Pith. sign in

REVIEW 3 major objections 4 minor 51 references

Accelerating Fermionic System Simulation on Quantum Computers

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read Molecular Hamiltonians' $O(N^4)$ Pauli terms can be packed into $O(N^2)$ commuting groups, cutting simulation cost by $N^3$.

desk verdict Genuinely new Med/Bia Pauli grouping with an O(N^2) group count, but the published partition omits the two-body XX/YY strings, so the central claim is not yet supported. read the letter →

arxiv 2505.08206 v1 pith:6HLL3WGR submitted 2025-05-13 quant-ph physics.chem-ph

Qing-Song Li , Jiaxuan Zhang , Huan-Yu Liu , Qingchun Wang , Yu-Chun Wu , Guo-Ping Guo This is my paper · ORCID
classification quant-phphysics.chem-ph
keywords fermionicHamiltoniansimulationJordan-WignertransformationPaulistringgroupingcommutingoperatorgroupsTrotterevolutiondepthmeasurementreductionquantumchemistryvariationaleigensolver
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

The paper claims that the roughly $O(N^4)$ Pauli terms in a molecular Hamiltonian can be partitioned into only $O(N^2)$ families of mutually commuting operators, using the structure the Jordan-Wigner transform imposes. If true, one Trotter step of Hamiltonian evolution would have circuit depth $O(N^3\log N)$ rather than $O(N^4\log N)$, and estimating the energy would need $O(N^2)$ measurement circuits rather than $O(N^3)$ or $O(N^4)$. The grouping is done by direct rules based on Pauli-string type and two index invariants, so it avoids building the expensive commutativity graph. Because the number of groups and the shots per group both shrink, the total time for evolution plus measurement falls by a factor of $N^3$.

What carries the argument

The load-bearing object is the taxonomy of Jordan-Wigner Pauli strings into sixteen types, together with the grouping invariants for four-body strings and the Clifford unitary $U_n = \prod_i (T_i+\sigma_i)/\sqrt{2}$, which rotates an arbitrary fully-commuting family into a qubit-wise commuting family. That rotation lets parity be copied to rotation qubits so all phase rotations in a family are applied in parallel, and it also underlies the simultaneous measurement scheme. The Med and Bia invariants are what make the group count quadratic in $N$ rather than cubic: fixing the symmetry axis and the bias of the two substrings forces enough overlap among the Pauli supports that every pair in a family commutes.

What would settle it

Take a molecular Hamiltonian at, say, $N=50$ orbitals, generate all Pauli strings under the Jordan-Wigner transform, run the paper's grouping rule, and check every pair within each output group for commutation; a single non-commuting pair, or a term that the rule fails to assign, would refute the $O(N^2)$ claim. A second check is to compute a minimum clique cover of the commutativity graph for small molecules and compare the clique number with the number of groups produced; if the minimum exceeds $25N^2+1$, the bound is wrong.

Watch

Extended reading notes

Core claim

Under the Jordan-Wigner transformation, every term of a molecular Hamiltonian becomes one of sixteen Pauli-string types. The paper's central claim is that these strings can be assigned, by type and by two index invariants ($\mathrm{Med}=(j+k)/2$ and $\mathrm{Bia}=(l-k)-(j-i)$, with a second pair $\mathrm{Med}_1=(i+j)/2$, $\mathrm{Med}_2=(k+l)/2$ for the crossed types), to eight families $G_1$ through $G_8$, so that each family contains only pairwise-commuting strings and the total number of families is $O(N^2)$. On top of this grouping, the paper constructs a parallel evolution circuit using parity and rotation ancillas: one Trotter step has depth $O(N^3\log N)$ instead of $O(N^4\log N)$, and simultaneous measurement of each commuting family brings the number of measurement circuits down to $O(N^2)$. Numerical tests on molecules up to 48 qubits and on alkanes up to $C_9H_{20}$ show group counts scaling as $O(N^{2.16})$.

Load-bearing premise

The argument depends on the assertion that the eight families $G_1$ through $G_8$ cover every Pauli string a molecular Hamiltonian can produce under the Jordan-Wigner transform and that every pair inside each family commutes; the paper proves the commutation in detail only for $G_8$ and states that the other families follow along the same lines, while Algorithm 2 has no explicit branch for the two-body XX and YY types.

