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REVIEW 3 major objections 4 minor 95 references

Improved Accreditation of Analogue Quantum Simulation and Establishing Quantum Advantage

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

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Pith's one-line read Analogue quantum simulators can be accredited with only single-qubit gates.

desk verdict A genuinely better accreditation protocol in conception, but the proof bounds only the averaged inversion channel while the traps need pointwise closeness, so Theorem 3 does not go through. read the letter →

arxiv 2502.06463 v1 pith:F2K7LVQ2 submitted 2025-02-10 quant-ph

Andrew Jackson , Animesh Datta This is my paper · ORCID
classification quant-ph PACS 03.67.-a03.67.Lx
keywords analoguequantumsimulationaccreditationverificationideal-actualvariationdistanceadvantagesingle-qubitgatesHamiltonianinversionhybrid
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

This paper claims that analogue quantum simulators can be accredited—certified to produce outputs within a stated distance of the ideal simulation—using a protocol that needs only single-qubit gates in addition to the native time evolution. This removes three practical obstacles of the previous scheme: no reduction to a universal Hamiltonian, no extra qubits, and no two-qubit gates. It also drops the assumption that errors are identical across separate runs of the same simulation, so slow drifts and non-Markovian noise between runs no longer break the argument. The protocol returns the measurement outcomes of the target simulation together with an upper bound on its ideal-actual variation distance at a chosen accuracy and confidence, which is exactly the quantity used in recent complexity-theoretic proposals for quantum advantage. The improved realism makes accredited verification applicable to present-day programmable analogue simulators.

What carries the argument

The load-bearing ingredient is an approximate Hamiltonian inversion: Algorithm 2 builds a block $B(H,t,\epsilon,1)$ that interleaves the forward evolution $e^{-iHt/M}$ with uniformly random single-qubit Pauli gates drawn from the set $G'_H$, which is obtained from a hypergraph colouring of the Hamiltonian's interaction graph so that every term in $H$ anti-commutes with some element. Averaging over the random choices makes the block approximate $e^{iHt/(L-1)}$ to arbitrary additive error $\epsilon$ in the diamond norm, with $M = O(t^2/\epsilon)$ steps. Combined with a forward block $e^{-iHt/L}$, the block forms a modified 1-vanishing block that is (near-)identity in the ideal case, so any deviation in a trap is a detectable error; the corresponding 0-vanishing block implements the actual evolution $e^{-iHt}$. Random Pauli and Hadamard gates around the trap convert residual errors to stochastic Pauli errors that are detected with probability at least $1/2$, and averaging over trap runs gives the bound on the target via the redaction-class error assumptions.

What would settle it

For a small spin Hamiltonian, generate many random inversion circuits with Algorithm 2 and compute the diamond-norm distance of each individual circuit to $e^{iHt/(L-1)}$. If a non-negligible fraction of the circuits exceed the claimed $\epsilon$ while their average is within $\epsilon$, then an errorless trap can produce a wrong outcome and the protocol's bound on the target simulation no longer follows.

Watch

Extended reading notes

Core claim

The central result is Theorem 3: assuming the error model E1–E3, Protocol 5 performs accredited analogue simulation as defined in Def. 7. The experimenter picks a random position for the target simulation among $N_{\mathrm{tr}}+1$ runs, executes $N_{\mathrm{tr}}$ trap simulations generated from the same Hamiltonian, and reports the target outcomes plus $\epsilon_{\mathrm{VD}} = 2\cdot\text{(fraction of traps that gave the correct outcome)}$, using $N_{\mathrm{tr}} = \left\lceil \frac{2}{\theta^2} \ln\left(\frac{2}{1-\alpha}\right)\right\rceil + 1$. The returned $\epsilon_{\mathrm{VD}}$ upper bounds the ideal-actual variation distance $\nu(\tilde{C})$ of the target execution with accuracy $\theta$ and confidence $\alpha$. The protocol works for any spin Hamiltonian and any evolution time. The number of single-qubit gates grows as $O(Nt^2/\epsilon)$, while the total evolution time is unchanged.

Load-bearing premise

The protocol requires that every individual random inversion block be close to the ideal reversed evolution, but the proof only establishes this closeness for the average over random choices.

