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REVIEW 4 major objections 6 minor 30 references

Co-designed Quantum Discrete Adiabatic Linear System Solver Via Dynamic Circuits

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A discrete adiabatic quantum linear system solver can be run at constant circuit depth by measuring, classically reconstructing, and re-encoding the state after each evolution step.

desk verdict The advertised O(depth(U)) depth reduction is a resource-accounting artifact: it ignores the cost of measuring, classically reconstructing, and re-preparing the full state after every segment. read the letter →

arxiv 2505.24626 v1 pith:JGHD3KBU submitted 2025-05-30 quant-ph

Boxuan Ai , Shuo He , Xiang Zhao , Lin Yang , Guozhen Liu , Pengfei Gao , Hongbao Liu , Tao Tang
show 2 more authors
Jiecheng Yang Jie Wu
This is my paper
classification quant-ph
keywords quantumlinearsystemsdiscreteadiabaticalgorithmdynamiccircuitsmid-circuitmeasurementcircuitdepthblockencodingnoisyintermediate-scaleevolution
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

Existing discrete adiabatic quantum linear system solvers pay a circuit depth that grows linearly with the number of evolution steps, quickly exceeding the coherence time of current hardware. This paper proposes a co-designed alternative that stops the evolution after each short segment, measures the resulting state, reconstructs it classically, and re-encodes it for the next segment. Because the Hamiltonian block structure keeps the first half of the state vector real and the second half imaginary, only the sign of each component is unknown, and a continuity-based sign predictor supplies it. The authors claim this reduces the depth scaling from $O(\text{steps}\times\text{depth}(U))$ to $O(\text{depth}(U))$ and, in simulations, keeps solution fidelity above 80% under decoherence noise for systems up to $16\times 16$ with condition numbers up to 50.

What carries the argument

The load-bearing object is the real-imaginary component separation identity: for $H_s=\begin{pmatrix}0&B\\C&0\end{pmatrix}$, applying $I - iH_s\,dt$ to a vector whose first $N$ entries are real and last $N$ are pure imaginary yields a vector of the same form. This makes the phase of every measured basis amplitude known modulo a sign, reducing full state tomography to $2N$ sign bits. The sign bits are supplied by the continuity rule Eq. (19), which compares each component with a linear extrapolation of the two previous segments, switching sign only when the amplitude is below a noise threshold. With the full state known, a classical controller schedules the next segment unitary on the fly and a dynamic-circuit re-encoding step restarts the evolution, so the total circuit depth is bounded by one segment rather than by the number of segments.

What would settle it

A direct test is to simulate the exact state after each segment alongside the state reconstructed by Eq. (19): if any segment has a sign or amplitude mismatch, the final fidelity will fail to converge as the number of steps increases. Counting the number of measurement shots required per segment also settles the point: if the total reconstruction overhead scales with the number of steps or the Hilbert space dimension, the wall-clock advantage over the serial circuit disappears.

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Extended reading notes

Core claim

The paper's central claim is that a discrete adiabatic linear system solver can be made depth-efficient by hardwiring the algorithm to the structure of the state it produces. Under the first-order evolution operator $I - iH\,dt$ with block off-diagonal $H$, the state after every step retains the form $(x_1,\ldots,x_N,\,i x_{N+1},\ldots,i x_{2N})^T$, so amplitude measurements determine every component up to a sign. The sign is predicted from continuity across steps with Eq. (19). Once the full intermediate state is known, it can be re-encoded classically, so the deep product of step unitaries never needs to be run as one coherent circuit. Circuit multiplexing then brings the circuit depth to $O(\text{depth}(U))$, and a post-processing step that truncates the imaginary components raises the fidelity of the final solution. The benchmarks are offered as evidence that this segmentation does not destroy adiabatic accuracy: systems up to $W=16$ and $\kappa=50$ stay above 80% fidelity under 0.001 decoherence noise, and above 90% fidelity noiseless for $W=16$.