Editorial extensions

If this is right

  • A single Trotter step of a molecular Hamiltonian can be executed in depth $O(N^3\log N)$, an $N$-fold reduction over the standard $O(N^4\log N)$ per-step depth.
  • Energy estimates require $O(N^2)$ measurement circuits rather than $O(N^3)$ for the best prior grouping schemes or $O(N^4)$ for term-by-term measurement.
  • Total runtime for Hamiltonian evolution plus measurement drops by a factor of $N^3$, which is the paper's headline speedup.
  • Measuring a whole commuting group needs fewer shots than measuring one term alone, because the group's total variance is smaller.
  • In the near-term regime the scheme degrades to a qubit-wise-commuting grouping with $O(N^3)$ groups and only shallow auxiliary circuits, still beating the $O(N^4)$ groups of other QWC schemes.

Reading between the lines

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

  • The paper does not test the grouping on fermion-to-qubit mappings other than Jordan-Wigner, but its own Clifford-conjugation argument suggests the same $O(N^2)$ group count would transfer to any mapping related by a Clifford circuit; a full proof there would extend the result without redoing the JW analysis.
  • Because the appendix proves pairwise commutation only for $G_8$ and says the other families follow similarly, a complete proof for $G_3$ through $G_7$ would remove the largest gap in the central claim.
  • The observed group-variance reduction suggests a natural follow-up: adaptively distributing shots across groups by their variances could lower the total number of circuit executions below the equal-shot estimate, though the paper does not analyze that allocation.
  • For fault-tolerant operation, the $O(N^2)$ auxiliary parity and rotation qubits may dominate physical resources before the depth savings matter; whether that trade-off is favorable in practice is not addressed by the paper.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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. The manuscript proposes a deterministic grouping of the Pauli terms obtained from the Jordan-Wigner transform of a molecular Hamiltonian. It defines eight families of groups, G1-G8, and claims that the O(N^4) Hamiltonian terms can be partitioned into O(N^2) mutually commuting groups. On this basis it gives a parallel Trotter evolution circuit with per-step depth O(N^3 log N) and a measurement scheme requiring O(N^2) circuits, and it reports numerical counts of terms and groups for small molecules and for a series of alkanes.

Significance. If the grouping theorem were fully established, the paper would provide a genuinely better asymptotic construction than graph-based clique-cover methods, reducing the number of groups from O(N^3) to O(N^2) with classical preprocessing cost O(N^4). The authors deserve credit for deriving the group-count scaling analytically from the group definitions rather than from fitted parameters, and for presenting the numerical data as observations rather than as input to the claimed scaling. The overall idea is appealing and the identified gaps appear locally repairable, but the completeness of the partition and the commutativity of the groups are not yet established as written.

major comments (3)
  1. [Sec. III, Eq. (11), Table I, Algorithm 2] The partition into G1-G8 is incomplete. The JW image of a_i^dagger a_j for i<j includes the strings X_i Z_{i+1}...Z_{j-1} X_j and Y_i Z_{i+1}...Z_{j-1} Y_j, listed as the XX and YY types in Table I. However, the group G2(a,b) in Eq. (11) contains only strings of the forms Z_i X_a X_b, X_a Z_j X_b, and X_a X_b Z_k (together with their Y counterparts), and never a plain X_a X_b or Y_a Y_b. Algorithm 2 confirms the omission: its type dispatch covers I/Z/ZZ, ZXX/ZYY/XZX/YZY/XXZ/YYZ, XXXX/YYYY/XXYY/YYXX, and XYYX/YXXY, with no branch for the two-body "XX" or "YY" types, so such terms are not inserted into any group. Since off-diagonal one-body integrals are generically nonzero in molecular Hamiltonians, real Hamiltonians contain terms outside the claimed partition. The asymptotic count may survive a repair (for instance by adding plain X_a X_b and Y_a Y_b to G2(a,b)), but as written the central claim that all O(N^4) terms are partitioned into O(N^2) groups is not supported.
  2. [Appendix A] The commutativity proof is only given for G8; the text states that for the other groups "the proof follows a similar approach." This is not sufficient. The G3-G6 families are grouped by the nontrivial Med/Bia conditions of Eq. (12), and G7 uses the Med1/Med2 conditions of Eq. (15); pairwise commutation within these families is not immediate and needs an explicit algebraic argument or an exhaustive machine-checked verification for small N. Since the parallel evolution and simultaneous measurement protocols require every group to be fully commuting, this proof gap is load-bearing. The sketched case analysis for G8 is also informal and should be replaced with a complete argument covering all index orderings.
  3. [Algorithm 2] Algorithm 2 does not implement the grouping rules as defined in the main text. Equation (12) defines Bia = (l-k)-(j-i), but line 15 of Algorithm 2 computes index2 = (l-k)-(j-l), which is a different quantity. The comment on the same line also says that "j and k are the indices of the third and fourth Pauli X (Y) operators," which conflicts with the notation X_i X_j X_k X_l in Table I. These discrepancies must be corrected for the algorithm to reproduce the theoretical groups.
minor comments (4)
  1. [Throughout] There are several typographical errors that should be cleaned up: "workss" in the introduction, "Hamitonian" in Algorithm 2, "correspongding" in Sec. III, and "tt is easy" in Appendix A.
  2. [Sec. III, after Eq. (12)] The range for Bia is stated as [4-N, N-4] "assuming N <= 4"; this should presumably be N >= 4, since the range is empty for N < 4.
  3. [Sec. III, after Table I] The abbreviated notation "\Z_i X_a X_b" is introduced informally; the paper should state explicitly, for each abbreviated form, which qubits carry the omitted consecutive Z operators, especially for the XZX and YZY types where the omitted Z string contains a gap.
  4. [Sec. III, paragraph on other fermion-to-qubit mappings] The claim that "using different mappings does not affect our grouping results" is too strong as stated. Pairwise commutation is indeed basis-independent, but the actual Pauli terms change under the Bravyi-Kitaev transformation, so the grouping is not literally identical; the paper should clarify that the JW grouping is used as a template for the BK grouping.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the O(N^2) grouping bound is derived from the group definitions and counting, not from fitted data or self-citation.

