Physical Chemistry, 83(8):905–912, 1979

    1979

  14. [23]

    Quantum amplitude ampli- 115 fication and estimation, 2002

    Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp. Quantum amplitude ampli- 115 fication and estimation, 2002. ISSN 0271-4132. URLhttp://dx.doi.org/10.1090/ conm/305/05215

    2002

  15. [24]

    SIAM Journal on Scientific Computing, 16:1190–1208, 1995

    R.H.Byrd,P.Lu,J.Nocedal,andC.Zhu.Alimitedmemoryalgorithmforboundconstrained optimization. SIAM Journal on Scientific Computing, 16:1190–1208, 1995. doi: 10.1137/ 0916069

    1995

  16. [25]

    Quantum chemistry in the age of quantum computing.Chemical reviews, 119(19):10856– 10915, 2019

    Yudong Cao, Jonathan Romero, Jonathan P Olson, Matthias Degroote, Peter D Johnson, Mária Kieferová, Ian D Kivlichan, Tim Menke, Borja Peropadre, Nicolas PD Sawaya, et al. Quantum chemistry in the age of quantum computing.Chemical reviews, 119(19):10856– 10915, 2019

    2019

  17. [26]

    Savage, and Matthias Troyer

    JosephCarlson,DavidJ.Dean,MortenHjorth-Jensen,DavidKaplan,JohnPreskill,Kenneth Roche, Martin J. Savage, and Matthias Troyer. Quantum computing for theoretical nuclear physics, a white paper prepared for the u.s. department of energy, office of science, office of nuclear physic...

    2018

  18. [27]

    Application of quantum computing to biochemical systems: A look to the future.Frontiers in Chemistry, 8, 2020

    Hai-PingCheng,ErikDeumens,JamesK.Freericks,ChenglongLi,andBeverlyA.Sanders. Application of quantum computing to biochemical systems: A look to the future.Frontiers in Chemistry, 8, 2020. doi: 10.3389/fchem.2020.587143. URLhttps://par.nsf.gov/ biblio/10291929

    2020

  19. [28]

    Hamiltoniansimulationusinglinearcombinationsof unitary operations.Quantum Inf

    AndrewM.ChildsandNathanWiebe. Hamiltoniansimulationusinglinearcombinationsof unitary operations.Quantum Inf. Comput., 12(11-12):901–924, 2012. ISSN 1533-7146

    2012

  20. [29]

    Childs, Yuan Su, Minh C

    Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu. Theory of trotter error with commutator scaling.Physical Review X, 11(1), February 2021. ISSN 2160-3308. doi: 10.1103/physrevx.11.011020. URL http://dx.doi.org/10.1103/ PhysRevX.11.011020

    2021 doi

  21. [30]

    Rodeo algorithm for quantum computing

    Kenneth Choi, Dean Lee, Joey Bonitati, Zhengrong Qian, and Jacob Watkins. Rodeo algorithm for quantum computing. Phys. Rev. Lett., 127(4):040505, 2021. doi: 10. 1103/PhysRevLett.127.040505.URL https://journals.aps.org/prl/abstract/10. 1103/PhysRevLett.127.040505

    2021

  22. [31]

    Coello Pérez, Joey Bonitati, Dean Lee, Sofia Quaglioni, and Kyle A

    Eduardo A. Coello Pérez, Joey Bonitati, Dean Lee, Sofia Quaglioni, and Kyle A. Wendt. Quantum state preparation by adiabatic evolution with custom gates.Phys. Rev. A, 105: 032403, Mar 2022. doi: 10.1103/PhysRevA.105.032403. URLhttps://link.aps.org/ doi/10.1103/PhysRevA.105.032403

    2022 doi

  23. [32]

    J. Cox, C. Gattringer, K. Holland, B. Scarlet, and U.-J. Wiese. Meron-cluster solution of fermion and other sign problems.Nuclear Physics B - Proceedings Supplements, 83–84: 777–791, April 2000. ISSN 0920-5632. doi: 10.1016/s0920-5632(00)91804-8. URL http://dx.doi.org/10.1016/...

    doi

  24. [33]

    Córcoles, Maika Takita, Ken Inoue, Scott Lekuch, Zlatko K

    A.D. Córcoles, Maika Takita, Ken Inoue, Scott Lekuch, Zlatko K. Minev, Jerry M. Chow, andJayM.Gambetta. Exploitingdynamicquantumcircuitsinaquantumalgorithmwithsu- perconductingqubits. PhysicalReviewLetters ,127(10),August2021. ISSN1079-7114. doi: 10.1103/physrevlett.127.100501...

    doi

  25. [34]

    Dibner and C.E

    K.A. Dibner and C.E. Snow. Science Literacy: Concepts, Contexts, and Consequences. National Academies Press, 2016. ISBN 9780309447591. URLhttps://books.google. com/books?id=57fODQAAQBAJ