Load-bearing premise

The scheme assumes that after every short segment the $2N$-dimensional state can be fully recovered from amplitude measurements plus the continuity-based sign prediction, and that re-preparing that state costs no more than one segment's unitary; if prediction errors or measurement shot counts grow, the claimed $O(\text{depth}(U))$ depth reduction no longer holds.

Editorial extensions

If this is right

  • Increasing the number of adiabatic steps no longer deepens the quantum circuit; the same $O(\text{depth}(U))$ circuit is reused regardless of precision.
  • On simulated decoherence noise of level 0.001, the solver keeps solution fidelity above 80% after 2000 steps for matrix dimensions 2, 4, 8, 16 and condition numbers 10 to 50.
  • Precision requirements are decoupled from decoherence time, so higher-accuracy runs can be attempted on the same hardware without lengthening coherent execution.
  • The real-imaginary separation plus truncation of imaginary components gives a noise-resilient post-processing step that works for any $N\times N$ system of this block form.

Reading between the lines

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

  • The measure-reconstruct-re-encode pattern is not restricted to linear systems: any time-dependent simulation whose evolution operator preserves a known phase structure could be segmented in the same way, provided the classical reconstruction cost stays smaller than the saved circuit depth.
  • The $O(\text{depth}(U))$ claim counts quantum circuit depth; the end-to-end wall-clock cost also includes the classical sign-prediction and re-encoding computation plus the number of measurement shots, so the true quantum-classical tradeoff will depend on those constants.
  • A hardware implementation with feed-forward mid-circuit measurement could encode predicted signs directly as classical bit conditions instead of post-processing, turning the sign predictor into an online controller and removing one round-trip to classical storage.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes a co-designed quantum discrete adiabatic linear system solver that uses dynamic circuits and real-time classical processing. The idea is to split the adiabatic evolution into discrete segments and, after each segment, measure the evolved state, reconstruct it classically, and re-encode it for the next segment. The authors claim this reduces circuit depth from O(steps × depth(U)) to O(depth(U)). They benchmark the method on 2×2, 4×4, 8×8, and 16×16 linear systems with condition numbers 10–50, reporting over 80% fidelity under a noise model. The central claim, however, is that the depth reduction is achieved without accounting for the cost of measurement, classical reconstruction, and repeated state preparation; the paper also leaves the non-unitary nature of the first-order evolution operator unanalyzed.

Significance. If the central claim were sound, this would be a significant practical advance for near-term quantum linear solvers, because it would decouple circuit depth from the number of adiabatic evolution steps. The paper correctly identifies a structural feature of the block Hamiltonians used (real/imaginary component separation), and it provides numerical benchmarks for small systems. However, the advertised O(depth(U)) scaling is not established as a resource bound: it is obtained by measuring and classically reconstructing the full state after every step, and the costs of that reconstruction are never counted. The real-imaginary separation alone does not remove the need for tomography-like measurement overhead. Since the central complexity claim is load-bearing and unsupported, the contribution as stated cannot be accepted.

