Pith. sign in

REVIEW 4 major objections 3 minor 138 references

Programming optical-lattice Fermi-Hubbard quantum simulators

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

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

Pith's one-line read A programmable optical-lattice Fermi-Hubbard simulator prepares strongly correlated ground states faster than adiabatic ramping.

desk verdict Solid, honest ladder benchmarks for fermionic state preparation, but the 2D 'beyond classical' claim is an extrapolation the authors should temper or support. read the letter →

arxiv 2502.05067 v1 pith:P5ZMA5AZ submitted 2025-02-07 quant-ph cond-mat.quant-gascond-mat.str-el

Cristian Tabares , Christian Kokail , Peter Zoller , Daniel González-Cuadra , Alejandro González-Tudela This is my paper · ORCID
classification quant-phcond-mat.quant-gascond-mat.str-el
keywords Fermi-Hubbardmodelopticallatticesprogrammablequantumsimulatorground-statepreparationvariationalcircuitadiabaticfusionimaginary-timeevolutionLanczosalgorithm
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 argues that fermionic atoms in optical lattices, recently made locally programmable through superlattices and single-site control, can act as a fermionic quantum processor whose native Fermi-Hubbard dynamics provide the gate set. It proposes ground-state preparation protocols built from quench evolutions under these native gates: pre-compiled hybrid variational-adiabatic circuits that prepare local and extended Fermi-Hubbard ground states in considerably less time than adiabatic ramps, and a variational quantum imaginary-time evolution with Quantum Lanczos post-processing that improves energy estimates even under shot noise. The protocols are benchmarked on ladder geometries but are designed for two-dimensional experiments, with the goal of reaching parameter regimes that classical simulation cannot access.

What carries the argument

The central object is the fermionic gate set $\mathcal{G}$: unitary evolutions $\exp(-i[\hat H_t(t_{ij})+\hat H_U(U)+\hat H_n(\mu_i)]T)$ generated by the native Fermi-Hubbard Hamiltonian on a superlattice, with global control of tunnelings, Hubbard interaction, and chemical potentials. The argument's load-bearing mechanism is the hybrid variational-adiabatic (HyVA) circuit: short pre-compiled variational circuits prepare exact ground states of uncoupled dimers and plaquettes, and the remaining correlations are built by adiabatically fusing plaquettes, an efficient step when the target state's correlation length is finite. For extended models, evolutions under next-nearest-neighbor tunneling are synthesized from nearest-neighbor gates using fermionic SWAP operations. The VarQITE and QLanczos protocols reuse the same gate set and turn measured energy expectations into an improved ground-state energy estimate.

What would settle it

A tensor-network calculation of the ground-state correlation length of the two-dimensional doped extended Fermi-Hubbard model at $U/t=8$, $t'/t=-0.25$, and $\delta=1/3$ would settle the premise: if the correlation length substantially exceeds the plaquette size used in the pre-compiled circuits, the HyVA protocol's infidelity should grow with system size, and a cold-atom experiment measuring the same fidelity as a function of ladder length would reveal it.

Watch

Extended reading notes

Core claim

The central claim is that a programmable optical-lattice Fermi-Hubbard simulator can prepare strongly correlated fermionic ground states, including extended models with next-nearest-neighbor tunneling that are not natively implemented, within current coherence times. This is achieved by first using classically pre-compiled variational circuits, optimized on small plaquettes, to build correlations quickly, and then adiabatically fusing the plaquettes; the fusion is efficient because the target ground state has finite correlation length comparable to the plaquette size. The paper also shows that a variational approximation to imaginary-time evolution, implemented with the same fermionic gates and followed by Quantum Lanczos post-processing, improves ground-state energy estimates relative to the hybrid adiabatic protocol at equivalent implementation time, and remains effective with a realistic number of experimental runs.

Load-bearing premise

The final adiabatic fusion of plaquettes is efficient only because the target ground state has a finite correlation length comparable to the plaquette size; if a two-dimensional doped extended Hubbard target has longer-ranged correlations, the claimed time advantage would shrink or disappear.