Editorial extensions

If this is right

  • A laboratory with a programmable analogue simulator that can pause evolution to apply single-qubit gates can now certify a given run's output without needing universal Hamiltonian gadgets or two-qubit gates.
  • Because the error model no longer assumes identically distributed errors across runs, the accreditation guarantee covers drift and non-Markovian noise, making the protocol more faithful to real devices.
  • The bound produced is exactly the ideal-actual variation distance required by complexity-theoretic advantage arguments: an accredited simulation with $\epsilon_{\mathrm{VD}} \le 1 - 1/\sqrt{2} \approx 0.292$ would simultaneously certify that the task is classically intractable under those assumptions.
  • Resource overhead stays reasonable: no extra qubits, total evolution time unchanged, $O(Nt^2/\epsilon)$ additional single-qubit gates, and the number of traps grows only quadratically in $1/\theta$.
  • The reduced hardware requirements align the protocol with the Hamiltonian of Ref. [24], allowing a near-term simulation-based route to established quantum advantage that includes verification.

Reading between the lines

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

  • The proof of Theorem 2 bounds only the averaged random channel; the protocol's traps, however, are individual random realizations. A concentration bound showing that most realizations are within $\epsilon$ of the ideal inversion would close this gap, but the paper does not supply one.
  • One testable extension is to implement Algorithm 2 on a small programmable simulator and compare the accredited $\epsilon_{\mathrm{VD}}$ with the directly measured variation distance across many random single-qubit gate choices; systematic looseness would guide how to set $\theta$ and $\alpha$ in practice.
  • The same random-Pauli inversion technique could serve other tasks that need approximate time reversal, such as Loschmidt-echo fidelity measurements, where a certified reversal block would improve noise characterisation.
  • The protocol's bound is conservative because E2 asserts that adding gates cannot reduce error; on devices where idle time causes comparable error to gate time, this monotonicity may fail, and accounting for it would require a modified redaction structure.
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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

3 major / 4 minor

Summary. This paper proposes an accreditation protocol for analogue quantum simulations. The authors replace the exact XY-Hamiltonian inversion of earlier work with an approximate inversion of general spin Hamiltonians, implemented by inserting random single-qubit gates into a split time evolution. They define trap and target simulations built around "vanishing blocks", and claim that Protocol 5, using a number of trap runs quadratic in 1/θ, returns an upper bound ε_VD on the ideal-actual variation distance of the target run with confidence α and accuracy θ. The main result is stated as Theorem 3.

Significance. If the proof were sound, the result would be a practical step forward: it removes the need for universal Hamiltonians and two-qubit gates in analogue accreditation, and it relaxes the identical-error assumption used in Ref. [13]. The resource counts are explicit and the connection to quantum-advantage experiments is interesting. However, the central inversion proof applies to the averaged random channel rather than to the individual circuits actually produced by Algorithm 2, and this breaks the deterministic trap property on which the accreditation bound depends. The protocol's error estimate also appears to invert the measured quantity. These are load-bearing gaps, not minor presentation issues, so the central claim is not established as written.

major comments (3)
  1. [Theorem 2 / Appendix A; Lemma 5] The proof of Theorem 2 establishes a bound on the averaged channel only. In Appendix A, Φ is defined as the one-step channel averaged uniformly over σ∈G''_H (Eq. A8), and Eqs. (A8)-(A14) show that the M-fold averaged channel Φ^M is within ε of e^{iHt/(L-1)}. Algorithm 2, however, produces a single random sequence σ_1,...,σ_M; the actual errorless block in an execution is the unitary U_seq = ∏_{k=1}^M σ_k e^{-itH/M} σ_k. No bound is shown for ‖U_seq − e^{iHt/(L−1)}‖⋄, and the first-order term, which vanishes only after averaging over σ, is not cancelled in a single sequence. Lemma 5 uses Theorem 2 to conclude that the errorless 1-vanishing block is approximately the identity, but for a random realization this conclusion is unsupported. Consequently the noiseless trap is not guaranteed to have a deterministic outcome, the trap error probability is contaminated by the inversion error, and the bound in Lemma 6 does not follow. This gap is load-bearing for Theorem 3.
  2. [Lemma 5, Eq. (9)] The proof of Lemma 5 contains an algebraic error: it replaces the approximation from Theorem 2, B(H,t'_2,ε,1)≈ e^{iHt'_2/(L−1)}, by e^{iHt'_2/[L+1]}. With L+1 the exponent is (L−1)t/[L(L+1)] rather than t/L, so the claimed cancellation e^{−iHt'_1} e^{iHt'_2/[L+1]} = I does not hold. The cancellation works only with L−1, so this is likely a typo, but as written the proof of the lemma is incorrect and must be fixed.
  3. [Protocol 5, step 4; Lemma 6] The quantity returned by Protocol 5 is calculated incorrectly. Lemma 6 requires doubling the average probability of error over the trap simulations, which is estimated by the fraction of traps that detect an error. Protocol 5 step 4 instead computes ε_VD = 2 × (number of correct traps)/(Ntr+1). This estimates 2(1−P) rather than 2P, and the denominator Ntr+1 includes the target simulation, which is not part of K in Lemma 6. The returned ε_VD is therefore not in general an upper bound on the target's ideal-actual variation distance, and the accuracy parameter θ is not tied to the target error. This must be corrected for the statement of Theorem 3 to be meaningful.
minor comments (4)
  1. [Section IV.B, E2] The statement of E2 is terse: the inequality ν(˜C) ≥ ν(˜C′) for C in a redaction class and C′ in a reduced redaction class is asserted from empirical gate-error observations, but it would be helpful to state explicitly how the single-qubit gates are removed and why the variation distance is monotonically non-increasing.
  2. [Section VI] The sentence beginning "The latter is particularly amenable to the original accreditation protocol [13] is particularly well suited" is garbled and should be rewritten.
  3. [References] References [28] and [43] appear to refer to the same work; if so, the duplicate entry should be removed and the citations consolidated.
  4. [Algorithm 2, line 3] The summation in the definition of M, ∑_{j=1} |c_j|, is missing an upper limit; it should run over all terms in the Hamiltonian.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central derivation does not reduce to its inputs; the flagged issues are proof gaps, not definitional circularity.

