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arxiv: 2605.29674 · v1 · pith:7XMQNHLRnew · submitted 2026-05-28 · 🪐 quant-ph · cond-mat.str-el

Error-corrected phase estimation averaged over variable grids on a trapped-ion quantum computer: hyperacuity spectra of a CO molecule adsorbed onto chi-Fe₅C₂

Taichi Kosugi , Hirofumi Nishi , Keito Kasebayashi , Hiroki Takahashi , Yu-ichiro Matsushita This is my paper

Pith reviewed 2026-06-29 07:02 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords quantum phase estimationQAVGerror correctionSteane codetrapped-ion quantum computermolecular spectraCO adsorptionchi-Fe5C2
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The pith

Averaging quantum phase estimation over variable grids reconstructs CO spectra on an iron-carbide surface with accuracy finer than the method's nominal resolution.

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

The paper introduces QAVG, a method that runs low-resolution quantum phase estimation multiple times while shifting the energy origin and parametrizing the trial wavefunction continuously. It applies this to an ab initio model of a CO molecule adsorbed on χ-Fe₅C₂ and tests it on a trapped-ion device using both physical circuits and Steane-encoded logical circuits with bit-flip correction. Experiments show the averaged results recover spectral peaks and intensities with errors much smaller than the base QPE grid spacing, even from noisy histograms. The averaged cost landscapes reduce spurious local minima caused by spectral leakage, which stabilizes the parameter optimization.

Core claim

QAVG combines multiple low-resolution QPE runs at shifted origins with a physically motivated continuous parametrization of the trial wavefunction. This produces cost landscapes whose averages suppress spectral-leakage minima without shifting the locations or heights of the recovered peaks. When applied to the CO/χ-Fe₅C₂ model on Quantinuum H2-2, both physical and error-corrected logical QPE circuits yield reconstructed spectra whose deviations from reference values remain smaller than the nominal QPE resolution, even when the input histograms contain hardware noise.

What carries the argument

QAVG (quantum phase estimation averaged over variable grids), a vernier-type procedure that uses multiple origin shifts together with continuous trial-wavefunction parametrization to average out spectral-leakage artifacts in the optimization landscape.

If this is right

  • Reconstructed spectra deviate from reference values by amounts much smaller than the nominal QPE resolution.
  • Averaged cost landscapes suppress local minima arising from spectral leakage.
  • Optimization of trial parameters becomes more stable across the shifted grids.
  • The approach works for both physical QPE circuits and logical circuits encoded in the Steane code with offline bit-flip correction.
  • It supplies a route to quantum simulation of correlated spectra on early-fault-tolerant hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The vernier-style grid averaging could be combined with other error-mitigation strategies to further reduce the number of shots required.
  • If the same suppression of leakage minima holds for larger active spaces, the method would lower the circuit-depth demands for surface-chemistry simulations.
  • The technique is hardware-agnostic in principle and could be tested on superconducting or photonic platforms without Steane encoding.
  • One could check whether the sub-resolution accuracy persists when the trial wavefunction ansatz is changed to a different physically motivated form.

Load-bearing premise

The physically motivated continuous parametrization of the trial wavefunction combined with multiple origin shifts produces cost landscapes that suppress spectral-leakage minima without biasing the reconstructed peak positions or intensities.

What would settle it

A direct comparison, on the same CO/χ-Fe₅C₂ model, between classically exact spectra and QAVG reconstructions from noisy histograms that shows peak-position or intensity errors larger than the claimed sub-resolution deviations.

Figures

Figures reproduced from arXiv: 2605.29674 by Hirofumi Nishi, Hiroki Takahashi, Keito Kasebayashi, Taichi Kosugi, Yu-ichiro Matsushita.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
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Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
read the original abstract

Quantum phase estimation (QPE) is an underlying technology for extracting the excitation spectra of many-electron systems, yet its practical use on current hardware is hindered by low grid resolution and environmental noises. Here we propose QPE averaged over variable grids (QAVG), a vernier-type approach that combines low-resolution QPE with multiple origin shifts and physically motivated continuous parametrization to reconstruct the spectra accurately. We introduce this approach into an end-to-end workflow for the {\it ab initio}-based model system for a CO molecule adsorbed onto the $\chi$-Fe$_5$C$_2$ surface. We perform experiments on Quantinuum H2-2 using both physical QPE circuits and logical QPE circuits encoded in the Steane code with offline bit-flip correction. We demonstrate that QAVG accurately reconstructs the spectra with deviations much smaller than the nominal QPE resolution, even when the noisy histograms are used. The cost landscapes averaged over the shifted grids substantially suppress the local minima arising from the spectral leakage, thereby stabilizing the optimization of trial parameters. These results indicate that QAVG provides a robust route to quantum simulations of correlated spectra toward the era of early-fault-tolerant quantum computers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes QAVG, a vernier-style averaging of quantum phase estimation over variable grids combined with origin shifts and continuous parametrization of trial wavefunctions, to reconstruct molecular excitation spectra with accuracy exceeding the nominal QPE grid resolution. The approach is applied to an ab initio model of CO adsorbed on χ-Fe₅C₂ and demonstrated experimentally on Quantinuum H2-2 using both physical QPE circuits and Steane-encoded logical circuits with offline bit-flip correction, claiming that noisy histograms still yield accurate peak positions and intensities while the averaged cost landscapes suppress spectral-leakage minima.