Editorial extensions

If this is right

  • Pre-compiled variational circuits can replace much longer adiabatic ramps for preparing Fermi-Hubbard ground states at half filling and finite doping, reducing the coherence-time burden in cold-atom experiments.
  • Extended Fermi-Hubbard models, such as those with next-nearest-neighbor tunneling relevant to $d$-wave superconductivity, become addressable without engineering the extended terms, because their evolution is synthesized from native nearest-neighbor gates.
  • The same fermionic circuits implement a variational approximation to imaginary-time evolution whose measured data can be post-processed by Quantum Lanczos to improve ground-state energy estimates beyond what the prepared state alone gives.
  • The protocols are designed to transfer directly to two-dimensional optical-lattice experiments, where they could probe system sizes beyond classical simulation.
  • Shot-noise estimates indicate the required number of experimental runs is within reach of current cold-atom repetition rates.

Reading between the lines

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

  • If the finite-correlation-length premise fails for a target state, e.g. a two-dimensional doped extended Hubbard model with longer-ranged stripe or superconducting correlations, the adiabatic fusion step will require longer times; a direct test would be measuring the fidelity of HyVA preparation as a function of system size.
  • The variational Trotter times in the adiabatic Trotter circuit could be promoted to variational parameters and optimized on the hardware, potentially shortening the circuit beyond the fixed Trotter schedule.
  • The same gate set could be used for real-time Trotter evolution and many-body spectroscopy, extending the programming approach beyond ground-state preparation.
  • Combining QLanczos with other post-processing, such as filtering or statistical phase estimation, could further reduce the coherence time needed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 3 minor

Summary. The manuscript develops ground-state preparation protocols for a programmable optical-lattice Fermi-Hubbard simulator in which the native Fermi-Hubbard dynamics are used as a fermionic gate set. The authors propose hybrid variational-adiabatic circuits: small-unit-cell ground states are optimized classically and then adiabatically fused, and they claim this is considerably faster than purely adiabatic ramps. They also introduce a variational approximation to imaginary-time evolution (VarQITE) and use it as a subroutine for a QLanczos energy-improvement step. The protocols are benchmarked on ladder geometries for the local Fermi-Hubbard model at half filling and at finite doping, and for an extended model with next-nearest-neighbor tunneling relevant to d-wave superconductivity. The appendices contain explicit constructions of the fSWAP-based extended-tunneling circuits, measurement schemes for the required observables, and derivations of the QITE and QLanczos procedures.

Significance. If the main claims hold, the paper is significant: it presents a platform-native route to preparing strongly correlated fermionic ground states without a full quantum-classical variational optimization loop, and it gives concrete experimental circuits and measurement prescriptions. The ladder benchmarks are well defined, with infidelity and residual energy evaluated against independent exact diagonalization and DMRG ground states, and the gate-set construction is concrete and tailored to current cold-atom capabilities. The main limitation is that the headline applicability to 2D systems beyond classical methods is an extrapolation from ladder data, and the paper's own finite-correlation-length proviso is not quantitatively tested for the doped and extended target states.