full rationale

I walked the derivation chain from Theorem 2 through Lemma 5, Lemma 6, and Theorem 3. The approximate inversion theorem rests on an external algebraic identity (Lemma 10, attributed to Ref. [25]) and on Taylor/diamond-norm chaining arguments; it does not assume the accreditation conclusion. The trap/target relationship is imported from the authors' earlier PNAS paper (Ref. [13]), but that is an independent, published, non-fitted result rather than an assumption that presupposes Theorem 3. No parameter is fitted to data and then renamed a prediction: the protocol's eps_VD is an empirical trap-outcome fraction, and the paper does not define the trap in terms of the target's variation distance. The explicitly omitted proof of Lemma 2 is a deference to a published lemma, not a definitional loop. The skeptic's concerns are about the validity of the proof (averaged channel vs. per-instance closeness in Theorem 2, and the apparent sign inversion in Protocol 5 step 4), not about an equation being identical to its input by construction. Since I can exhibit no step in which the claimed output is equivalent to the input by definition, the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No fitted parameters. The protocol rests on error-model axioms E1-E3, an external algebra identity from Ref [25], and an unproven pointwise interpretation of the randomized inversion.

assumptions (5)
  • domain assumption E1: errors are CPTP maps and are independent across simulation executions.
    Explicit error model in Section IV B; the independence of CPTP maps across simulations is acknowledged as suspect in Section VII.
  • domain assumption E2: implementing more gates cannot reduce the ideal-actual variation distance.
    Justified only by empirical gate-count scaling in Section IV C; used to order trap and target variation distances in Lemma 6.
  • domain assumption E3: errors on single-qubit gates are independent of which gate is applied.
    Standard gate-independent noise assumption, stated in Section IV C and used throughout the trap construction.
  • domain assumption Lemma 10 from Ref [25]: sum over sigma in G'_H of sigma H sigma equals L Tr(H)/2^N times identity.
    External theorem used without proof in Eq. A7; it is the algebraic core of the approximate inversion.
  • ad hoc to paper Each execution of Algorithm 2 is close to e^{iHt/(L-1)}, not only the channel averaged over random choices.
    Theorem 2 proves only an averaged channel bound, but Lemma 5 and deterministic trap outcomes require pointwise closeness. No pointwise bound is derived.

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Pith. "Pith review of Improved Accreditation of Analogue Quantum Simulation and Establishing Quantum Advantage." pith.science (2026). https://pith.science/paper/F2K7LVQ2

@misc{pith2026250206463,
  author       = {Pith},
  title        = {Pith review of: Improved Accreditation of Analogue Quantum Simulation and Establishing Quantum Advantage},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F2K7LVQ2}},
  note         = {Machine review of arXiv:2502.06463}
}
read the original abstract

We improve on the results of [A. Jackson et al. Proc. Natl. Acad. Sci. U.S.A 121 (6). 2024] on the verification of analogue quantum simulators by eliminating the use of universal Hamiltonians, removing the need for two-qubit gates, and no longer assuming error is represented by identical maps across simulations. This new protocol better reflects the reality of extant analogue simulators. It integrates well with recent complexity theoretic results, leading to a near-term feasible simulation-based route to establishing quantum advantage.

Figures

Figures reproduced from arXiv: 2502.06463 by the authors.