major comments (4)
  1. [Section 3.1, 'Dynamic Circuit Design Scheme'; Fig. 1] The claimed reduction from O(steps × depth(U)) to O(depth(U)) is not a resource reduction. Equations (2) and (16) still describe L sequential applications of the evolution operator, and the proposed protocol inserts a full measurement, classical reconstruction, and re-encoding after every step. The paper counts only the depth of a single segment, but the total execution includes L rounds of state preparation, measurement, and classical processing. No shot count, total runtime, or combined circuit-plus-classical depth is provided, so the O(depth(U)) statement is a restatement of 'each segment is shallow' rather than a bound on the full algorithm.
  2. [Section 3.1, Eq. (19)] The sign-prediction rule is load-bearing and unanalyzed. Reconstructing the 2N-dimensional intermediate state requires the sign of every component, but Eq. (19) can assign the wrong sign whenever |x_i^k| < δ, and the paper gives no bound on how often this occurs, on the resulting fidelity loss, or on the number of measurement shots needed to estimate the amplitudes |x_i|^2 to the required precision. For a general state, estimating all 2N amplitudes to fixed relative precision requires Ω(2N/η^2) shots per segment, so the total cost is Ω(L · 2N/η^2) executions of the step circuit. The paper does not analyze any of these costs, and without them the claimed O(depth(U)) scaling collapses.
  3. [Section 3.1, Eqs. (9)–(10) and Appendix A] The first-order operator I − iH dt is non-unitary, yet the paper applies it as though it were a standard quantum operation. Appendix A invokes block encoding for non-unitary matrices, but block encoding is a probabilistic embedding: the desired operation succeeds only with a certain probability, and the success probability and any amplitude-amplification overhead are not analyzed. The numerical simulations in Section 4 appear to apply the non-unitary operator exactly to a state vector, so they do not demonstrate that the per-segment circuit can be implemented at the claimed depth or success rate.
  4. [Section 4, Figs. 3 and 4] The numerical experiments are not circuit-level or sampling-based simulations. They do not include mid-circuit measurement shot noise, classical reconstruction, the sign-prediction heuristic, or re-encoding costs. The 'decoherence noise' model is not specified (the text only says '0.001 decoherence noise'), and the reported fidelity curves therefore cannot validate the dynamic-circuit protocol described in Section 3. A statevector simulation that directly applies the non-unitary operator is not evidence that the proposed stop-measure-reconstruct-reprepare loop works under realistic conditions.
minor comments (6)
  1. [Section 2.2 heading] The heading 'Quanutm Linear System Problem' contains a typo and should read 'Quantum Linear System Problem'.
  2. [Section 3.1, paragraph before Eq. (15)] There is an unresolved citation '[cite]' in the sentence introducing the initial condition (b1, b2, 0, 0)^T; this should be replaced with a proper reference or removed.
  3. [General / Fig. 1] The term 'circuit multiplexing' is used repeatedly but never defined; Fig. 1(b) shows dynamic circuits, but the multiplexing mechanism is not described.
  4. [Section 3.1, Eq. (19)] The linear extrapolation x'_i = 2 x_i^k − x_i^{k−1} is used without specifying how x_i^{k−1} is handled at k = 1, and without stating conditions under which this approximation is valid.
  5. [Fig. 2] Figure 2's axes and curves are not fully explained; the caption should state what quantity is plotted on each axis and what the blue and red curves represent quantitatively.
  6. [Appendix A] Appendix A contains an equation numbered '(1)' that conflicts with the numbering of Eq. (1) in Section 2.1; renumbering is needed.

Circularity Check

1 steps flagged · score 6.0 of 10

The advertised O(depth(U)) circuit-depth reduction is obtained by redefining circuit depth as the depth of a single measured-and-reprepared segment, while the total number of executed gates remains L×depth(U); the resource claim is therefore true by construction rather than by a shorter total computation.

  1. self definitional [Abstract; Section 1 'Introduction'; Section 3.1 'Dynamic Circuit Design Scheme']
    "By using measurement-assisted computation, we can split a deep quantum circuit into several shallower ones. ... This approach, combined with circuit multiplexing, reduces depth complexity from O(steps×depth(U)) to O(depth(U)), significantly curtailing the overall circuit depth. ... This resultant quantum state is then re-encoded and introduced into the subsequent discrete evolution stage. This step-wise approach considerably diminishes the depth of the quantum circuit involved in computations."