    2016

  26. [35]

    Quantum games and quantum strate- gies

    Jens Eisert, Martin Wilkens, and Maciej Lewenstein. Quantum games and quantum strate- gies. Physical Review Letters, 83(15):3077–3080, October 1999. ISSN 1079-7114. doi: 10.1103/physrevlett.83.3077. URL http://dx.doi.org/10.1103/PhysRevLett.83. 3077

    1999 doi

  27. [36]

    Reviews of Modern Physics, 81(4):1773–1825, December 2009

    E.Epelbaum,H.-W.Hammer,andUlf-G.Meißner.Moderntheoryofnuclearforces. Reviews of Modern Physics, 81(4):1773–1825, December 2009. ISSN 1539-0756. doi: 10.1103/ revmodphys.81.1773. URLhttp://dx.doi.org/10.1103/RevModPhys.81.1773

    2009 doi

  28. [37]

    Example: Su(2) to so(3), 2020

    Jonny Evans. Example: Su(2) to so(3), 2020. URL https://jde27.uk/lgla/17_ example_homo.html. Licensed under CC-BY-SA 4.0

    2020

  29. [38]

    Quantumcomputation by adiabatic evolution, 2000

    EdwardFarhi,JeffreyGoldstone,SamGutmann,andMichaelSipser. Quantumcomputation by adiabatic evolution, 2000. URLhttps://arxiv.org/abs/quant-ph/0001106

    2000 arXiv

  30. [39]

    R. P. Feynman. Forces in molecules. Phys. Rev., 56:340–343, Aug 1939. doi: 10.1103/ PhysRev.56.340. URLhttps://link.aps.org/doi/10.1103/PhysRev.56.340

    1939 doi

  31. [40]

    R. P. Feynman. Simulating physics with computers. Int. J. Theor. Phys., 21:467, 1982. doi: 10.1007/BF02650179. URL https://link.springer.com/article/10.1007/ BF02650179

    1982 doi

  32. [41]

    E. Fradkin. Field theories of condensed matter physics. Cambridge University Press, 2013. doi: 10.1017/cbo9781139015509

    2013 doi

  33. [42]

    Frame, R

    D. Frame, R. He, I. C. F. Ipsen, D. Lee, D. Lee, and E. Rrapaj. Eigenvector continuation with subspace learning.Physical Review Letters, 121, 2018. doi: 10.1103/physrevlett.121. 032501

    2018 doi

  34. [43]

    Efficient encoding of the weighted max k-cut on a quantum computer using qaoa, 2020

    Franz Georg Fuchs, Herman Øie Kolden, Niels Henrik Aase, and Giorgio Sartor. Efficient encoding of the weighted max k-cut on a quantum computer using qaoa, 2020. URL https://arxiv.org/abs/2009.01095

    2020 arXiv

  35. [44]

    Fucito, E

    F. Fucito, E. Marinari, G. Parisi, and C. Rebbi. A Proposal for Monte Carlo Simulations of Fermionic Systems.Nucl. Phys. B, 180:369, 1981. doi: 10.1016/0550-3213(81)90055-9. 117

    1981 doi

  36. [45]

    Gallager

    R. Gallager. Information Theory and Reliable Communication: Course held at the De- partment for Automation and Information July 1970. CISM International Centre for Mechanical Sciences. Springer Vienna, 2014. ISBN 9783709129456. URL https: //books.google.com/books?id=KOkkBAAAQBAJ

    1970

  37. [46]

    Ignacio Cirac

    Yimin Ge, Jordi Tura, and J. Ignacio Cirac. Faster ground state preparation and high- precision ground energy estimation with fewer qubits, 2018. URLhttps://arxiv.org/ abs/1712.03193

    2018 arXiv

  38. [47]

    Quantumcellmodelforbosons

    H.A.GerschandG.C.Knollman. Quantumcellmodelforbosons. Phys.Rev.,129:959–967, Jan1963. doi: 10.1103/PhysRev.129.959. URLhttps://link.aps.org/doi/10.1103/ PhysRev.129.959

    doi

  39. [48]

    Granade, C

    C. Granade, C. Ferrie, and S. Flammia. Practical adaptive quantum tomography. New Journal of Physics, 19:113017, 2017. doi: 10.1088/1367-2630/aa8fe6

    2017 doi

  40. [49]

    Griffiths

    D.J. Griffiths. Introduction to Quantum Mechanics. Cambridge University Press, 2017. ISBN 9781107179868. URLhttps://books.google.com/books?id=0h-nDAAAQBAJ

    2017

  41. [50]

    Lov K. Grover. A fast quantum mechanical algorithm for database search, 1996. URL https://arxiv.org/abs/quant-ph/9605043