Figure 1
Figure 1. FIG. 1. A depiction of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. A depiction of a subcircuit, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (Ref.[ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (Ref.[ [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Depiction of a modified [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. A target (top) and trap (bottom) simulation corresponding [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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Reference graph

Works this paper leans on

95 extracted references · 72 canonical work pages

  1. [13]

    A simulation duration, t∈ R,

  2. [1]

    The number of gates required for a modest (for an ana- logue simulator) simulation on a digital quantum com- puter quickly becomes prohibitive. For instance, a sim- ulation of the Hubbard model on a 10× 10 lattice for a duration of 10ℏJ−1 is already feasible on analogue sim- ulators, however a digital quantum computer would re- quire over a million gates [9]

  3. [2]

    Analogue simulators are typically far larger than their contemporaneous digital counterparts [9, Table. 1]. It is therefore important to develop methods (known as veri- fication protocols) to ascertain the correctness of noisy, error- prone real-world analogue quantum simulations. This is also important as verification is a key to demonstrating quantum ad...

    arXiv 2025

  4. [6]

    while timeStep≤ M do (a) AddI⊗Ne−itH/MI⊗N to circ (b) timeStep + = 1 Return : circ ... ... ... I e−iHt/M I I I I I I I Repeat M times FIG. 1. A depiction ofB(H, t,ϵ, 0), that is equivalent to e−iHt. Definition 2. GH⊆ qσ|σ∈ {X,Y,Z,I}N, q∈ {±1,±i} depends exclusively onH = P u∈J cuPu and is defined by: ∀u∈ J\{⃗0},∃σ∈ GH such that σ,Pu = 0. (2) As shown in L...

  5. [7]

    Calculate the G′ H required to invertH, as defined in Def. 3

  6. [8]

    Calculate M = 2t2 P j=1 |c j| 2L ϵ(L− 1)

  7. [10]

    Using the sets and variables defined above, we present Al- gorithm 2 to generateBH, t,ϵ, 1)

    while timeStep≤ M do (a) Choose σ uniformly at random from G′ H (b) Add σe−itH/Mσ to circ (c) timeStep + = 1 Return : circ L is independent of M, and N only provides a bound on L as 4N bounds the number of terms in the Hamiltonian, which in turn bounds the size of G′ H. Using the sets and variables defined above, we present Al- gorithm 2 to generateBH, t,...

  8. [11]

    The description of an initial product state|ψ0⟩,

Show all 95 references
  1. [12]

    A time-independent Hamiltonian,H,

  2. [14]

    The simulation prepares|ψ0⟩ then applies the time evolution generated byH, for the duration t, followed by the measure- ments inM

    A set of single-qubit measurements,M. The simulation prepares|ψ0⟩ then applies the time evolution generated byH, for the duration t, followed by the measure- ments inM. It returns, as the final output, the results of the measurements inM. While an analogue quantum simulator ha...

  3. [15]

    As promised, we now define accredited analogue quantum simulations and accreditation protocols, in Def

    An ordered set, S, of single-qubit3 quantum gates with corresponding time-stamps{tγ|γ∈ S} denoting when each is applied. As promised, we now define accredited analogue quantum simulations and accreditation protocols, in Def. 7. Definition 7. An accredited analogue quantum simu...

  4. [16]

    reduces all error occurring to stochastic Pauli error

  5. [17]

    4 which includes the use of randomly chosen gates

    detects Pauli error with probability at least 1/2. 4 which includes the use of randomly chosen gates. 6 The target simulations:

  6. [18]

    are equivalent to applying e −iHt to a specified single- qubit product state before performing specified single- qubit measurements,M

  7. [19]

    1) variation distance in executing it is always less than that in executing a trap

    experiences error such that the ideal-actual (as defined in Def. 1) variation distance in executing it is always less than that in executing a trap. Proof. Instead of a full proof we sketch the overall approach:

  8. [20]

    6, in the traps, the protocol in Ref

    As in Fig. 6, in the traps, the protocol in Ref. [13] ap- plies single-qubit gates: a uniformly random Pauli and a Hadamard gate, with probability 0 .5, on each qubit before and afterJ(H, t,ϵ, 1). 2.J(H, t,ϵ, 1) is equivalent to the identity, so any oper- ator applied when J(H...