full rationale

The paper's central scaling claims are analytic. Section III defines the groups G1 through G8 in Eqs. (10)-(16), and the O(N^2) group count is obtained by counting possible values of the index parameters: G1 contributes one group, G2 contributes fewer than N^2, G3-G6 contribute fewer than 16N^2, and G7-G8 contribute fewer than 8N^2. No fitted parameter enters this counting. The numerical fits in Section VI, such as the fit giving O(N^2.81) for small molecules and O(N^2.16) for alkanes, are empirical observations only; the text explicitly distinguishes them from the theoretical guarantee of O(N^2), so the fits are not used to define or justify the claimed scaling. The unitary transformation U_n used for simultaneous evolution and measurement is taken from Bravyi et al. [51], an external independent construction, not from the authors' own prior results. The self-citations that do appear, namely [39] (PyChemiQ, used only to obtain Hamiltonians) and [48] (a background fermion-to-qubit mapping reference), are not load-bearing inputs to the derivation. The manuscript does contain completeness gaps, but they are not circularity: Appendix A explicitly proves commutativity only for G8 and asserts that other groups follow similarly, and Algorithm 2 has no branch for plain XX and YY two-body Pauli strings even though Section III lists those as products of the Jordan-Wigner transform. These omissions would undermine the completeness of the claimed partition if unaddressed, but they do not make any prediction reduce to its own input by construction. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are used in the central analytic claims. The numerical fits (2.81 and 2.16 exponents) are empirical illustrations and are not used to derive the O(N^2) bound. The axioms are the completeness of the 16-type classification, the pairwise commutation of the constructed groups, and the assumption that the omitted XX/YY terms can be grouped at O(N^2) cost.

assumptions (4)
  • domain assumption The 16-type classification in Table I is complete for molecular Hamiltonians under the JWT.
    The paper derives the types from the possible index patterns of one- and two-electron integrals in Sec III. It does not prove that no other Pauli string types appear.
  • ad hoc to paper The Med/Bia and Med1/Med2 grouping rules guarantee pairwise commutation for all groups G3-G8.
    Appendix A proves this only for G8 and asserts the rest by a similar argument; no counterexample is considered.
  • ad hoc to paper The two-body XX and YY terms are either covered by a group family or can be grouped at O(N^2) cost.
    The text and Algorithm 2 do not assign XX/YY terms to any group; the reported group counts implicitly assume such a grouping exists.
  • standard math Standard Pauli commutation relations and the Jordan-Wigner transformation mapping.
    Used throughout Secs II-III; these are standard and not in question.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Accelerating Fermionic System Simulation on Quantum Computers." pith.science (2026). https://pith.science/paper/6HLL3WGR

@misc{pith2026250508206,
  author       = {Pith},
  title        = {Pith review of: Accelerating Fermionic System Simulation on Quantum Computers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6HLL3WGR}},
  note         = {Machine review of arXiv:2505.08206}
}
abstract