    1996 arXiv

  42. [51]

    Practical optimization for hybrid quantum-classical algorithms, 2017

    Gian Giacomo Guerreschi and Mikhail Smelyanskiy. Practical optimization for hybrid quantum-classical algorithms, 2017. URLhttps://arxiv.org/abs/1701.01450

    2017 arXiv

  43. [52]

    Gustafson

    Erik J. Gustafson. Projective cooling for the transverse Ising model.Phys. Rev. D, 101 (7):071504(R), 5, 2020. ISSN 2470-0010,2470-0029. doi: 10.1103/physrevd.101.071504. URL https://doi.org/10.1103/physrevd.101.071504

    2020 doi

  44. [53]

    Rieffel, Davide Venturelli, and Rupak Biswas

    Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor G. Rieffel, Davide Venturelli, and Rupak Biswas. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz.Algorithms, 12(2):34, February 2019. ISSN 1999-4893. doi: 10.3390/a12020034. URL ...

    2019 doi

  45. [54]

    Coupled-cluster computations of atomic nuclei.Reports on Progress in Physics, 77(9):096302, September 2014

    G Hagen, T Papenbrock, M Hjorth-Jensen, and D J Dean. Coupled-cluster computations of atomic nuclei.Reports on Progress in Physics, 77(9):096302, September 2014. ISSN 1361-6633. doi: 10.1088/0034-4885/77/9/096302. URLhttp://dx.doi.org/10.1088/ 0034-4885/77/9/096302

    2014 doi

  46. [55]

    William W. Hager. Applied Numerical Linear Algebra. SIAM, 2021. doi: 10. 1137/1.9781611976861.ch7. URL https://epubs.siam.org/doi/abs/10.1137/1. 9781611976861.ch7

    2021 doi

  47. [56]

    B.C. Hall. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. Graduate Texts in Mathematics. Springer, 2003. ISBN 9780387401225. URL https: 118 //books.google.com/books?id=m1VQi8HmEwcC

    2003

  48. [57]

    Zurtheoriedesferromagnetismus

    W.Heisenberg. Zurtheoriedesferromagnetismus. ZeitschriftFrPhysik ,49:619–636,1928. doi: 10.1007/bf01328601

    1928 doi

  49. [58]

    Holland, Kyle A

    Eric T. Holland, Kyle A. Wendt, Konstantinos Kravvaris, Xian Wu, W. Erich Ormand, Jonathan L DuBois, Sofia Quaglioni, and Francesco Pederiva. Optimal control for the quantum simulation of nuclear dynamics.Phys. Rev. A, 101:062307, Jun 2020. doi: 10. 1103/PhysRevA.101.062307. U...

    2020

  50. [59]

    An Enquiry Concerning Human Understanding

    David Hume. An Enquiry Concerning Human Understanding. Project Gutenberg, 2006. URL https://www.gutenberg.org/ebooks/9662. eBook #9662, Project Gutenberg

    2006

  51. [60]

    https://quantum-computing.ibm.com, 2021

    IBM Quantum. https://quantum-computing.ibm.com, 2021. URL https:// quantum-computing.ibm.com

    2021

  52. [61]

    M. A. H. Ibrahim, M. Mamat, and W. J. Leong. The hybrid bfgs-cg method in solving unconstrained optimization problems.Abstract and Applied Analysis, 2014:1–6, 2014. doi: 10.1155/2014/507102

    2014 doi

  53. [62]

    J. R. Johansson, P. D. Nation, and F. Nori. QuTiP: An open-source Python frame- work for the dynamics of open quantum systems. Comput. Phys. Commun., 183(8): 1760, 2012. ISSN 0010-4655. doi: doi.org/10.1016/j.cpc.2012.02.021. URL https: //www.sciencedirect.com/science/article/...

    2012 doi

  54. [63]

    QuTiP2: APythonframeworkforthedynamicsof openquantumsystems

    J.R.Johansson,P.D.Nation,andF.Nori. QuTiP2: APythonframeworkforthedynamicsof openquantumsystems. Comput.Phys.Commun. ,184(4):1234,2013. ISSN0010-4655. doi: doi.org/10.1016/j.cpc.2012.11.019. URLhttps://www.sciencedirect.com/science/ article/pii/S0010465512003955

    2013 doi

  55. [64]

    Approxima- tions in transmon simulation.arXiv e-prints, art

    TylerJones,KaiahSteven,XavierPoncini,MatthewRose,andArkadyFedorov. Approxima- tions in transmon simulation.arXiv e-prints, art. arXiv:2102.09721, February 2021. URL https://arxiv.org/abs/2102.09721

    2021 arXiv

  56. [65]