  9. [21]

    The uniformly random Pauli gates reduce5 the error oc- curring in the implementation of J(H, t,ϵ, 1), and the single-qubit gates themselves, to stochastic Pauli error

  10. [22]

    The stochastic Hadamard gates mean any Pauli error is detectible with probability at least 0 .5 [13, Lemma 3], as the traps give a single definite outcome if there is no error [13, Lemma 6]

  11. [23]

    [13, Lemma 8] provide a bound on the ideal-actual variation distance in traps

    Multiple runs of the trap simulation estimate the proba- bility of error occurring and Ref. [13, Lemma 8] provide a bound on the ideal-actual variation distance in traps

  12. [24]

    [13, Lemma 2], the ideal-actual variation dis- tance is greater in traps than in the target simulation

    By Ref. [13, Lemma 2], the ideal-actual variation dis- tance is greater in traps than in the target simulation. □ Corollary 1. In any accreditation protocol using Lemma 3 to generate trap and target simulations6, the trap simulations are all in the same redaction class and the...

  13. [25]

    t′ 1− t′ 2 L− 1 = 0. Proof. Lemma 4 follows from substituting in the definitions of t′ 1 and t′ 2 from Def. 13:

  14. [26]

    t′ 1 + t′ 2 = t L + (L− 1)t L = (L− 1 + 1)t L = t,

  15. [27]

    □ Lemma 5

    t′ 1− t′ 2 L− 1 = t L− 1 L− 1 (L− 1)t L = t L− t L = 0. □ Lemma 5. The errorless implementation of a modified j- vanishing block, J(H, t,ϵ, j), is equivalent (but only up to additive errorϵ in the diamond norm when j = 1) to e−i(1− j)Ht, where t∈ R is as can be inferred from t...

  16. [28]

    (8) Likewise, by Theorem 2,B(H, t′ 2,ϵ, 1)≈ eiHt′ 2/[L+1], hence a 1-vanishing block,J(H, t,ϵ, 1), may be approximated as: e−iHt′ 1eiHt′ 2/[L+1] = e−iH(t′ 1−t′ 2/[L+1]) = e0 =I

    = e−iHt. (8) Likewise, by Theorem 2,B(H, t′ 2,ϵ, 1)≈ eiHt′ 2/[L+1], hence a 1-vanishing block,J(H, t,ϵ, 1), may be approximated as: e−iHt′ 1eiHt′ 2/[L+1] = e−iH(t′ 1−t′ 2/[L+1]) = e0 =I. (9) □ Due to Lemma 5, all the requirements of Lemma 3 are met. This provides the required ...

  17. [31]

    Apply⊗N j=1 A′ j to circ

  18. [34]

    ApplyB(H, t′ 2,ϵ, 0) to circ, using Algorithm 1

  19. [35]

    Apply⊗N j=1 D′ j to circ

  20. [36]

    Measure each qubit in the Z-basis Return : circ Algorithm 4: Trap simulation construction algorithm Input : • A Hamiltonian,H • A evolution duration, t∈ R • A number of qubitsH acts on , N∈ N • A maximum permissible additive error – in terms of the diamond norm – in the approx...

  21. [37]

    Initialize a blank circuit, circ

  22. [38]

    Prepare the state|0⟩⊗N as the input state to circ

  23. [39]

    Choose h∈{ 0, 1} uniformly at random

  24. [40]

    For qubit j: (a) With probability 0.5, apply a PauliZ gate to qubit j (b) Choose Pauli gateP j uniformly at random (c) ApplyP jHh to qubit j

  25. [41]

    Calculate t′ 1 and t′ 2, as defined in Def. 13

  26. [42]

    Apply e−iHt′ 1 to circ

  27. [43]

    ApplyB(H, t′ 2,ϵ, 1) to circ, with additive error in the inverted time evolution bounded byϵ, using Algorithm 2

  28. [44]

    For qubit j: (a) Apply HhP j to qubit j (b) With probability 0.5 apply a PauliZ gate to qubit j

  29. [45]

    1) of the execution of the corresponding (to the traps) target simulation, and Probe is the probability of error occur- ring in its argument simulation execution

    Measure each qubit in theZ-basis Return : circ 8 where ν ˜Ctarg is the ideal-actual variation distance (as in Eqn. 1) of the execution of the corresponding (to the traps) target simulation, and Probe is the probability of error occur- ring in its argument simulation execution....

  30. [46]

    Calculate the required number of traps Ntr = 2 θ2 ln 2 1−α + 1

  31. [47]

    Pick uniformly at random an integer between 1 and N + 1 to be the index of the target simulation

  32. [48]

    Generate the target simulation using Algorithm 3 ii

    For i = 1 to Ntr + 1 (a) If simulation i is the target simulation: i. Generate the target simulation using Algorithm 3 ii. Execute the target simulation just generated iii. Record the measurement outcomes (b) If simulation i is a trap simulation: i. Generate a trap simulation ...