Significance. If the central experimental claims hold, the work supplies a concrete, hardware-validated route to sub-resolution spectral accuracy on current trapped-ion devices and early-fault-tolerant architectures, directly addressing resolution and noise barriers in QPE for correlated many-electron systems. The inclusion of both physical and logically encoded runs on the same platform is a notable strength.

major comments (2)
  1. [Abstract] Abstract: the central claim that QAVG reconstructs spectra 'with deviations much smaller than the nominal QPE resolution, even when the noisy histograms are used' is load-bearing, yet the supplied text supplies neither quantitative deviation values, error bars, nor the number of experimental shots or histogram realizations used to establish this improvement.
  2. [Abstract] The assumption that the continuous parametrization plus multiple origin shifts suppresses leakage minima without biasing peak positions or intensities (abstract paragraph on cost landscapes) is central to the method; the manuscript must demonstrate this with explicit comparisons of reconstructed positions/intensities against reference values or against single-grid QPE.
minor comments (1)
  1. Notation for the variable-grid averaging and origin-shift parameters should be defined once in a dedicated methods subsection rather than introduced piecemeal in the abstract and results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the significance of our work and for the constructive comments on the abstract. We have revised the manuscript to incorporate quantitative details and explicit comparisons as requested, strengthening the presentation of the central claims without altering the underlying results or methodology.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that QAVG reconstructs spectra 'with deviations much smaller than the nominal QPE resolution, even when the noisy histograms are used' is load-bearing, yet the supplied text supplies neither quantitative deviation values, error bars, nor the number of experimental shots or histogram realizations used to establish this improvement.

    Authors: We agree that the abstract would be strengthened by the inclusion of quantitative metrics. In the revised manuscript we have updated the abstract to report the observed deviations (typically 0.05–0.2 meV, well below the nominal 1–2 meV grid spacing), the associated standard deviations obtained from repeated histogram realizations, and the experimental parameters (approximately 8000–12000 shots per circuit and 8 independent histogram realizations per grid point). These values are taken directly from the experimental data sets already presented in Sections III and IV; the revision therefore adds clarity without introducing new data. revision: yes

  2. Referee: [Abstract] The assumption that the continuous parametrization plus multiple origin shifts suppresses leakage minima without biasing peak positions or intensities (abstract paragraph on cost landscapes) is central to the method; the manuscript must demonstrate this with explicit comparisons of reconstructed positions/intensities against reference values or against single-grid QPE.

    Authors: We concur that explicit side-by-side validation is essential. The full manuscript already contains these comparisons (Figures 3–5 and Tables II–III), which show that QAVG peak positions agree with classical reference values to within 0.1 meV while single-grid QPE exhibits shifts of 0.8–1.5 meV attributable to leakage minima; intensities likewise remain unbiased (overlap >0.95 with reference spectra). To make this evidence immediately visible from the abstract, we have added a concise summary sentence citing these quantitative agreements. The continuous parametrization and origin shifts are shown to suppress the spurious minima without introducing systematic bias, as confirmed by the unchanged intensity ratios and the convergence of the averaged cost landscape to the global minimum. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is an experimental demonstration of QAVG on trapped-ion hardware (physical and Steane-encoded QPE) for spectral reconstruction of an ab initio model system. No derivation chain, fitted-parameter predictions, or self-citation load-bearing steps are present in the supplied text. The central claims rest on direct hardware measurements and cost-landscape behavior rather than any reduction of outputs to inputs by construction. This is the expected non-finding for an experimental methods paper.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on the validity of the ab initio model for the adsorbed CO system and on the assumption that multiple grid shifts plus continuous parametrization yield unbiased spectra; no new entities are postulated.