    Chow, and Jay M

    Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta. Hardware-efficient variational quantum eigen- solver for small molecules and quantum magnets.Nature, 549(7671):242–246, September

  57. [66]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization, 2017. URL https://arxiv.org/abs/1412.6980

    2017 arXiv

  58. [67]

    Kirkpatrick, C

    S. Kirkpatrick, C. D. Gelatt, and M. Vecchi. Optimization by simulated annealing.Science, 119 220:671–680, 1983. doi: 10.1126/science.220.4598.671

    1983 doi

  59. [69]

    A. Yu. Kitaev. Quantum measurements and the abelian stabilizer problem, 1995. URL https://arxiv.org/abs/quant-ph/9511026

    1995 arXiv

  60. [70]

    Kitaev, A

    A.Y. Kitaev, A. Shen, and M.N. Vyalyi.Classical and Quantum Computation. Graduate studiesinmathematics.AmericanMathematicalSociety,2002.ISBN9780821832295.URL https://books.google.com/books?id=qYHTvHPvmG8C

    2002

  61. [71]

    JensKoch,TerriM.Yu,JayGambetta,A.A.Houck,D.I.Schuster,J.Majer,AlexandreBlais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Charge-insensitive qubit design derived from the cooper pair box.Phys. Rev. A, 76:042319, Oct 2007. doi: 10.1103/PhysRevA.76. 042319. URL https://jo...

    2007 doi

  62. [72]

    A. F. Kockum and F. Nori. Quantum bits with josephson junctions.Fundamentals and FrontiersoftheJosephsonEffect ,pages703–741,2019. doi: 10.1007/978-3-030-20726-7_ 17

    2019 doi

  63. [73]

    Special issue on quantum computing with superconducting qubits

    Alexander Korotkov. Special issue on quantum computing with superconducting qubits. Quantum Information Processing - QUANTUM INF PROCESS, 8:51–54, 06 2009. doi: 10.1007/s11128-009-0104-2

    2009 doi

  64. [74]

    Aquantum engineer’s guide to superconducting qubits

    P.Krantz,M.Kjaergaard,F.Yan,T.P.Orlando,S.Gustavsson,andW.D.Oliver. Aquantum engineer’s guide to superconducting qubits. Appl. Phys. Rev., 6(2):021318, 2019. doi: 10.1063/1.5089550. URL https://doi.org/10.1063/1.5089550

    2019 doi

  65. [75]

    URLhttps://arxiv.org/abs/1606.03879

    KurtLangfeldandBiagioLucini.Formthedensity-of-statesmethodtofinitedensityquantum field theory, 2016. URLhttps://arxiv.org/abs/1606.03879

    2016 arXiv

  66. [76]

    E.L. Lawler. The Travelling Salesman Problem: A Guided Tour of Combinatorial Opti- mization. Wiley-Interscience series in discrete mathematics and optimization. John Wiley & Sons, 1985. URLhttps://books.google.com/books?id=qbFlMwEACAAJ

    1985

  67. [77]

    Nuclear lattice simulations with chiral effectivefieldtheory

    Dean Lee, Bu ¯gra Borasoy, and Thomas Schaefer. Nuclear lattice simulations with chiral effectivefieldtheory. PhysicalReviewC ,70(1),July2004. ISSN1089-490X. doi: 10.1103/ physrevc.70.014007. URLhttp://dx.doi.org/10.1103/PhysRevC.70.014007

    doi

  68. [78]

    Projected cooling algorithm for quantum computation

    Dean Lee, Joey Bonitati, Gabriel Given, Caleb Hicks, Ning Li, Bing-Nan Lu, Abudit Rai, Avik Sarkar, and Jacob Watkins. Projected cooling algorithm for quantum computation. Physics Letters B, 807:135536, 2020. ISSN 0370-2693. doi: https://doi.org/10.1016/j. physletb.2020.135536...

    2020

  69. [79]

    S. Lloyd. Universal Quantum Simulators. Science, 273(5278):1073, 1996. ISSN 0036-

    1996

  70. [80]

    Ignacio Cirac

    Sirui Lu, Mari Carmen Bañuls, and J. Ignacio Cirac. Algorithms for quantum simulation at finiteenergies. PRXQuantum,2(2),May2021. ISSN2691-3399. doi: 10.1103/prxquantum. 2.020321. URL http://dx.doi.org/10.1103/PRXQuantum.2.020321

    doi

  71. [81]

    Lubasch, J

    M. Lubasch, J. Joo, P. Moinier, M. Kiffner, and D. Jaksch. Variational quantum algorithms for nonlinear problems.Physical Review A, 101, 2020. doi: 10.1103/physreva.101.010301

    2020 doi

  72. [82]