  33. [49]

    reducing the Hamiltonian to HA = P (i, j)∈E Ji, jZiZ j

    Calculate ϵVD = 2 Number of correct traps Ntr + 1 Return : Target simulation measurement outcomes andϵVD. reducing the Hamiltonian to HA = P (i, j)∈E Ji, jZiZ j . The latter is particularly amenable to the original accreditation protocol [13] is particularly well suited – in s...

  34. [50]

    Lloyd, Universal Quantum Simulators, Science 273, 1073 (1996)

    S. Lloyd, Universal Quantum Simulators, Science 273, 1073 (1996)

    1996

  35. [51]

    Poulin, M

    D. Poulin, M. Hastings, D. Wecker, N. Wiebe, A. C. Doberty, and M. Troyer, The Trotter step size required for accurate quan- tum simulation of quantum chemistry, Quantum Inf. Comput. 15, 361 (2015)

    2015

  36. [52]

    M. Heyl, P. Hauke, and P. Zoller, Quantum localization bounds Trotter errors in digital quantum simulation, Science Advances 5, eaau8342 (2019)

    2019

  37. [53]

    Benedetti, M

    M. Benedetti, M. Fiorentini, and M. Lubasch, Hardware- efficient variational quantum algorithms for time evolution (2020), arXiv:2009.12361 [quant-ph]

    2020 arXiv

  38. [54]

    Clinton, T

    L. Clinton, T. Cubitt, B. Flynn, F. M. Gambetta, J. Klassen, A. Montanaro, S. Piddock, R. A. Santos, and E. Sheridan, To- wards near-term quantum simulation of materials, Nature Com- munications 15, 211 (2024)

    2024

  39. [55]

    A. N. Chowdhury, R. D. Somma, and Y . Subas ¸ı, Computing partition functions in the one-clean-qubit model, Physical Re- view A 103, 032422 (2021)

    2021

  40. [56]

    Jackson, T

    A. Jackson, T. Kapourniotis, and A. Datta, Partition-function estimation: Quantum and quantum-inspired algorithms, Physi- cal Review A 107, 012421 (2023)

    2023

  41. [57]

    Cornelissen and Y

    A. Cornelissen and Y . Hamoudi, A sublinear-time quantum al- gorithm for approximating partition functions, in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algo- rithms (SODA), pp. 1245–1264

    2023

  42. [58]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Practical quantum advantage in quan- tum simulation, Nature 607, 667 (2022)

    2022

  43. [59]

    Bairey, I

    E. Bairey, I. Arad, and N. H. Lindner, Learning a local hamil- tonian from local measurements, Phys. Rev. Lett. 122, 020504 (2019)

    2019

  44. [60]

    Carrasco, A

    J. Carrasco, A. Elben, C. Kokail, B. Kraus, and P. Zoller, The- oretical and experimental perspectives of quantum verification, PRX Quantum 2, 010102 (2021)

    2021

  45. [61]

    Sha ffer, E

    R. Sha ffer, E. Megidish, J. Broz, W.-T. Chen, and H. H ¨affner, Practical verification protocols for analog quantum simulators, npj Quantum Information 7 (2021)

    2021

  46. [62]

    Jackson, T

    A. Jackson, T. Kapourniotis, and A. Datta, Accreditation of analogue quantum simulators, Proceedings of the National Academy of Sciences 121, e2309627121 (2024)

    2024

  47. [63]

    T. S. Cubitt, A. Montanaro, and S. Piddock, Universal quan- tum hamiltonians, Proceedings of the National Academy of Sci- ences 115, 9497–9502 (2018)

    2018

  48. [64]

    Zhou and D

    L. Zhou and D. Aharonov, Strongly universal hamiltonian sim- ulators (2021), arXiv:2102.02991 [quant-ph]

    2021 arXiv

  49. [65]

    Kohler, S

    T. Kohler, S. Piddock, J. Bausch, and T. Cubitt, General condi- tions for universality of quantum hamiltonians, PRX Quantum 3, 010308 (2022)

    2022

  50. [66]

    J. J. Wallman and J. Emerson, Noise tailoring for scalable quan- tum computation via randomized compiling, Physical Review A 94, 052325 (2016)

    2016

  51. [67]

    Hashim, R

    A. Hashim, R. K. Naik, A. Morvan, J.-L. Ville, B. Mitchell, J. M. Kreikebaum, M. Davis, E. Smith, C. Iancu, K. P. O’Brien, I. Hincks, J. J. Wallman, J. Emerson, I. Siddiqi, et al. , Ran- domized compiling for scalable quantum computing on a noisy superconducting quantum proces...