    The claimed reduction O(steps×depth(U))→O(depth(U)) is built into the definition of 'overall circuit depth' used in Fig. 1(b): the original product of L evolution operators (Eq. (2)) is replaced by a loop of L independent segments, each of depth O(depth(U)), with a full mid-circuit measurement, classical state reconstruction, and re-encoding between segments. Counting only one segment's depth makes the advertised scaling true by construction, while the total number of executed quantum gates and the total measurement repetitions remain L·depth(U) (plus an unanalyzed Ω(2N/η²) shot overhead for amplitude estimation). No resource accounting for the reconstruction/re-encoding loop is provided, so the depth improvement is a metric redefinition rather than a derived shorter computation.

full rationale

The central circular element is the depth metric: once the algorithm's 'circuit depth' is taken to be the depth of one discrete segment rather than the whole repeated process, the O(depth(U)) claim follows immediately from the decision to measure and re-encode after every step (Sections 1 and 3.1). This is a self-definitional reduction of the resource claim. The paper does not contain load-bearing self-citations: references [3], [5], [6], [7] are prior work by Costa, An, Lin, Tong, Berry, etc., not by the present authors. The sign-prediction rule in Eq. (19), the truncation threshold ϵ=0.1||x||2, and the missing '[cite]' in Section 3.1 are correctness/justification risks (the sign heuristic could fail near zero crossings, and shot counts are not given), but they are not themselves circular arguments. The noiseless and noisy fidelity curves (Figs. 3-4) are numerical demonstrations of the proposed heuristic loop, not independent predictions derived from first principles. Because the main advertised contribution — depth independent of steps — reduces to a redefinition of the resource being counted, a partial-circularity score of 6 is appropriate.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard adiabatic background plus several ad hoc choices: the first-order non-unitary step, the sign-continuity heuristic, hand-set thresholds, and the assumption that full classical state reconstruction is free. The most consequential uncharged premise is that knowing the complete 2N-dimensional state classically at every step either costs nothing or is compatible with a quantum advantage, which the paper never addresses.

free parameters (3)
  • Evolution step count L (and segment duration dt) = L up to 2000; dt = T/L with T unspecified
    The discrete adiabatic solver requires choosing L (and total time T) large enough to satisfy the adiabatic condition; the paper does not derive L from kappa and instead sweeps L from 200 to 2000 and selects curves that reach high fidelity.
  • Sign-prediction noise threshold delta = Not given numerically
    Introduced in Eq. (19) as the threshold below which the sign is inferred by linear extrapolation; no rule is given for setting it, and it controls the accuracy of state reconstruction.
  • Post-processing truncation threshold = 0.1||x||2
    Section 3.2 defines the imaginary-part truncation threshold as 0.1||x||2 with no derivation; if the imaginary norm exceeds it, T and dt are modified, so this threshold directly determines when the algorithm counts a run as successful.
assumptions (6)
  • standard math Adiabatic theorem: a system starting in the ground state of H(0) and evolving slowly stays in the instantaneous ground state when Eq. (1) holds.
    Invoked in Section 2.1 to justify the discrete evolution mapping H0 ground state to H1 ground state.
  • standard math The Hamiltonians H0 and H1 in Eqs. (4)-(5) have ground states |0,b> and |0,x> with eigenvalue 0.
    Used to define the adiabatic path; true for positive definite A but requires the block structure and the relation A|x>=|b>.
  • domain assumption The first-order Taylor approximation I-iHdt is a valid replacement for e^{-iHdt} for the chosen dt.
    Used throughout Section 3.1; it is a standard numerical approximation but makes the evolution non-unitary, and the paper does not analyze the postselection overhead of implementing it with block encoding.
  • standard math The quantum state has the real/imaginary component structure of Eq. (17) after each step.
    Proved by induction in Appendices B and C for the exact and first-order operators, but relies on the block-off-diagonal form of Hs.
  • ad hoc to paper The sign of each component changes only when the amplitude is near zero, so Eq. (19) can predict signs from previous steps.
    Introduced without proof in Section 3.1; it is a continuity heuristic not guaranteed by the adiabatic theorem, especially under noise.
  • domain assumption Randomly generated positive definite matrices A with specified kappa are representative of the QLSP.
    The numerical section uses 'suitable matrices' generated by an unspecified program; no distribution is defined, so generalization is assumed.