    Ising formulations of many np problems

    Andrew Lucas. Ising formulations of many np problems. Frontiers in Physics, 2, 2014. ISSN 2296-424X. doi: 10.3389/fphy.2014.00005. URLhttp://dx.doi.org/10.3389/ fphy.2014.00005

    2014

  73. [83]

    Detecting qubit-coupling faults in ion-trap quantum computers, 2021

    AndriiO.Maksymov,JasonNguyen,VandiverChaplin,YunseongNam,andIgorL.Markov. Detecting qubit-coupling faults in ion-trap quantum computers, 2021. URL https:// arxiv.org/abs/2108.03708

    2021 arXiv

  74. [84]

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics, 18:023023, 2016. doi: 10.1088/1367-2630/18/2/023023

    2016 doi

  75. [85]

    McClean, Sergio Boixo, Vadim N

    Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes.Nature Communi- cations, 9(1), November 2018. ISSN 2041-1723. doi: 10.1038/s41467-018-07090-4. URL http://dx.doi.org/10.1038/s4...

    2018 doi

  76. [86]

    M. E. S. Morales, J. D. Biamonte, and Z. Zimborás. On the universality of the quantum approximateoptimizationalgorithm. QuantumInformationProcessing ,19(9),August2020. ISSN 1573-1332. doi: 10.1007/s11128-020-02748-9. URL http://dx.doi.org/10. 1007/s11128-020-02748-9

    doi

  77. [87]

    Motzoi, J

    F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm. Simple pulses for elimination of leakage in weakly nonlinear qubits. Phys. Rev. Lett., 103:110501, Sep 2009. doi: 10.1103/PhysRevLett.103.110501. URLhttps://journals.aps.org/prl/abstract/ 10.1103/PhysRevLett.103.110501

    2009 doi

  78. [88]

    To quantum or not to quantum: towards algorithm selection in near-term quantum optimization

    Charles Moussa, Henri Calandra, and Vedran Dunjko. To quantum or not to quantum: towards algorithm selection in near-term quantum optimization. Quantum Science and Technology,5(4):044009,October2020.ISSN2058-9565.doi: 10.1088/2058-9565/abb8e5. URL http://dx.doi.org/10.1088/205...

    doi

  79. [89]

    Khaneja and T

    N. Khaneja and T. Reiss and C. Kehlet and T. Schulte-Herbrüggen and S. J. Glaser. Op- timal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson., 172(2):296, 2005. ISSN 1090-7807. doi: 10.1016/ j.jmr.2004.11.004. URL ht...

    2005

  80. [90]

    Subspace-searchvariationalquantum eigensolver for excited states.Physical Review Research, 1(3), October 2019

    KenM.Nakanishi,KosukeMitarai,andKeisukeFujii. Subspace-searchvariationalquantum eigensolver for excited states.Physical Review Research, 1(3), October 2019. ISSN 2643-

    2019

  81. [91]

    J. A. Nelder and R. Mead. A Simplex Method for Function Minimization.The Computer Journal, 7(4):308–313, 01 1965. ISSN 0010-4620. doi: 10.1093/comjnl/7.4.308. URL https://doi.org/10.1093/comjnl/7.4.308

    1965 doi

  82. [92]

    M. A. Nielsen and I. L. Chuang.Quantum Computation and Quantum Information. Cam- bridge University Press, 2010. doi: 10.1017/CBO9780511976667

    2010 doi

  83. [93]

    2022 codata value: Newtonian constant of gravitation

    NIST. 2022 codata value: Newtonian constant of gravitation. The NIST Reference on Con- stants, Units, and Uncertainty, May 2024. URLhttps://physics.nist.gov/cgi-bin/ cuu/Value?bg. https://physics.nist.gov/cgi-bin/cuu/Value?bg

    2022

  84. [94]

    http://www.w3.org/1998/math/mathml

    A. Nogga, P. Navrátil, B. R. Barrett, and J. P. Vary. Spectra and binding energy predictions of chiral interactions for<mml:math xmlns:mml="http://www.w3.org/1998/math/mathml" display="inline"><mml:mmultiscripts><mml:mi mathvari- ant="normal">li</mml:mi><mml:mprescripts /><mml...

    1998 doi

  85. [95]

    Elsevier, 2024

    Gaopei Pan and Zi Yang Meng.The sign problem in quantum Monte Carlo simulations, page 879–893. Elsevier, 2024. ISBN 9780323914086. doi: 10.1016/b978-0-323-90800-9. 00095-0. URL http://dx.doi.org/10.1016/B978-0-323-90800-9.00095-0

    2024 doi

  86. [96]

    Y. Pan, Y. Tong, and Y. Yang. Automatic depth optimization for a quantum approximate optimization algorithm.Physical Review A, 105, 2022. doi: 10.1103/physreva.105.032433

    2022 doi

  87. [97]

    Digital-analog quantum computation

    Adrian Parra-Rodriguez, Pavel Lougovski, Lucas Lamata, Enrique Solano, and Mikel Sanz. Digital-analog quantum computation. Physical Review A, 101(2), February 2020. ISSN 2469-9934. doi: 10.1103/physreva.101.022305. URL http://dx.doi.org/10.1103/ PhysRevA.101.022305

    2020 doi

  88. [98]

    QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers, page 240–258

    Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz.Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers, page 240–258. Springer Nature Switzerland, 2023. ISBN 9783031320415. doi: 10.1007/978-3-031-32041-5_13. 122 URL http://dx.doi.org/10.100...