A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in the second quantization representation, the number of terms in many fermion-system Hamiltonians, such as molecular Hamiltonians, is substantial, approximately $\mathcal{O}(N^4)$, where $N$ is the number of molecular orbitals. Due to this, the computational resources required for Hamiltonian evolution and expectation value measurements could be excessively large. To address this, we introduce a grouping strategy that partitions these $\mathcal{O}(N^4)$ Hamiltonian terms into $\mathcal{O}(N^2)$ groups, with the terms in each group mutually commuting. Based on this grouping method, we propose a parallel Hamiltonian evolution scheme that reduces the circuit depth of Hamiltonian evolution by a factor of $N$. Moreover, our grouping measurement strategy reduces the number of measurements needed to $\mathcal{O}(N^2)$, whereas the current best grouping measurement schemes require $\mathcal{O}(N^3)$ measurements. Additionally, we find that measuring the expectation value of a group of Hamiltonian terms requires fewer repetitions than measuring a single term individually, thereby reducing the number of quantum circuit executions. Our approach saves a factor of $N^3$ in the overall time for Hamiltonian evolution and measurements, significantly decreasing the time required for quantum computers to simulate fermionic systems.

Figures

Figures reproduced from arXiv: 2505.08206 by the authors.

Figure 1
Figure 1. FIG. 1. The circuits to simulate the evolution of the one [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The circuit for parallel simulation of a qubit-wise commuting group. The copy-parity circuit is used to copy the parity [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The circuit to measure expectation values of Pauli [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Dependencies of the total number of terms and the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Dependencies of the total number of terms and the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Variance of individual measurement scheme (red line) [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The relationship of Pauli substrings in P1 and P2. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 29 canonical work pages

  1. [1]

    R. P. Feynman, Simulating physics with computers, in Feynman and computation (CRC Press, 2018) pp. 133– 153

    work page 2018

  2. [2]

    Babbush, N

    R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. K.-L. Chan, Low-depth quantum simu- lation of materials, Physical Review X 8, 011044 (2018)

    work page 2018

  3. [3]

    Reiher, N

    M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, Elucidating reaction mechanisms on quantum computers, Proceedings of the National Academy of Sci- ences 114, 7555 (2017)

    2017

  4. [4]

    Y. Cao, J. Romero, and A. Aspuru-Guzik, Potential of quantum computing for drug discovery, IBM Journal of Research and Development 62, 6 (2018)

    2018

  5. [5]

    Kassal, J

    I. Kassal, J. D. Whitfield, A. Perdomo-Ortiz, M.-H. Yung, and A. Aspuru-Guzik, Simulating chemistry using quantum computers, Annual review of physical chemistry 62, 185 (2011)

    work page 2011

  6. [6]

    D. Lu, B. Xu, N. Xu, Z. Li, H. Chen, X. Peng, R. Xu, and J. Du, Quantum chemistry simulation on quantum computers: theories and experiments, Physical Chem- istry Chemical Physics 14, 9411 (2012)

    work page 2012

  7. [7]

    Aspuru-Guzik, R

    A. Aspuru-Guzik, R. Lindh, and M. Reiher, The mat- ter simulation (r) evolution, ACS central science 4, 144 (2018)

    work page 2018

  8. [8]

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Physical Review A 86, 032324 (2012)

    2012

Show all 51 references
  1. [9]

    Peruzzo, J

    A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, A variational eigenvalue solver on a photonic quantum processor, Nature communications 5, 1 (2014)

    2014

  2. [10]

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru- Guzik, The theory of variational hybrid quantum- classical algorithms, New Journal of Physics 18, 023023 (2016)

    2016

  3. [11]

    Peddireddy, U

    D. Peddireddy, U. Priyam, and V. Aggarwal, Noisy tensor-ring approximation for computing gradients of a variational quantum eigensolver for combinatorial opti- mization, Physical Review, A 108 (2023)

    2023

  4. [12]

    S. E. Ghasempouri, G. W. Dueck, and S. De Baerdemacker, Modular cluster circuits for the variational quantum eigensolver, The Journal of Physical Chemistry A 127, 8168 (2023)

    2023

  5. [13]

    H. F. Trotter, On the product of semi-groups of opera- tors, Proceedings of the American Mathematical Society 10, 545 (1959)

    1959

  6. [14]

    Suzuki, General theory of higher-order decomposi- tion of exponential operators and symplectic integrators, Physics Letters A 165, 387 (1992)