    2021

  52. [68]

    W. Feng, L. Liu, and T. Liu, On deterministically approximating total variation distance (2023), arXiv:2309.14696 [cs.DS]

    2023 arXiv

  53. [69]

    Gao, S.-T

    X. Gao, S.-T. Wang, and L.-M. Duan, Quantum supremacy for simulating a translation-invariant ising spin model, Phys. Rev. Lett. 118, 040502 (2017)

    2017

  54. [70]

    Bermejo-Vega, D

    J. Bermejo-Vega, D. Hangleiter, M. Schwarz, R. Raussendorf, and J. Eisert, Architectures for quantum simulation showing a quantum speedup, Phys. Rev. X 8, 021010 (2018)

    2018

  55. [71]

    Kapourniotis and A

    T. Kapourniotis and A. Datta, Nonadaptive fault-tolerant ver- ification of quantum supremacy with noise, Quantum 3, 164 10 (2019)

    2019

  56. [72]

    Ringbauer, M

    M. Ringbauer, M. Hinsche, T. Feldker, P. K. Faehrmann, J. Bermejo-Vega, C. Edmunds, L. Postler, R. Stricker, C. D. Marciniak, M. Meth, I. Pogorelov, R. Blatt, P. Schindler, J. Eisert, T. Monz, and D. Hangleiter, Verifiable measurement- based quantum random sampling with trappe...

    2024 arXiv

  57. [73]

    Z. Liu, D. Devulapalli, D. Hangleiter, Y .-K. Liu, A. J. Koll ´ar, A. V . Gorshkov, and A. M. Childs, Efficiently verifiable quan- tum advantage on near-term analog quantum simulators (2024), arXiv:2403.08195 [quant-ph]

    2024 arXiv

  58. [74]

    Odake, H

    T. Odake, H. Kristj ´ansson, P. Taranto, and M. Murao, Univer- sal algorithm for transforming hamiltonian eigenvalues (2024), arXiv:2312.08848 [quant-ph]

    2024 arXiv

  59. [75]

    Jackson, Accreditation against limited adversarial noise (2024), arXiv:2409.03995 [quant-ph]

    A. Jackson, Accreditation against limited adversarial noise (2024), arXiv:2409.03995 [quant-ph]

    2024

  60. [76]

    Derbyshire, J

    E. Derbyshire, J. Y . Malo, A. J. Daley, E. Kashefi, and P. Wallden, Randomized benchmarking in the analogue setting, Quantum Science and Technology 5, 034001 (2020)

    2020

  61. [77]

    Ferracin, S

    S. Ferracin, S. T. Merkel, D. McKay, and A. Datta, Experimen- tal accreditation of outputs of noisy quantum computers, Phys. Rev. A 104, 042603 (2021)

    2021

  62. [78]

    Erhard, J

    A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson, and R. Blatt, Char- acterizing large-scale quantum computers via cycle benchmark- ing, Nature Communications 10, 5347 (2019)

    2019

  63. [79]

    Carignan-Dugas, J

    A. Carignan-Dugas, J. J. Wallman, and J. Emerson, Character- izing universal gate sets via dihedral benchmarking, Phys. Rev. A 92, 060302 (2015)

    2015

  64. [80]

    D. Lu, H. Li, D.-A. Trottier, J. Li, A. Brodutch, A. P. Kris- manich, A. Ghavami, G. I. Dmitrienko, G. Long, J. Baugh, and R. Laflamme, Experimental estimation of average fidelity of a clifford gate on a 7-qubit quantum processor, Phys. Rev. Lett. 114, 140505 (2015)

    2015

  65. [81]

    S. T. Merkel, J. M. Gambetta, J. A. Smolin, S. Poletto, A. D. C´orcoles, B. R. Johnson, C. A. Ryan, and M. Ste ffen, Self- consistent quantum process tomography, Phys. Rev. A 87, 062119 (2013)

    2013

  66. [82]

    S. T. Flammia and Y .-K. Liu, Direct fidelity estimation from few pauli measurements, Phys. Rev. Lett. 106, 230501 (2011)

    2011

  67. [83]

    M. L. Dahlhauser and T. S. Humble, Modeling noisy quantum circuits using experimental characterization, Physical Review A 103, 042603 (2021)

    2021

  68. [84]

    Moussa, M

    O. Moussa, M. P. da Silva, C. A. Ryan, and R. Laflamme, Practical experimental certification of computational quantum gates using a twirling procedure, Phys. Rev. Lett. 109, 070504 (2012)

    2012

  69. [85]

    Harper, S

    R. Harper, S. T. Flammia, and J. J. Wallman, E fficient learning of quantum noise, Nature Physics 16, 1184 (2020)

    2020

  70. [86]