    2023 doi

  89. [99]

    Love, Alán Aspuru-Guzik, and Jeremy L

    AlbertoPeruzzo,JarrodMcClean,PeterShadbolt,Man-HongYung,Xiao-QiZhou,PeterJ. Love, Alán Aspuru-Guzik, and Jeremy L. O’Brien. A variational eigenvalue solver on a photonic quantum processor.Nature Communications, 5(1), July 2014. ISSN 2041-1723. doi: 10.1038/ncomms5213. URLhttp:...

    2014 doi

  90. [100]

    S. C. Pieper and R. B. Wiringa. Quantum monte carlo calculations of light nuclei.Annual Review of Nuclear and Particle Science, 51:53–90, 2001. doi: 10.1146/annurev.nucl.51. 101701.132506

    2001

  91. [101]

    and Qarry, A

    Poulin, D. and Qarry, A. and Somma, R. and Verstraete, F. Quantum Simulation of Time- DependentHamiltoniansandtheConvenientIllusionofHilbertSpace. Phys.Rev.Lett. ,106: 170501, Apr 2011. doi: 10.1103/PhysRevLett.106.170501. URL https://journals. aps.org/prl/abstract/10.1103/Phy...

    2011 doi

  92. [102]

    Poundstone

    W. Poundstone. Prisoner’s Dilemma. Doubleday, 1992. ISBN 9780385415675. URL https://books.google.com/books?id=9uruAAAAMAAJ

    1992

  93. [103]

    Preskill

    J. Preskill. Quantum computing in the nisq era and beyond.Quantum, 2:79, 2018. doi: 10.22331/q-2018-08-06-79

    2018 doi

  94. [104]

    Pérez-Obiol, A

    A. Pérez-Obiol, A. M. Romero, J. Menéndez, A. Rios, A. García-Sáez, and B. Juliá- Díaz. Nuclear shell-model simulation in digital quantum computers.Scientific Reports, 13(1), July 2023. ISSN 2045-2322. doi: 10.1038/s41598-023-39263-7. URL http: //dx.doi.org/10.1038/s41598-023-39263-7

    2023 doi

  95. [105]

    Demonstration of the rodeo algorithm on a quantum computer, 2024

    Zhengrong Qian, Jacob Watkins, Gabriel Given, Joey Bonitati, Kenneth Choi, and Dean Lee. Demonstration of the rodeo algorithm on a quantum computer, 2024. URLhttps: //arxiv.org/abs/2110.07747

    2024 arXiv

  96. [106]

    Browne, and Hans J

    Robert Raussendorf, Daniel E. Browne, and Hans J. Briegel. Measurement-based quantum computation on cluster states.Physical Review A, 68(2), August 2003. ISSN 1094-1622. doi: 10.1103/physreva.68.022312. URLhttp://dx.doi.org/10.1103/PhysRevA.68. 022312

    2003 doi

  97. [107]

    Roggero, C

    A. Roggero, C. Gu, A. Baroni, and T. Papenbrock. Preparation of excited states for nuclear dynamics on a quantum computer.Phys. Rev. C, 102:064624, Dec 2020. doi: 10.1103/ PhysRevC.102.064624. URL https://journals.aps.org/prc/abstract/10.1103/ PhysRevC.102.064624

    2020

  98. [108]

    Saad.Iterative methods for sparse linear systems

    Y. Saad.Iterative methods for sparse linear systems. Philadelphia, PA, 2003. doi: 10.1137/ 1.9780898718003

    2003

  99. [109]

    quantumcomputing: aprimer

    M.Sadiku,M.Tembely,andS.Musa. quantumcomputing: aprimer. InternationalJournal 123 of Advanced Research in Computer Science and Software Engineering, 7:129, 2017. doi: 10.23956/ijarcsse.v7i11.501

    2017

  100. [110]

    Parrish, Nicholas C

    Raffaele Santagati, Alan Aspuru-Guzik, Ryan Babbush, Matthias Degroote, Leticia González, Elica Kyoseva, Nikolaj Moll, Markus Oppel, Robert M. Parrish, Nicholas C. Rubin, Michael Streif, Christofer S. Tautermann, Horst Weiss, Nathan Wiebe, and Clemens Utschig-Utschig. Drug des...