    M. Suzuki, General theory of higher-order decomposi- tion of exponential operators and symplectic integrators, Physics Letters A 165, 387 (1992)

    1992

  7. [15]

    Huang, R

    H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measure- 14 ments, Nature Physics 16, 1050 (2020)

    2020

  8. [16]

    Hadfield, S

    C. Hadfield, S. Bravyi, R. Raymond, and A. Mezzacapo, Measurements of quantum hamiltonians with locally- biased classical shadows, Communications in Mathemat- ical Physics 391, 951 (2022)

    2022

  9. [17]

    Elben, S

    A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The random- ized measurement toolbox, Nature Reviews Physics 5, 9 (2023)

    2023

  10. [18]

    Gresch and M

    A. Gresch and M. Kliesch, Guaranteed efficient en- ergy estimation of quantum many-body hamiltonians us- ing shadowgrouping, Nature Communications 16, 689 (2025)

    2025

  11. [19]

    Jordan and E

    P. Jordan and E. P. Wigner, About the pauli exclusion principle, Z. Phys 47, 14 (1928)

    1928

  12. [20]

    Jiang, A

    Z. Jiang, A. Kalev, W. Mruczkiewicz, and H. Neven, Op- timal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning, Quan- tum 4, 276 (2020)

    2020

  13. [21]

    W. J. Huggins, J. R. McClean, N. C. Rubin, Z. Jiang, N. Wiebe, K. B. Whaley, and R. Babbush, Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers, npj Quantum Informa- tion 7, 23 (2021)

    2021

  14. [22]

    Motta, E

    M. Motta, E. Ye, J. R. McClean, Z. Li, A. J. Minnich, R. Babbush, and G. K.-L. Chan, Low rank representa- tions for quantum simulation of electronic structure, npj Quantum Information 7, 83 (2021)

    2021

  15. [23]

    Peng and K

    B. Peng and K. Kowalski, Highly efficient and scalable compound decomposition of two-electron integral ten- sor and its application in coupled cluster calculations, Journal of Chemical Theory and Computation 13, 4179 (2017)

    2017

  16. [24]

    Romero, R

    J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. J. Love, and A. Aspuru-Guzik, Strategies for quantum com- puting molecular energies using the unitary coupled clus- ter ansatz, Quantum Science and Technology 4, 014008 (2018)

    2018

  17. [25]

    Hamamura and T

    I. Hamamura and T. Imamichi, Efficient evaluation of quantum observables using entangled measurements. npj quantum information, 6 (1) (2020)

    2020

  18. [26]

    T.-C. Yen, V. Verteletskyi, and A. F. Izmaylov, Measur- ing all compatible operators in one series of single-qubit measurements using unitary transformations, Journal of chemical theory and computation 16, 2400 (2020)

    2020

  19. [27]

    Choi, T.-C

    S. Choi, T.-C. Yen, and A. F. Izmaylov, Improving quan- tum measurements by introducing “ghost” pauli prod- ucts, Journal of Chemical Theory and Computation 18, 7394 (2022)

    2022

  20. [28]

    Gokhale, O

    P. Gokhale, O. Angiuli, Y. Ding, K. Gui, T. Tomesh, M. Suchara, M. Martonosi, and F. T. Chong, o(n3) mea- surement cost for variational quantum eigensolver on molecular hamiltonians, IEEE Transactions on Quantum Engineering 1, 1 (2020)

    2020

  21. [29]

    Javadi-Abhari, M

    A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, et al. , Quantum computing with qiskit, arXiv preprint arXiv:2405.08810 (2024)

    2024 arXiv

  22. [30]

    A. Jena, S. N. Genin, and M. Mosca, Optimization of variational-quantum-eigensolver measurement by parti- tioning pauli operators using multiqubit clifford gates on noisy intermediate-scale quantum hardware, Physical Re- view A 106, 042443 (2022)

    2022

  23. [31]

    Verteletskyi, T.-C

    V. Verteletskyi, T.-C. Yen, and A. F. Izmaylov, Measure- ment optimization in the variational quantum eigensolver using a minimum clique cover, The Journal of chemical physics 152 (2020)

    2020

  24. [32]

    F. T. Leighton, A graph coloring algorithm for large scheduling problems, Journal of research of the national bureau of standards 84, 489 (1979)

    1979

  25. [33]

    R. D. Dutton and R. C. Brigham, A new graph colouring algorithm, The Computer Journal 24, 85 (1981)

    1981

  26. [34]