    Ferracin, A

    S. Ferracin, A. Hashim, J.-L. Ville, R. Naik, A. Carignan- Dugas, H. Qassim, A. Morvan, D. I. Santiago, I. Siddiqi, and J. J. Wallman, Efficiently improving the performance of noisy quantum computers (2022), arXiv:2201.10672 [quant-ph]

    2022 arXiv

  71. [87]

    Emerson, M

    J. Emerson, M. Silva, O. Moussa, C. Ryan, M. Laforest, J. Baugh, D. G. Cory, and R. Laflamme, Symmetrized char- acterization of noisy quantum processes, Science 317, 1893 (2007)

    2007

  72. [88]

    T. P. Harty, D. T. C. Allcock, C. J. Ballance, L. Guidoni, H. A. Janacek, N. M. Linke, D. N. Stacey, and D. M. Lucas, High- fidelity preparation, gates, memory, and readout of a trapped- ion quantum bit, Phys. Rev. Lett. 113, 220501 (2014)

    2014

  73. [89]

    Wright, K

    K. Wright, K. M. Beck, S. Debnath, J. M. Amini, Y . Nam, N. Grzesiak, et al., Benchmarking an 11-qubit quantum com- puter, Nature Communications 10, 5464 (2019)

    2019

  74. [90]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019)

    2019

  75. [91]

    Ferracin, T

    S. Ferracin, T. Kapourniotis, and A. Datta, Accrediting outputs of noisy intermediate-scale quantum computing devices, New Journal of Physics 21, 113038 (2019)

    2019

  76. [92]

    Ferracin, S

    S. Ferracin, S. T. Merkel, D. McKay, and A. Datta, Experimen- tal accreditation of outputs of noisy quantum computers, Phys- ical Review A 104, 042603 (2021)

    2021

  77. [93]

    Hoeffding, Probability inequalities for sums of bounded ran- dom variables, Journal of the American Statistical Association 58, 13 (1963)

    W. Hoeffding, Probability inequalities for sums of bounded ran- dom variables, Journal of the American Statistical Association 58, 13 (1963)

    1963

  78. [94]

    Preskill, Quantum computing and the entanglement frontier (2012), arXiv:1203.5813 [quant-ph]

    J. Preskill, Quantum computing and the entanglement frontier (2012), arXiv:1203.5813 [quant-ph]

    2012 arXiv

  79. [95]

    A. W. Harrow and A. Montanaro, Quantum computational supremacy, Nature 549, 203–209 (2017)

    2017

  80. [96]

    Fujii and T

    K. Fujii and T. Morimae, Commuting quantum circuits and complexity of ising partition functions, New Journal of Physics 19, 033003 (2017)

    2017

  81. [97]

    Browaeys and T

    A. Browaeys and T. Lahaye, Many-body physics with individ- ually controlled rydberg atoms, Nature Physics 16, 132 (2020)

    2020

  82. [98]

    Bluvstein, H

    D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V . Vuleti´c, and M. D. Lukin, A quantum processor based on coherent transport of entangled atom arrays, Nature 604, 451 (2022). Appendix A: Proof of Theorem 2

    2022

  83. [99]

    Definition 14

    Basic Definitions in Graph Theory To enable the discussion in this appendix, we first present foundational definitions of graphs and hypergraphs. Definition 14. A hypergraph, h = (V, E), is a set of two sets:V and E. Elements of V are referred to as vertices and each element i...

  84. [100]

    Remove the colour of k from unUsed

    for every vertex, k, sharing a hyperedge with v do (a) if k is already coloured then i. Remove the colour of k from unUsed

  85. [101]

    A hypergraph, h = (Vh, Eh), is k-colourable if and only if there exists a colouring mapping,χ: Vh−→{1, 2,..., k}, i.e

    Assign to v the minimum value in unUsed as its colour Return : The colouring constructed above Definition 16. A hypergraph, h = (Vh, Eh), is k-colourable if and only if there exists a colouring mapping,χ: Vh−→{1, 2,..., k}, i.e. a colouring (as in Def. 15) with the image{1, 2,...

  86. [102]

    Interaction Hypergraph Preparatory Definition and Results Definition 19. We define the greedy colouring of a graph as the colouring of that graph generated by Algorithm 6 We then begin the journey towards proving Theorem 2 with some relevant graph theory to represent the inter...

  87. [103]

    Proving Theorem 2: Main Section The diamond norm has many useful properties, but the most useful for this paper is the chain property, proven in Lemma 9. Lemma 9. Any sub-multiplicative norm bounded by one on CPTP maps, · sub, exhibits the chaining property, i.e. for any opera...

Pith tools

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