    2024 doi

  101. [111]

    A. J. Sarty et al. Measurement of the reaction He-3 (gamma, pp) n and its relation to three-body forces.Phys. Rev. C, 47:459–467, 1993. doi: 10.1103/PhysRevC.47.459

    1993 doi

  102. [112]

    Hamlib: Alibraryofhamiltoniansforbenchmarkingquantumalgorithmsand hardware, 2024

    Nicolas PD Sawaya, Daniel Marti-Dafcik, Yang Ho, Daniel P Tabor, David E Bernal Neira, Alicia B Magann, Shavindra Premaratne, Pradeep Dubey, Anne Matsuura, Nathan Bishop, Wibe A de Jong, Simon Benjamin, Ojas D Parekh, Norm Tubman, Katherine Klymko, and DaanCamps. Hamlib: Alibr...

    2024 arXiv

  103. [113]

    Scalettar, G

    R. Scalettar, G. G. Batrouni, A. P. Kampf, and G. T. Zimányi. Simultaneous diagonal and off-diagonal order in the bose-hubbard hamiltonian.Physical Review B, 51:8467–8480,

  104. [114]

    Shende, Igor L

    Vivek V. Shende, Igor L. Markov, and Stephen S. Bullock. Minimal universal two-qubit controlled-not-based circuits.Phys. Rev. A, 69:062321, Jun 2004. doi: 10.1103/PhysRevA. 69.062321. URL https://link.aps.org/doi/10.1103/PhysRevA.69.062321

    2004 doi

  105. [115]

    Image from wikimedia commons.https://commons.wikimedia.org/ w/index.php?curid=5829358, 2024

    Smite-Meister. Image from wikimedia commons.https://commons.wikimedia.org/ w/index.php?curid=5829358, 2024. CC BY-SA 3.0

    2024

  106. [116]

    Forbidden subspaces for level-1 quantum approximate optimization algorithm and instantaneous quantum polynomial circuits.Physical Review A, 102(4), October 2020

    Michael Streif and Martin Leib. Forbidden subspaces for level-1 quantum approximate optimization algorithm and instantaneous quantum polynomial circuits.Physical Review A, 102(4), October 2020. ISSN 2469-9934. doi: 10.1103/physreva.102.042416. URL http://dx.doi.org/10.1103/Phy...

    2020 doi

  107. [117]

    Generalized Trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems.Comm

    Masuo Suzuki. Generalized Trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems.Comm. Math. Phys.,51(2):183–190,1976. ISSN0010-3616,1432-0916. URL http://projecteuclid. org/euclid.cmp/1103900351

    1976

  108. [118]

    Amplitude estimation without phase estimation.Quantum Information Processing,19(2),January2020

    Yohichi Suzuki, Shumpei Uno, Rudy Raymond, Tomoki Tanaka, Tamiya Onodera, and Naoki Yamamoto. Amplitude estimation without phase estimation.Quantum Information Processing,19(2),January2020. ISSN1573-1332. doi: 10.1007/s11128-019-2565-2. URL http://dx.doi.org/10.1007/s11128-019...

    doi

  109. [119]

    Szabo and N.S

    A. Szabo and N.S. Ostlund.Modern Quantum Chemistry: Introduction to Advanced Elec- tronic Structure Theory. Dover Books on Chemistry. Dover Publications, 1996. ISBN 9780486691862. URL https://books.google.com/books?id=6mV9gYzEkgIC

    1996

  110. [120]

    Quantum simulation.Nature Phys., 8(4):263, 2012

    Andreas Trabesinger. Quantum simulation.Nature Phys., 8(4):263, 2012. doi: 10.1038/ nphys2258

    2012

  111. [121]

    H. F. Trotter. On the product of semi-groups of operators.Proc. Amer. Math. Soc., 10: 545–551,1959. ISSN0002-9939,1088-6826. doi: 10.2307/2033649. URLhttps://doi. org/10.2307/2033649

    1959 doi

  112. [122]

    Optimal quantum circuits for general two-qubit gates

    Farrokh Vatan and Colin Williams. Optimal quantum circuits for general two-qubit gates. Phys. Rev. A, 69:032315, Mar 2004. doi: 10.1103/PhysRevA.69.032315. URL https: //link.aps.org/doi/10.1103/PhysRevA.69.032315

    2004 doi

  113. [123]

    Venkateswaran, M

    C. Venkateswaran, M. Ramachandran, R. Kurinjimalar, P. Vidhya, and G. Mathivanan. Application of simulated annealing in various field.Materials and Its Characterization, 1: 01–08, 2022. doi: 10.46632/mc/1/1/1

    2022 doi

  114. [124]