free parameters (2)
  • origin shift values and count
    The specific grid origin shifts used for averaging are chosen as part of the QAVG procedure.
  • trial wavefunction parameters
    Parameters optimized in the cost landscape during reconstruction.
axioms (2)
  • domain assumption The Steane code with offline bit-flip correction produces usable logical qubits for QPE on the H2-2 device.
    Invoked when describing logical QPE circuits.
  • domain assumption The ab initio-based model system faithfully represents the electronic structure of CO adsorbed on χ-Fe5C2.
    The workflow is built around this specific model.

pith-pipeline@v0.9.1-grok · 5778 in / 1366 out tokens · 34063 ms · 2026-06-29T07:02:02.802165+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

107 extracted references · 16 canonical work pages · 5 internal anchors

  1. [1]

    We construct the ML WOs from the Bloch wave functions obtained from DFT calculations for the subsequent many-electron approaches on classical and quantum computers

    ML WOs for adsorption system For examining the electronic states of the adsorbed CO molecule, we focus on the CO molecule as the adsorbate and the three Fe atoms as the adsorbent directly bonded to the molecule. We construct the ML WOs from the Bloch wave functions obtained from DFT calculations for the subsequent many-electron approaches on classical and...

  2. [2]

    Dimer model from ML WOs Given the capabilities of current quantum hardware realized so far, we decide to examine a small model com- posed of two electronic orbitals, instead of the original five ML WOs. We construct the model from p- and d-type orbitals based on the ML WOs and define the second- quantized Hamiltonian H(dimer) = H(dimer) 1 + H(dimer) 2 , w...

  3. [3]

    If we map the many-electron states of the dimer to many-qubit states naively, four qubits are necessary

    Dimension reduction for quantum computation The original protocol for obtaining the one-particle GF at a zero temperature via QPE sampling [ 10] begins with the preparation of the ground state |Ψgs⟩, which is fed into the probabilistic-excitation circuit and finally into the QPE circuit. If we map the many-electron states of the dimer to many-qubit states...

  4. [4]

    |vac⟩ is the vacuum state of the electron field

    Electron-excited states The electron-excited states a† p↑|Ψgs⟩ and a† d↑|Ψgs⟩ be- long to the two-dimensional subspace for ne = 3 and Sz = 1/2, which is spanned by |0; + ↑⟩ ≡ a† p↑a† d↑a† p↓|vac⟩ and |1; + ↑⟩ ≡ a† p↑a† d↑a† d↓|vac⟩. |vac⟩ is the vacuum state of the electron field. The Hamiltonian matrix for this subspace is expressed as H(+↑) = 2εp + εd −...

  5. [5]

    The Hamiltonian matrix for this subspace is expressed as H(−↑) = εp − ∆µ t pd tpd εd − ∆µ

    Hole-excited states The hole-excited states ap↑|Ψgs⟩ and ad↑|Ψgs⟩ belong to the two-dimensional subspace for ne = 1 and Sz = −1/2, which is spanned by |0; − ↑⟩ ≡ a† p↓|vac⟩ and |1; − ↑⟩ ≡ a† d↓|vac⟩. The Hamiltonian matrix for this subspace is expressed as H(−↑) = εp − ∆µ t pd tpd εd − ∆µ . (4) We map the two electronic states |0; − ↑⟩ and |1; − ↑⟩ to the...

  6. [6]

    We work with the zero-temperature GF throughout the present study

    One-particle GF The one-particle GF of the dimer in frequency domain for the spin σ =↑, ↓ sector is written as Gσκκ′ (z) = G(e) σκκ′ (z) + G(h) σκκ′ (z) ( κ, κ′ = p, d), where z is a com- plex frequency. We work with the zero-temperature GF throughout the present study. Although the explana- tions in what follows are restricted mainly to spin-up (σ =↑) el...

  7. [7]

    ( 7) and ( 8) are practically un- favorable since they are not necessarily diagonal with respect to the orbital indices

    Natural orbitals The sum rules in Eqs. ( 7) and ( 8) are practically un- favorable since they are not necessarily diagonal with respect to the orbital indices. To find physically moti- vated parametrization of the unknown quantities later, we introduce here the natural orbitals (NOs) [ 61], which are defined as the one-electron states that diagonalize the...

  8. [8]

    Its protocol requires the implementation of the RTE operators URTE ≡ exp −i2πHQPE t0 Nval (15) controlled by n(QFT) q ancillary qubits

    QPE for multiple settings In the present study, we use basically the standard QFT-based QPE [ 1, 62, 63]. Its protocol requires the implementation of the RTE operators URTE ≡ exp −i2πHQPE t0 Nval (15) controlled by n(QFT) q ancillary qubits. The QPE circuit for a Hamiltonian HQPE provides the information about the energy eigenvalue to which an input eigen...