    Hertz, A fast algorithm for coloring meyniel graphs, Journal of Combinatorial Theory, Series B 50, 231 (1990)

    A. Hertz, A fast algorithm for coloring meyniel graphs, Journal of Combinatorial Theory, Series B 50, 231 (1990)

    1990

  27. [35]

    A. Zhao, A. Tranter, W. M. Kirby, S. F. Ung, A. Miyake, and P. J. Love, Measurement reduction in variational quantum algorithms, Phys. Rev. A 101, 062322 (2020)

    2020

  28. [36]

    Shlosberg, A

    A. Shlosberg, A. J. Jena, P. Mukhopadhyay, J. F. Haase, F. Leditzky, and L. Dellantonio, Adaptive estimation of quantum observables, Quantum 7, 906 (2023)

    2023

  29. [37]

    B. Wu, J. Sun, Q. Huang, and X. Yuan, Overlapped grouping measurement: A unified framework for mea- suring quantum states, Quantum 7, 896 (2023)

    2023

  30. [38]

    Crawford, B

    O. Crawford, B. v. Straaten, D. Wang, T. Parks, E. Campbell, and S. Brierley, Efficient quantum measure- ment of Pauli operators in the presence of finite sampling error, Quantum 5, 385 (2021)

    2021

  31. [39]

    Wang, H.-Y

    Q. Wang, H.-Y. Liu, Q.-S. Li, Y. Li, Y. Chai, Q. Gong, H. Wang, Y.-C. Wu, Y.-J. Han, G.-C. Guo, et al. , Chemiq: A chemistry simulator for quantum computer, arXiv preprint arXiv:2106.10162 (2021)

    2021 arXiv

  32. [40]

    Cross, The ibm q experience and qiskit open-source quantum computing software, in APS March meeting ab- stracts, Vol

    A. Cross, The ibm q experience and qiskit open-source quantum computing software, in APS March meeting ab- stracts, Vol. 2018 (2018) pp. L58–003

    2018

  33. [41]

    J. R. McClean, N. C. Rubin, K. J. Sung, I. D. Kivlichan, X. Bonet-Monroig, Y. Cao, C. Dai, E. S. Fried, C. Gid- ney, B. Gimby, et al., Openfermion: the electronic struc- ture package for quantum computers, Quantum Science and Technology 5, 034014 (2020)

    2020

  34. [42]

    S. B. Bravyi and A. Y. Kitaev, Fermionic quantum com- putation, Annals of Physics 298, 210 (2002)

    2002

  35. [43]

    J. T. Seeley, M. J. Richard, and P. J. Love, The bravyi- kitaev transformation for quantum computation of elec- tronic structure, The Journal of chemical physics 137, 224109 (2012)

    2012

  36. [44]

    Tranter, S

    A. Tranter, S. Sofia, J. Seeley, M. Kaicher, J. McClean, R. Babbush, P. V. Coveney, F. Mintert, F. Wilhelm, and P. J. Love, The b ravyi–k itaev transformation: Proper- ties and applications, International Journal of Quantum Chemistry 115, 1431 (2015)

    2015

  37. [45]

    Somma, G

    R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Simulating physical phenomena by quan- tum networks, Physical Review A 65, 042323 (2002)

    2002

  38. [46]

    M. A. Nielsen et al., The fermionic canonical commuta- tion relations and the jordan-wigner transform, School of Physical Sciences The University of Queensland 59 (2005)

    2005

  39. [47]

    J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Sim- ulation of electronic structure hamiltonians using quan- tum computers, Molecular Physics 109, 735 (2011)

    2011

  40. [48]

    Li, H.-Y

    Q.-S. Li, H.-Y. Liu, Q. Wang, Y.-C. Wu, and G.-P. Guo, A unified framework of transformations based on the jordan-wigner transformation, The Journal of Chemical Physics 157 (2022)

    2022

  41. [49]

    Miller, Z

    A. Miller, Z. Zimbor´ as, S. Knecht, S. Maniscalco, and G. Garc´ ıa-P´ erez, Bonsai algorithm: Grow your own fermion-to-qubit mappings, PRX Quantum 4, 030314 15 (2023)

    2023

  42. [50]

    Y.-A. Chen, A. V. Gorshkov, and Y. Xu, Error-correcting codes for fermionic quantum simulation, SciPost Physics 16, 033 (2024)

    2024

  43. [51]

    Bravyi, J

    S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, Tapering off qubits to simulate fermionic hamiltonians, arXiv preprint arXiv:1701.08213 (2017)

    2017 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.