major comments (4)
  1. [Sec. III.A and Conclusions] The claim that the protocols 'can be readily applied to 2D experimental setups to address regimes beyond the capabilities of current classical methods' is not supported by the evidence in the manuscript. The efficiency of the HyVA2→3 protocol is explicitly stated to rely on the finite correlation length of the target state (Sec. III.A, after Fig. 2), and the paper itself notes that the doped targets have a smaller gap and therefore a longer correlation length (Sec. III.B). The system-size scaling shown in Figs. 6(c,d) is confined to ladders and compares QLanczos with HyVA; it does not establish the scaling of the HyVA fusion time in 2D or its dependence on the correlation length. Please add 2D or cylinder numerical evidence, or provide a quantitative gap/correlation-length argument, or revise the abstract and conclusions to present the 2D extension as a conjecture.
  2. [Sec. III.A, Fig. 2] The paper's headline speedup over 'competing adiabatic protocols' is not benchmarked for the full target system. The adiabatic comparisons in Figs. 2(e)-(h) are for the two-site and four-site substeps, while the final HyVA2→3 step in Figs. 2(i)-(j) is compared only with the fully variational protocol. A full adiabatic ramp from the original product state to the 2x4 or 2x6 ladder would provide the missing baseline for the abstract's claim that the pre-compiled circuits 'require considerably less time than adiabatic protocols'; without it, the speedup claim applies to the substeps rather than to the complete state-preparation time.
  3. [Sec. III.C, Fig. 5] The benchmark for the extended FH model reaches only 86% fidelity after the full AT protocol, starting from an initial HyVA state with about 87% fidelity for the local FH model. No convergence of the AT protocol in TTrotter or in system size is shown, and no comparison with a direct adiabatic ramp in t' is provided. The conclusion that the protocol can 'faithfully prepare' the ground state of extended FH models is therefore stronger than the numerics; please either add a convergence study or soften the wording to qualitative preparation of the relevant correlations.
  4. [Sec. IV.B, Eq. (24) and App. D] The recursive QLanczos formulas contain inconsistent half-integer indices. Applying the exact derivation of D18-D19 to |Ψ_{α+1/2}⟩ and |Ψ_{β+1/2}⟩ gives S_{α+1/2,β+1/2}=c_{α+1/2}c_{β+1/2}/c^2_{(α+β+1)/2} and H_{α+1/2,β+1/2} evaluated at τ_{(α+β+1)/2}, whereas Eq. (24) uses c_α c_β and τ_{(α+β)/2}. As written, Eq. (24) implies H_{1/2,1/2}=⟨ψ(τ_0)|H|ψ(τ_0)⟩, which is inconsistent with the definition of the Krylov states. Please correct the notation or state the additional approximation used; this is necessary to validate the approximate QLanczos implementation.
minor comments (3)
  1. [Sec. II.A] There is a typo: 'in the absent of error correction' should read 'in the absence of error correction'.
  2. [Sec. IV.C] The phrase 'the for initial plaquette state' should read 'the initial plaquette state'.
  3. [Fig. 5 caption] The caption should state the equivalent physical implementation time, since the main text explains that the total physical time is T = 2 TTrotter; otherwise the quoted TTrotter t = 10 may be confused with the experimental duration.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all reported predictions are benchmarked against externally computed exact ground states, and the critical identities are exact derivations.

full rationale

The paper's central derivations are self-contained and benchmarked against independent exact results. The variational parameters in Eq. (8) are optimized by minimizing the expectation value of the target Hamiltonian, while the reported figures of merit, residual energy ε and infidelity I (Eqs. (9)-(10)), are evaluated against E_GS and |ψ_GS⟩ obtained from external exact diagonalization/DMRG calculations (ITensor, as stated in the acknowledgments). The fSWAP decomposition of Eq. (A2) is an exact identity: conjugating a nearest-neighbor tunneling quench by fSWAP gates produces the NNN tunneling evolution with tT = t'T', and is numerically checked. The QLanczos recursion in Eqs. (24)-(25) follows algebraically from the definitions of S and H in Eqs. (22)-(23), not from fitting. The variational QITE update uses measured g and b (Eq. (21)) and is benchmarked against exact imaginary-time evolution (Fig. 6(a)), so the approximation is externally validated. The only caveats are extrapolative rather than circular: the 2D speedup relies on the explicitly stated finite-correlation-length assumption in Sec. III A, and the adiabatic baseline is one particular linear ramp. These affect the strength of the 2D claim but do not reduce any derivation to its inputs. Self-citations (Refs. 55, 56, 99, 129) are contextual or concern measurement techniques and are not load-bearing for the reported predictions.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The quantitative claims (fidelity numbers, speedup factors) depend on tuned circuit depths, evolution times, and sampling rates, which are listed as free parameters. The physical assumptions are the availability of fast global quenches, preparable product states, and finite-correlation-length target states. None of these are newly invented entities.