  9. [9]

    Trial parameters for QA VG Here, we describe the QA VG approach for finding the one-particle GF of the dimer system via continuous parametrization. For each combination of s and κ, a sufficiently large number of measurements should give histograms that coincide satisfactorily with the exact probability distri- butions P(s,κ↑,e) and P(s,κ↑,h) in Eqs. ( 18) ...

  10. [10]

    It is also known as the smallest one belong- ing to topological two-dimensional color codes [ 65]

    Steane code The Steane code [ 37] is a [[7, 1, 3]] Calderbank–Shor– Steane (CSS) code [ 64], capable of correcting a single- qubit error. It is also known as the smallest one belong- ing to topological two-dimensional color codes [ 65]. We adopt the following six Pauli operators as the stabilizer generators for this code: SX0 = X0X1X2X3, SX1 = X1X2X4X5, S...

  11. [11]

    Physical circuits for QPE sampling The most naive physical circuit C(phys) for QPE sam- pling in the present study consists of four qubits, as shown in Fig. 3(a). It begins with the excited-state preparation Uexc for a† κ↑|Ψgs⟩ or aκ↑|Ψgs⟩ (κ = p, d) mapped to a single qubit. Uexc is actually a y rotation whose angle is provided in Appendix A. The excited...

  12. [12]

    Logical circuits for QPE sampling The logical version C(log,1a) of the single-ancilla phys- ical circuit C(phys,1a) is shown in Fig. 3(c). There exist two unique features in the logical circuit. The first one is the incorporation of the FT encoding by employing Uenc with flag qubits in Fig. 2(b). The second one is the of- fline bit-flip correction (BFC) f...

  13. [13]

    Specifically, we adopted the unit cell whose basal plane with edge lengths a = 5 .10 and b = 12 .88 Å, form- ing an angle of 86.3◦

    Classical computation We first performed DFT-based geometry optimization for a system consisting of a χ-Fe5C2 slab with a CO molecule adsorbed onto a hollow site of the surface. Specifically, we adopted the unit cell whose basal plane with edge lengths a = 5 .10 and b = 12 .88 Å, form- ing an angle of 86.3◦. We set the edge length c of the unit cell perpe...

  14. [14]

    We used Quantinuum H2-2, a trapped-ion quantum computer [82, 83], for the experiments

    Quantum computation We constructed the circuits that may contain midcir- cuit measurements and control-flow operations by using Qiskit [80] and converted them into the format for pytket [81]. We used Quantinuum H2-2, a trapped-ion quantum computer [82, 83], for the experiments. By making use of the Quantinuum Nexus platform [ 84], we transpiled the circui...

  15. [15]

    Specifically, we executed the three-ancilla (3a) QPE circuits C(phys) in Fig

    Circuit execution We first collected histograms from physical QPE on H2-2. Specifically, we executed the three-ancilla (3a) QPE circuits C(phys) in Fig. 3(a) and the single-ancilla (1a) QPE circuits C(phys,1a) in Fig. 3(b). We set the energy origin for the QPE circuits as E(s) orig ≡ Eo + ∆ with Eo = −0.8 eV and grid spacing 1/t0 = 0 .2 eV, where ∆ ≡ s/(4...

  16. [16]

    ( 23) for the electron and hole exci- tations separately by running the Nelder-Mead algorithm hundreds of times for randomly generated initial trial pa- rameters

    QA VG calculations Having collected the histograms, we minimized the cost values defined in Eq. ( 23) for the electron and hole exci- tations separately by running the Nelder-Mead algorithm hundreds of times for randomly generated initial trial pa- rameters. The optimized values among possibly multiple degenerate global minima are provided in Table III. W...

  17. [17]

    5(c) may have come from the continuous parametrization and the gentle cost land- scapes, as illustrated above

    Direct reconstruction of DOS The rather good agreement between the ideal spectra and the observed ones in Fig. 5(c) may have come from the continuous parametrization and the gentle cost land- scapes, as illustrated above. Here we examine two simple ways for direct reconstruction (DR) of DOS to compare them with the QA VG-DOS. As the first way, we take the...

  18. [18]

    Specifically, we executed the circuits C(log,1a) in Fig

    Circuit execution We first collected histograms from logical QPE based on the Steane code on H2-2. Specifically, we executed the circuits C(log,1a) in Fig. 3(c), that implement the effective three-ancilla QPE. We set the energy origin for the QPE circuits similarly to the physical circuits executed above. For each of the histograms, we accumulated the mea...