    Everything is a quantum ising model, 2023

    Ruben Verresen. Everything is a quantum ising model, 2023. URLhttps://arxiv.org/ abs/2301.11917

    2023 arXiv

  115. [125]

    Vidal and C

    G. Vidal and C. M. Dawson. Universal quantum circuit for two-qubit transformations with three controlled-not gates.Phys. Rev. A, 69:010301, Jan 2004. doi: 10.1103/PhysRevA.69. 010301. URL https://link.aps.org/doi/10.1103/PhysRevA.69.010301

    2004 doi

  116. [126]

    GraphicalModels,ExponentialFamilies,andVariational Inference

    M.J.WainwrightandM.I.Jordan. GraphicalModels,ExponentialFamilies,andVariational Inference. Foundations and trends in machine learning. Now Publishers, 2008. ISBN 9781601981844. URL https://books.google.com/books?id=zp5Mo3VsJbgC

    2008

  117. [127]

    Wales and Jonathan P

    David J. Wales and Jonathan P. K. Doye. Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms.The Journal ofPhysicalChemistryA ,101(28):5111–5116,1997. doi: 10.1021/jp970984n. URLhttps: //doi.org/10.1021/jp970984n

    1997 doi

  118. [128]

    C. P. Williams. Quantum gates. Texts in Computer Science, pages 51–122, 2011. doi: 10.1007/978-1-84628-887-6_2

    2011 doi

  119. [129]

    Gpu- accelerated simulations of quantum annealing and the quantum approximate optimization algorithm

    DennisWillsch,MaditaWillsch,FengpingJin,KristelMichielsen,andHansDeRaedt. Gpu- accelerated simulations of quantum annealing and the quantum approximate optimization algorithm. Computer Physics Communications, 278:108411, September 2022. ISSN 0010-

    2022

  120. [130]

    Xian Wu, S. L. Tomarken, N. Anders Petersson, L. A. Martinez, Yaniv J. Rosen, and 125 Jonathan L. DuBois. High-fidelity software-defined quantum logic on a superconducting qudit. Phys.Rev.Lett. ,125:170502,Oct2020. doi: 10.1103/PhysRevLett.125.170502. URL https://link.aps.org/...

    doi

  121. [131]

    quantumannealingforindustryapplications: introduction and review.Reports on Progress in Physics, 85:104001, 2022

    S.Yarkoni,E.Raponi,T.Bäck,andS.Schmitt. quantumannealingforindustryapplications: introduction and review.Reports on Progress in Physics, 85:104001, 2022. doi: 10.1088/ 1361-6633/ac8c54

    2022

  122. [132]

    The global risks report 2024, 2024

    Saadia Zahidi. The global risks report 2024, 2024. URLhttps://www3.weforum.org/ docs/WEF_The_Global_Risks_Report_2024.pdf. ISBN: 978-2-940631-64-3

    2024

  123. [133]

    Variationalquantumeigensolversbyvariance minimization, 2020

    Dan-BoZhang,Zhan-HaoYuan,andTaoYin. Variationalquantumeigensolversbyvariance minimization, 2020. URLhttps://arxiv.org/abs/2006.15781

    2020 arXiv

  124. [134]

    Artificialintelligencewarm-startapproach: optimizingthegeneralizationcapabilityofqaoaincomplexenergylandscapes

    R.Zhao,T.Cheng,R.Wang,X.Fan,andH.Ma. Artificialintelligencewarm-startapproach: optimizingthegeneralizationcapabilityofqaoaincomplexenergylandscapes. NewJournal of Physics, 26:053016, 2024. doi: 10.1088/1367-2630/ad4629. 126

    2024 doi

  125. [1564]

    URL http://dx.doi.org/10.1103/ PhysRevResearch.1.033062

    doi: 10.1103/physrevresearch.1.033062. URL http://dx.doi.org/10.1103/ PhysRevResearch.1.033062

    doi

  126. [1928]

    URL https://link.springer.com/article/10

    doi: 10.1007/BF01343193. URL https://link.springer.com/article/10. 1007/BF01343193

    doi

  127. [1995]

    doi: 10.1103/physrevb.51.8467

    doi

  128. [2017]

    doi: 10.1038/nature23879

    ISSN1476-4687. doi: 10.1038/nature23879. URLhttp://dx.doi.org/10.1038/ nature23879

    doi

  129. [4655]

    URL http://dx.doi.org/10.1016/j.cpc

    doi: 10.1016/j.cpc.2022.108411. URL http://dx.doi.org/10.1016/j.cpc. 2022.108411

    2022

  130. [8075]

    URLhttps://science.sciencemag.org/ content/273/5278/1073

    doi: 10.1126/science.273.5278.1073. URLhttps://science.sciencemag.org/ content/273/5278/1073

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.