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Cite this review

Pith. "Pith review of Co-designed Quantum Discrete Adiabatic Linear System Solver Via Dynamic Circuits." pith.science (2026). https://pith.science/paper/JGHD3KBU

@misc{pith2026250524626,
  author       = {Pith},
  title        = {Pith review of: Co-designed Quantum Discrete Adiabatic Linear System Solver Via Dynamic Circuits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JGHD3KBU}},
  note         = {Machine review of arXiv:2505.24626}
}
abstract

Existing quantum discrete adiabatic approaches are hindered by circuit depth that increases linearly with the number of evolution steps, a significant challenge for current quantum hardware with limited coherence times. To address this, we propose a co-designed framework that synergistically integrates dynamic circuit capabilities with real-time classical processing. This framework reformulates the quantum adiabatic evolution into discrete, dynamically adjustable segments. The unitary operator for each segment is optimized on-the-fly using classical computation, and circuit multiplexing techniques are leveraged to reduce the overall circuit depth scaling from $O(\text{steps}\times\text{depth}(U))$ to $O(\text{depth}(U))$. We implement and benchmark a quantum discrete adiabatic linear solver based on this framework for linear systems of $W \in \{2,4,8,16\}$ dimensions with condition numbers $\kappa \in \{10,20,30,40,50\}$. Our solver successfully overcomes previous depth limitations, maintaining over 80% solution fidelity even under realistic noise models. Key algorithmic optimizations contributing to this performance include a first-order approximation of the discrete evolution operator, a tailored dynamic circuit design exploiting real-imaginary component separation, and noise-resilient post-processing techniques.

Figures

Figures reproduced from arXiv: 2505.24626 by the authors.

Figure 1
Figure 1. Comparison of quantum circuits for the discrete adiabatic solver. (a) The original circuit implemented via [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Relationship between Decoherence Time and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Fidelity Performance Across Different Dimensions and Condition Numbers Without Noise. In the absence of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Evolution Results Under a Perturbed System with Decoherence Noise.We presents the evolution results for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

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Reference graph

Works this paper leans on

30 extracted references · 26 canonical work pages

  1. [1]

    Quantum algorithm for linear systems of equations.Physical review letters, 103(15):150502, 2009

    Aram W Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations.Physical review letters, 103(15):150502, 2009

    2009

  2. [2]

    Variational quantum linear solver.Quantum, 7:1188, 2023

    Carlos Bravo-Prieto, Ryan LaRose, Marco Cerezo, Yigit Subasi, Lukasz Cincio, and Patrick J Coles. Variational quantum linear solver.Quantum, 7:1188, 2023

    2023

  3. [3]

    Optimal scaling quantum linear- systems solver via discrete adiabatic theo- rem.PRX quantum, 3(4):040303, 2022

    Pedro CS Costa, Dong An, Yuval R Sanders, Yuan Su, Ryan Babbush, and Dominic W Berry. Optimal scaling quantum linear- systems solver via discrete adiabatic theo- rem.PRX quantum, 3(4):040303, 2022

    work page 2022

  4. [4]

    Quantum algorithms for systems of linear equations inspired by adiabatic quan- tum computing.Physical review letters, 122 (6):060504, 2019

    YiğitSubaşı, RolandoDSomma, andDavide Orsucci. Quantum algorithms for systems of linear equations inspired by adiabatic quan- tum computing.Physical review letters, 122 (6):060504, 2019

    work page 2019

  5. [5]

    Dong An and Lin Lin. Quantum linear sys- tem solver based on time-optimal adiabatic quantum computing and quantum approxi- mate optimization algorithm.ACM Trans- actions on Quantum Computing, 3(2):1–28, 2022

    work page 2022

  6. [6]

    Optimal polynomial based quantum eigenstate filtering with ap- plication to solving quantum linear systems

    Lin Lin and Yu Tong. Optimal polynomial based quantum eigenstate filtering with ap- plication to solving quantum linear systems. Quantum, 4:361, 2020

    work page 2020

  7. [7]

    The discrete adiabatic quan- tum linear system solver has lower con- stant factors than the randomized adiabatic solver