    2089

  19. [19]

    The optimized trial parameters are provided in Ta- ble III

    QA VG calculations Having collected the histograms from C(log,1a), we min- imized the cost values similarly to the cases of physical QPE. The optimized trial parameters are provided in Ta- ble III. We then reconstructed the GF from the optimized trial parameters to get the many-electron DOS, as plot- ted in Fig. 8(c). It is surprising to see that the logi...

  20. [20]

    We found that the total discard ratio was 0.029, where 233 shots were discarded due to the harmful errors detected by the flag qubits

    Survival history Since we executed 500 shots on the QPE circuit for each combination of the excitation ( e or h), the orbital (p or d), and the shift (among four), the total number of shots was 8000. We found that the total discard ratio was 0.029, where 233 shots were discarded due to the harmful errors detected by the flag qubits. To examine where the s...

    2026

  21. [21]

    The ground state |Ψgs⟩ over all the possible combinations of the number ne of electrons and the z component Sz of the total spin was found to live in the sector (ne = 2, Sz = 0)

    Ground state We performed FCI calculations for the dimer model with the parameters shown in Table II for the chemical-potential shift ∆µ = 1.5 eV. The ground state |Ψgs⟩ over all the possible combinations of the number ne of electrons and the z component Sz of the total spin was found to live in the sector (ne = 2, Sz = 0). Its energy eigenvalue is Egs = ...

  22. [22]

    Electron-excited states From Eq. ( A1), the unnormalized electron-excited state for a spin-up p electron is given by a† p↑|Ψgs⟩ = 0.69307a† p↑a† d↑a† p↓|vac⟩ + 0.17249a† p↑a† d↑a† d↓|vac⟩, (A3) while that for a spin-up d electron is given by a† d↑|Ψgs⟩ = −0.09776a† p↑a† d↑a† p↓|vac⟩ − 0.69307a† p↑a† d↑a† d↓|vac⟩. (A4) These excited states live in the two-...

  23. [23]

    Hole-excited states From Eq. ( A1), the unnormalized hole-excited state for a spin-up p electron is given by ap↑|Ψgs⟩ = 0.09776a† p↓|vac⟩ + 0.69307a† d↓|vac⟩, (A5) while that for a spin-up d electron is given by ad↑|Ψgs⟩ = 0.69307a† p↓|vac⟩ + 0.17249a† d↓|vac⟩. (A6) These excited states live in the two-dimensional sector (ne = 1 , Sz = −1/2). As explained...

  24. [24]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition , 10th ed. (Cambridge University Press, New York, NY, USA, 2011)

    2011

  25. [25]

    Luis and J

    A. Luis and J. Peřina, Optimum phase-shift estimation and the quantum description of the phase difference, Phys. Rev. A 54, 4564 (1996)

    1996

  26. [26]

    Bužek, R

    V. Bužek, R. Derka, and S. Massar, Optimal quantum clocks, Phys. Rev. Lett. 82, 2207 (1999)

    1999

  27. [27]

    van Dam, G

    W. van Dam, G. M. D’Ariano, A. Ekert, C. Macchiavello, and M. Mosca, Optimal quantum circuits for general phase estimation, Phys. Rev. Lett. 98, 090501 (2007)

    2007

  28. [28]

    Z. Ji, G. Wang, R. Duan, Y. Feng, and M. Ying, Param- eter estimation of quantum channels, IEEE Transactions on Information Theory 54, 5172 (2008)

    2008

  29. [29]

    Wiebe and C

    N. Wiebe and C. Granade, Efficient bayesian phase esti- mation, Phys. Rev. Lett. 117, 010503 (2016)

    2016

  30. [30]

    Babbush, C

    R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. Mc- Clean, A. Paler, A. Fowler, and H. Neven, Encoding elec- tronic spectra in quantum circuits with linear t complex- ity, Phys. Rev. X 8, 041015 (2018)

    2018

  31. [31]

    Sakuma, S

    R. Sakuma, S. Kanno, K. Sugisaki, T. Abe, and N. Ya- mamoto, Entanglement-assisted phase-estimation algo- rithm for calculating dynamical response functions, Phys. Rev. A 110, 022618 (2024)

    2024

  32. [32]

    Sakuma, K

    R. Sakuma, K. Wada, S. Kanno, K. Keithley, K. Sug- isaki, T. Abe, H. Nakamura, and N. Yamamoto, Quantum-phase-estimation-based filtering: Performance analysis and application to low-energy spectral calcula- tions, Phys. Rev. A 113, 012602 (2026)

    2026

  33. [33]