free parameters (5)
  • Circuit depths for half-filled protocol = D(1)=D(2)=D(3)=3
    The number of quench layers in each pre-compiled step is chosen by hand; it bounds expressibility and the achieved infidelity shown in Fig. 2.
  • Circuit depth for doped protocol = D=2
    The variational circuit (12) for the doped ladder uses D=2 layers (Sec. III B); this is tuned to the system size and target gap.
  • Trotter timestep and total time for AT protocol = delta T t = 0.05, T_Trotter t = 10
    These values (Sec. III C) balance Trotter error and total time; the final fidelity is about 86% and is sensitive to them.
  • QITE timestep delta tau = not specified in main text
    The recursive QLanczos approximation (Eq. 25) requires small delta tau, while measurement cost scales as 1/delta tau; the chosen value is a trade-off.
  • Number of samples per measured object for shot noise = M=2000
    Sec. IV C 3 uses M=2000 samples; the reported energy estimates depend on this finite-sampling choice.
assumptions (6)
  • standard math Fermionic anticommutation relations
    Used in App. C to simplify products of hopping operators (e.g., Eq. C8). Standard quantum mechanics.
  • domain assumption The resource FH Hamiltonian with controllable t, U, and mu can be quenched abruptly (free on/off switching)
    Sec. II A states this explicitly. Finite ramp times and residual excitations are not modeled; the circuits' fidelities depend on ideal quenches.
  • domain assumption Low-entropy product states with desired filling are experimentally preparable
    Sec. II B relies on pattern-loading and Mott-insulator preparation, which have been demonstrated in cited experiments; still an experimental premise.
  • domain assumption The adiabatic theorem applies to the HyVA fusion step (target gap remains finite)
    The speedup of HyVA over pure adiabatic relies on the final fusion being adiabatic in the presence of a gap; the paper assumes this for the considered parameters.
  • ad hoc to paper Finite correlation length of target ground states
    The good performance of HyVA is credited to finite correlation length (Sec. III A). This is a property of the specific target states, not a general guarantee, and is the load-bearing premise for the 2D extrapolation.
  • domain assumption Initial state has non-zero overlap with the exact ground state for VarQITE
    Standard requirement for imaginary-time evolution (Sec. IV). The chosen initial states satisfy this in the benchmarks, but no guarantee is given for larger systems.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Programming optical-lattice Fermi-Hubbard quantum simulators." pith.science (2026). https://pith.science/paper/P5ZMA5AZ

@misc{pith2026250205067,
  author       = {Pith},
  title        = {Pith review of: Programming optical-lattice Fermi-Hubbard quantum simulators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P5ZMA5AZ}},
  note         = {Machine review of arXiv:2502.05067}
}
abstract

Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body, high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational, pre-compiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of $d$-wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy, and as a subroutine for the Quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to 2D experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.

Figures

Figures reproduced from arXiv: 2502.05067 by the authors.

Figure 1
Figure 1. Schematic illustration of the programmable fermionic quantum simulator architecture introduced in this work. (a) We consider a fermionic quantum processor based on ultracold (spinfull) fermionic atoms on a 2D optical superlattice. The superlattice structure is generated using two counter-propagating laser beams in each direction, giving rise to a four-site unit cell structure. Our protocols start by first preparing … view at source ↗
Figure 2
Figure 2. Ground-state preparation for the local FH model at half filling. (a)–(d) Superlattice configurations employed to prepare the ground state of the local FH model on a 2 × 4 ladder at half filling and for U/t = 8, starting from an antiferromagnetic product state on a deep lattice (a). We employ quench evolutions under the corresponding Hamiltonians Hˆ (k) , where we depict the different non-zero tunneling elements in d… view at source ↗
Figure 3
Figure 3. Observables for the prepared states. (a) Spin￾spin correlations between the atoms forming one (uncoupled) plaquette, measured on the state prepared after the second step of our protocol [ [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Ground-state preparation for the local FH model at finite doping. (a) Initial state used to prepared the ground state of a 2 × 6 FH ladder with doping δ = 1/3 and U/t = 8. Atoms are loaded into the optical lattice, with certain sites left empty according to the expecte…
Figure 5
Figure 5. Figure 5: Extended Fermi-Hubbard model. (a) Using the UAT, we prepare the ground state of the eFH model on a 2 × 6 ladder, for U/t = 8, t/t′ = −0.25 and δ = 1/3. As described in the main text, we take as an initial state the ground state of the local FH model prepared with the H…
Figure 6
Figure 6. Figure 6: VarQITE and QLanczos for the local Fermi￾Hubbard ladder. (a) Comparison between the QITE pro￾tocol (solid lines) and the exact ITE (dashed lines) to prepare the ground state of a half-filled 2×12 ladder at U/t = 8, start￾ing from different initial states (see main text…
Figure 7
Figure 7. Figure 7: VarQITE and QLanczos for the Fermi￾Hubbard ladder with extended interactions. (a) Com￾parison between the QITE protocol (solid lines) and the exact ITE (dashed lines) to prepare the ground state of a half-filled 2 × 12 ladder at U/t = 8 and V /t = 2, starting from dif￾…
Figure 8
Figure 8. Figure 8: Effects of shot noise in Quantum Imaginary Time Evolution (QITE) and QLanczos. (a) Comparison between the QITE (solid lines) and the exact imaginary time Evolution (dashed lines) applied to the target local FH model with U/t = 8 in a 2×4 ladder, considering as initial …
Figure 9
Figure 9. Figure 9: Fermionic circuits for extended tunneling, (a) a fSWAP gate can be implemented between two NN sites i and j by evolving with the Hamiltonian HˆfS (A1) for a time π/(2t). (b) A unitary evolution under NNN tunneling terms Hˆ t ′ (red, diagonal in the plaquette) can be im…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