    Pedro Costa, Dong An, Ryan Babbush, and Dominic Berry. The discrete adiabatic quan- tum linear system solver has lower con- stant factors than the randomized adiabatic solver. 2023

    work page 2023

  8. [8]

    Quantum algorithm and circuit design solv- ing the poisson equation.New Journal of Physics, 15(1):013021, 2013

    Yudong Cao, Anargyros Papageorgiou, Ia- sonas Petras, Joseph Traub, and Sabre Kais. Quantum algorithm and circuit design solv- ing the poisson equation.New Journal of Physics, 15(1):013021, 2013

    work page 2013

Show all 30 references
  1. [9]

    The power of block-encoded matrix powers: improved regression tech- niques via faster hamiltonian simulation

    Shantanav Chakraborty, András Gilyén, and Stacey Jeffery. The power of block-encoded matrix powers: improved regression tech- niques via faster hamiltonian simulation. arXiv preprint arXiv:1804.01973, 2018

    2018 arXiv

  2. [10]

    Quantum algorithm for systems of linear equations with expo- nentially improved dependence on precision

    Andrew M Childs, Robin Kothari, and Rolando D Somma. Quantum algorithm for systems of linear equations with expo- nentially improved dependence on precision. SIAM Journal on Computing, 46(6):1920– 1950, 2017. 8 Figure 4: Evolution Results Under a Perturbed System with Decohere...

    1920

  3. [11]

    Quantum singular value transformation and beyond: exponential im- provements for quantum matrix arithmetics

    András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singular value transformation and beyond: exponential im- provements for quantum matrix arithmetics. InProceedings of the 51st annual ACM SIGACT symposium on theory of computing, pages 193–204, 2019

    2019

  4. [12]

    Quantum linear system al- gorithm for dense matrices.Physical review letters, 120(5):050502, 2018

    Leonard Wossnig, Zhikuan Zhao, and Anu- pam Prakash. Quantum linear system al- gorithm for dense matrices.Physical review letters, 120(5):050502, 2018

    2018

  5. [13]

    Vari- ational algorithms for linear algebra.Science Bulletin, 66(21):2181–2188, 2021

    Xiaosi Xu, Jinzhao Sun, Suguru Endo, Ying Li, Simon C Benjamin, and Xiao Yuan. Vari- ational algorithms for linear algebra.Science Bulletin, 66(21):2181–2188, 2021

    2021

  6. [14]

    The cost of solving linear differ- ential equations on a quantum computer: fast-forwarding to explicit resource counts

    David Jennings, Matteo Lostaglio, Robert B Lowrie, Sam Pallister, and Andrew T Sorn- borger. The cost of solving linear differ- ential equations on a quantum computer: fast-forwarding to explicit resource counts. Quantum, 8:1553, 2024

    2024

  7. [15]

    Barren plateaus in quantum neural network training landscapes.Nature com- munications, 9(1):4812, 2018

    Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes.Nature com- munications, 9(1):4812, 2018

    2018

  8. [16]

    Cost function dependent barren plateaus in shal- low parametrized quantum circuits.Nature communications, 12(1):1791, 2021

    Marco Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles. Cost function dependent barren plateaus in shal- low parametrized quantum circuits.Nature communications, 12(1):1791, 2021

    2021

  9. [17]

    Noise-induced barren plateaus in variational quantum algo- rithms.Nature communications, 12(1):6961, 2021

    Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles. Noise-induced barren plateaus in variational quantum algo- rithms.Nature communications, 12(1):6961, 2021

    2021

  10. [18]

    Variable time amplitude amplification and quantum algorithms for linear algebra problems

    Andris Ambainis. Variable time amplitude amplification and quantum algorithms for linear algebra problems. InSTACS’12 (29th Symposium on Theoretical Aspects of Com- puter Science), volume 14, pages 636–647. LIPIcs, 2012

    2012

  11. [19]

    Exploiting dy- namic quantum circuits in a quantum algo- rithm with superconducting qubits.Physical Review Letters, 127(10):100501, 2021