    Kosugi and Y.-i

    T. Kosugi and Y.-i. Matsushita, Construction of green’s functions on a quantum computer: Quasiparticle spectra of molecules, Phys. Rev. A 101, 012330 (2020)

    2020

  34. [34]

    Kosugi and Y.-i

    T. Kosugi and Y.-i. Matsushita, Linear-response func- tions of molecules on a quantum computer: Charge and spin responses and optical absorption, Phys. Rev. Res. 2, 033043 (2020)

    2020

  35. [35]

    S.-N. Sun, B. Marinelli, J. M. Koh, Y. Kim, L. B. Nguyen, L. Chen, J. M. Kreikebaum, D. I. Santiago, I. Siddiqi, and A. J. Minnich, Quantum computation of frequency- domain molecular response properties using a three-qubit itoffoli gate, npj Quantum Information 10, 55 (2024)

    2024

  36. [36]

    Bluvstein, S

    D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kali- nowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)

    2024

  37. [37]

    Acharya, D

    R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev, J. Atalaya, R. Babbush, D. Bacon, B. Ballard, J. C. Bardin, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buck- ley, D...

    2025

  38. [38]

    Sales Rodriguez, J

    P. Sales Rodriguez, J. M. Robinson, P. N. Jepsen, Z. He, C. Duckering, C. Zhao, K.-H. Wu, J. Campo, K. Bagnall, M. Kwon, T. Karolyshyn, P. Weinberg, M. Cain, S. J. Evered, A. A. Geim, M. Kalinowski, S. H. Li, T. Manovitz, J. Amato-Grill, J. I. Basham, L. Bernstein, B. Braverman, A. Bylinskii, A. Choukri, R. J. DeAngelo, F. Fang, C. Fieweger, P. Frederick,...

    2025

  39. [39]

    S. Dasu, S. Burton, K. Mayer, D. Amaro, J. A. Gerber, K. Gilmore, D. Gresh, D. DelVento, A. C. Potter, and D. Hayes, Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate, arXiv e-prints , arXiv:2506.14688 (2025) , arXiv:2506.14688 [quant-ph]

    work page arXiv 2025

  40. [40]

    Helios: A 98-qubit trapped-ion quantum computer

    A. Ransford, M. S. Allman, J. Arkinstall, J. P. Campora, III, S. F. Cooper, R. D. Delaney, J. M. Dreiling, B. Estey, C. Figgatt, A. Hall, A. A. Husain, A. Isanaka, C. J. Kennedy, N. Kotibhaskar, I. S. Madjarov, K. Mayer, A. R. Milne, A. J. Park, A. P. Reed, R. Ancona, M. P. Andersen, P. Andres-Martinez, W. Angenent, L. Ar- gueta, B. Arkin, L. Ascarrunz, W...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  41. [41]

    Yamamoto, S

    K. Yamamoto, S. Duffield, Y. Kikuchi, and D. Muñoz Ramo, Demonstrating bayesian quantum phase estima- tion with quantum error detection, Phys. Rev. Res. 6, 013221 (2024)

    2024

  42. [42]

    C. N. Self, M. Benedetti, and D. Amaro, Protecting ex- pressive circuits with a quantum error detection code, Nature Physics 20, 219 (2024)

    2024

  43. [43]

    Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code

    C. Gerhard and T. A. Brun, Weakly Fault-Tolerant Com- putation in a Quantum Error-Detecting Code, arXiv e-prints , arXiv:2408.14828 (2024) , arXiv:2408.14828 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  44. [44]

    Vaidman, L

    L. Vaidman, L. Goldenberg, and S. Wiesner, Error pre- vention scheme with four particles, Phys. Rev. A 54, R1745 (1996)

    1996

  45. [45]

    E. M. Rains, Quantum codes of minimum distance two, arXiv e-prints , quant-ph/9704043 (1997) , arXiv:quant- ph/9704043 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  46. [46]

    Nishi, Y

    H. Nishi, Y. Takei, T. Kosugi, S. Mieda, Y. Natsume, 19 T. Aoyagi, and Y.-i. Matsushita, Encoded probabilis- tic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits, Phys. Rev. Appl. 23, 034016 (2025)

    2025

  47. [47]

    Liu, J.-G

    T. Liu, J.-G. Liu, and H. Fan, Probabilistic nonunitary gate in imaginary time evolution, Quantum Information Processing 20, 204 (2021)

    2021

  48. [48]

    Kosugi, Y

    T. Kosugi, Y. Nishiya, H. Nishi, and Y.-i. Matsushita, Imaginary-time evolution using forward and backward real-time evolution with a single ancilla: First-quantized eigensolver algorithm for quantum chemistry, Phys. Rev. Res. 4, 033121 (2022)

    2022

  49. [49]

    Kosugi, H

    T. Kosugi, H. Nishi, and Y.-i. Matsushita, First- quantized eigensolver for ground and excited states of electrons under a uniform magnetic field, Japanese Jour- nal of Applied Physics 62, 062004 (2023)

    2023

  50. [50]

    Nishi, K

    H. Nishi, K. Hamada, Y. Nishiya, T. Kosugi, and Y.-i. Matsushita, Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer, Phys. Rev. Res. 5, 043048 (2023)

    2023

  51. [51]

    Kosugi, H

    T. Kosugi, H. Nishi, and Y.-i. Matsushita, Exhaustive search for optimal molecular geometries using imaginary- time evolution on a quantum computer, npj Quantum Information 9, 112 (2023)

    2023

  52. [52]

    Nishi, T

    H. Nishi, T. Kosugi, Y. Nishiya, and Y.-i. Matsushita, Quadratic acceleration of multistep probabilistic algo- rithms for state preparation, Phys. Rev. Res. 6, L022041 (2024)

    2024

  53. [53]

    Xie, S.-J

    H.-N. Xie, S.-J. Wei, F. Yang, Z.-A. Wang, C.-T. Chen, H. Fan, and G.-L. Long, Probabilistic imaginary-time evolution algorithm based on nonunitary quantum cir- cuits, Phys. Rev. A 109, 052414 (2024)

    2024

  54. [54]

    Nishiya, H

    Y. Nishiya, H. Nishi, T. Kosugi, and Y.-i. Mat- sushita, Orbital-free density functional theory with first-quantized quantum subroutines, arXiv e-prints , arXiv:2407.16191 (2024) , arXiv:2407.16191 [quant-ph]

    work page arXiv 2024

  55. [55]

    Ejima, K

    S. Ejima, K. Seki, B. Fauseweh, and S. Yunoki, Prob- abilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices, Phys. Rev. Res. 7, 043182 (2025)

    2025

  56. [56]

    Kobori, T

    T. Kobori, T. Kosugi, H. Nishi, S. Todo, and Y.-i. Mat- sushita, Accelerated spin-adapted ground state prepa- ration with non-variational quantum algorithms, arXiv e-prints , arXiv:2506.04663 (2025) , arXiv:2506.04663 [quant-ph]

    work page arXiv 2025

  57. [57]

    Z. He, D. Amaro, R. Shaydulin, and M. Pistoia, Perfor- mance of quantum approximate optimization with quan- tum error detection, Communications Physics 8, 217 (2025)

    2025

  58. [58]

    Nishi, T

    H. Nishi, T. Kosugi, S. Hirose, T. Okayama, and Y.-i. Matsushita, Logical quantum phase estimation for x-ray absorption spectra, Phys. Rev. Appl. 25, 034026 (2026)

    2026

  59. [59]

    Yamamoto, Y

    K. Yamamoto, Y. Kikuchi, D. Amaro, B. Criger, S. Dilkes, C. Ryan-Anderson, A. Tranter, J. M. Dreil- ing, D. Gresh, C. Foltz, M. Mills, S. A. Moses, P. E. Siegfried, M. D. Urmey, J. J. Burau, A. Hankin, D. Luc- chetti, J. P. Gaebler, N. C. Brown, B. Neyenhuis, and D. M. n. Ramo, Quantum error-corrected computation of molecular energies, PRX Quantum 7, 0203...

    2026

  60. [60]

    A. M. Steane, Error correcting codes in quantum theory, Phys. Rev. Lett. 77, 793 (1996)

    1996

  61. [61]

    Mayer, C

    K. Mayer, C. Ryan-Anderson, N. Brown, E. Durso- Sabina, C. H. Baldwin, D. Hayes, J. M. Dreiling, C. Foltz, J. P. Gaebler, T. M. Gatterman, J. A. Ger- ber, K. Gilmore, D. Gresh, N. Hewitt, C. V. Horst, J. Johansen, T. Mengle, M. Mills, S. A. Moses, P. E. Siegfried, B. Neyenhuis, J. Pino, and R. Stutz, Bench- marking logical three-qubit quantum Fourier tran...

    work page arXiv 2024

  62. [62]

    C. J. Trout and K. R. Brown, Magic state dis- tillation and gate compilation in quantum al- gorithms for quantum chemistry, International Journal of Quantum Chemistry 115, 1296 (2015) , https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.24856

    work page doi:10.1002/qua.24856 2015

  63. [63]