    Antonio D Córcoles, Maika Takita, Ken In- oue, Scott Lekuch, Zlatko K Minev, Jerry M Chow, and Jay M Gambetta. Exploiting dy- namic quantum circuits in a quantum algo- rithm with superconducting qubits.Physical Review Letters, 127(10):100501, 2021

    2021

  12. [20]

    Efficient long-range entan- glement using dynamic circuits.PRX Quan- tum, 5(3):030339, 2024

    Elisa Bäumer, Vinay Tripathi, Derek S 9 Wang, Patrick Rall, Edward H Chen, Swarnadeep Majumder, Alireza Seif, and Zlatko K Minev. Efficient long-range entan- glement using dynamic circuits.PRX Quan- tum, 5(3):030339, 2024

    2024

  13. [21]

    Com- bining quantum processors with real-time classical communication.Nature, pages 1–5, 2024

    Almudena Carrera Vazquez, Caroline Tornow, Diego Ristè, Stefan Woerner, Maika Takita, and Daniel J Egger. Com- bining quantum processors with real-time classical communication.Nature, pages 1–5, 2024

    2024

  14. [22]

    Symmetry-based quantum circuit mapping.Physical Review Applied, 22(2):024029, 2024

    Di Yu and Kun Fang. Symmetry-based quantum circuit mapping.Physical Review Applied, 22(2):024029, 2024

    2024

  15. [23]

    Dynamic quantum circuit compila- tion.arXiv preprint arXiv:2310.11021, 2023

    Kun Fang, Munan Zhang, Ruqi Shi, and Yi- nan Li. Dynamic quantum circuit compila- tion.arXiv preprint arXiv:2310.11021, 2023

    2023 arXiv

  16. [24]

    Quantum computing in the nisq era and beyond.Quantum, 2:79, 2018

    John Preskill. Quantum computing in the nisq era and beyond.Quantum, 2:79, 2018

    2018

  17. [25]

    Adi- abatic quantum computation.Reviews of Modern Physics, 90(1):015002, 2018

    Tameem Albash and Daniel A Lidar. Adi- abatic quantum computation.Reviews of Modern Physics, 90(1):015002, 2018

    2018

  18. [26]

    How to experimentally evaluate the adiabatic condition for quan- tum annealing.Scientific Reports, 14(1): 8177, 2024

    Yuichiro Mori, Shiro Kawabata, and Yuichiro Matsuzaki. How to experimentally evaluate the adiabatic condition for quan- tum annealing.Scientific Reports, 14(1): 8177, 2024

    2024

  19. [27]

    Explicit quantum circuits for block encodings of certain sparse matri- ces.SIAM Journal on Matrix Analysis and Applications, 45(1):801–827, 2024

    Daan Camps, Lin Lin, Roel Van Beeumen, and Chao Yang. Explicit quantum circuits for block encodings of certain sparse matri- ces.SIAM Journal on Matrix Analysis and Applications, 45(1):801–827, 2024

    2024

  20. [28]

    Fa- ble: Fast approximate quantum circuits for block-encodings

    Daan Camps and Roel Van Beeumen. Fa- ble: Fast approximate quantum circuits for block-encodings. pages 104–113, 2022. 10 A Block Encoding for Non-unitary Matrix A Since we only consider the first order of Taylor expansion of unitary operatore−iHdt, the evolution becomes non-un...

    2022

  21. [29]

    In block encoding,OA is used to construct a quantum circuit capable of accessing and manipulating the elements of matrixA

    OracleO A: OA is a black box that provides access to specific data. In block encoding,OA is used to construct a quantum circuit capable of accessing and manipulating the elements of matrixA. This Oracle encodes the elementsAi,j of matrixAinto the amplitude of an auxiliary qubi...

  22. [30]

    OracleO B: OB allows an algorithm to query the elements of matrixA. This is typically implemented via a quantum circuit that encodes the indices of the matrix and enables the retrieval of corresponding elements.O B correctly maps the matrix index(i,j). For example, the SWAP ga...

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