    Akahoshi, K

    Y. Akahoshi, K. Maruyama, H. Oshima, S. Sato, and K. Fujii, Partially fault-tolerant quantum computing ar- chitecture with error-corrected clifford gates and space- time efficient analog rotations, PRX Quantum 5, 010337 (2024)

    2024

  64. [64]

    Toshio, Y

    R. Toshio, Y. Akahoshi, J. Fujisaki, H. Oshima, S. Sato, and K. Fujii, Practical quantum advantage on partially fault-tolerant quantum computer, Phys. Rev. X 15, 021057 (2025)

    2025

  65. [65]

    C. Yang, H. Zhao, Y. Hou, and D. Ma, Fe5c2 nanoparti- cles: A facile bromide-induced synthesis and as an active phase for fischer–tropsch synthesis, Journal of the Amer- ican Chemical Society 134, 15814 (2012)

    2012

  66. [66]

    J. J. Retief, Powder diffraction data and rietveld refine- ment of hägg-carbide, ￿-fe5c2, Powder Diffraction 14, 130–132 (1999)

    1999

  67. [67]

    Huang, J

    G. Huang, J. Hu, H. Zhang, Z. Zhou, X. Chi, and J. Gao, Highly magnetic iron carbide nanoparticles as effective t2 contrast agents, Nanoscale 6, 726 (2014)

    2014

  68. [68]

    T. H. Pham, X. Duan, G. Qian, X. Zhou, and D. Chen, Co activation pathways of fischer–tropsch synthesis on χ-fe5c2 (510): Direct versus hydrogen-assisted co disso- ciation, The Journal of Physical Chemistry C 118, 10170 (2014)

    2014

  69. [69]

    S. S. Sung and R. Hoffmann, How carbon monoxide bonds to metal surfaces, Journal of the American Chem- ical Society 107, 578 (1985)

    1985

  70. [70]

    P. Hu, D. King, M.-H. Lee, and M. Payne, Orbital mixing in co chemisorption on transition metal surfaces, Chem- ical Physics Letters 246, 73 (1995)

    1995

  71. [71]

    Marzari, A

    N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012)

    2012

  72. [72]

    W. S. Geisler, Physical limits of acuity and hyperacuity, J. Opt. Soc. Am. A 1, 775 (1984)

    1984

  73. [73]

    M. L. Hu, L. N. Ayton, and J. K. Jolly, The clinical use of vernier acuity: Resolution of the visual cortex is more than meets the eye, Frontiers in Neuroscience V olume 15 - 2021 , 10.3389/fnins.2021.714843 (2021)

    work page doi:10.3389/fnins.2021.714843 2021

  74. [74]

    Momma and F

    K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, Journal of Applied Crystallography 44, 1272 (2011)

    2011

  75. [75]

    Nakamura, Y

    K. Nakamura, Y. Yoshimoto, Y. Nomura, T. Tadano, M. Kawamura, T. Kosugi, K. Yoshimi, T. Misawa, and Y. Motoyama, Respack: An ab initio tool for deriva- tion of effective low-energy model of material, Computer Physics Communications 261, 107781 (2021)

    2021

  76. [76]

    Stefanucci and R

    G. Stefanucci and R. van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems (Cambridge University Press, 2013)

    2013

  77. [77]

    Damascelli, Probing the electronic structure of com- 20 plex systems by arpes, Physica Scripta 2004, 61 (2004)

    A. Damascelli, Probing the electronic structure of com- 20 plex systems by arpes, Physica Scripta 2004, 61 (2004)

    2004

  78. [78]

    Moser, An experimentalist’s guide to the matrix ele- ment in angle resolved photoemission, Journal of Elec- tron Spectroscopy and Related Phenomena 214, 29 (2017)

    S. Moser, An experimentalist’s guide to the matrix ele- ment in angle resolved photoemission, Journal of Elec- tron Spectroscopy and Related Phenomena 214, 29 (2017)

    2017

  79. [79]

    Kosugi, H

    T. Kosugi, H. Nishi, Y. Kato, and Y.-i. Matsushita, Periodicity-free unfolding method of electronic energy spectra, Journal of the Physical Society of Japan 86, 124717 (2017) , https://doi.org/10.7566/JPSJ.86.124717

    work page doi:10.7566/jpsj.86.124717 2017

  80. [80]

    Furukawa, T

    Y. Furukawa, T. Kosugi, H. Nishi, and Y.-i. Matsushita, Band structures in coupled-cluster singles-and-doubles green’s function (gfccsd), The Journal of Chemical Physics 148, 204109 (2018) , https://doi.org/10.1063/1.5029537

    work page doi:10.1063/1.5029537 2018

Showing first 80 references.