138 extracted references · 32 canonical work pages

  1. [1]

    Local Fermi-Hubbard ladders Our results for the local FH ladder are summarized in Fig. 6, where we first show the expectation value of the target Hamiltonian ⟨ ˆH⟩ over the states evolved with our VarQITE protocol for a 2 × 12 ladder at half filling, and compare them with an exact QITE calculation [black dashed line in Fig. 6(a)]. These results show the i...

  2. [2]

    To illustrate this point, we now include an extra NN interaction term to the half-filled FH ladder target Hamiltonian, ˆHV = V X ⟨i,j⟩ ˆni ˆnj , (26) where we set V /t= 2

    Fermi-Hubbard ladder with extended interactions One of the main advantages of implementing the Var- QITE and the QLanczos protocols is that there is no need to directly engineer all the terms in the target Hamilto- nian ˆH to estimate its ground-state energy. To illustrate this point, we now include an extra NN interaction term to the half-filled FH ladde...

  3. [3]

    Effect of shot noise Finally, let us note that all the results shown for the VarQITE and the QLanczos algorithm so far assume an infinite number of measurements. We now conclude this study by investigating how our protocols are affected by the presence of shot noise stemming from a finite number of samples in the estimation of each measured object. In Fig...

  4. [4]

    Measurement of ⟨ ˆHt⟩ The first operator that we are interested in measuring is ˆHt. When computed over a two-dimensional square lattice, this operator can be divided in four commuting parts such as all the terms in each one of them can be measured simultaneously through the appropriate dimer- ization of the lattice. Labeling these commuting parts with th...

  5. [5]

    ˆc† r,σ′ ˆcs,σ′ + H.c

    Measurement of ⟨ ˆH 2 t ⟩ Now we turn our attention to the measurement of ⟨ ˆH 2 t ⟩, corresponding to a linear combination of O(N 2) four point correlation functions ⟨ ˆH 2 t ⟩ = X ⟨i,j⟩,σ X ⟨r,s⟩,σ′ ⟨ˆc† i,σˆcj,σˆc† r,σ′ ˆcs,σ′⟩ = 1 4 X ⟨i,j⟩,σ X ⟨r,s⟩,σ′ D ˆc† i,σˆcj,σ + H.c. ˆc† r,σ′ ˆcs,σ′ + H.c. E . (C5) We now introduce a measurement scheme for the...

  6. [6]

    Measurement of ℜ hD ˆHt ˆHU Ei and ℑ hD ˆHt ˆHU Ei Finally, let us outline the measurement of the crossed terms, which are necessary for the QITE protocol in Sec. IV. For the first case, let us write ℜ hD ˆHt ˆHU Ei as ℜ hD ˆHt ˆHU Ei = 1 2 D ˆHt ˆHU + ˆHU ˆHt E . (C9) Since ˆHt and ˆHU are both Hermitian operators, the sec- ond equality in (C9) is the ex...

  7. [7]

    Implementing the QLanczos algorithm using the data obtained with the QITE Finally, to implementation of the QLanczos algorithm, it is necessary to measure the matrices H and S, that read Hα,β = ⟨Ψ (τα)| ˆH |Ψ (τβ)⟩ , (D14) Sα,β = ⟨Ψ (τα) |Ψ (τβ)⟩ , (D15) where |Ψ(τα)⟩ = cαe−α∆τ ˆH |Ψ0⟩. To measure these ma- trices, one can always directly compute each mat...

  8. [8]

    Jaksch and P

    D. Jaksch and P. Zoller, Annals of Physics 315, 52 (2005), special Issue

    2005

Show all 138 references
  1. [9]

    Lewenstein, A

    M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De), and U. Sen, Advances in Physics56, 243379 (2007)

    2007

  2. [10]

    Gross and I

    C. Gross and I. Bloch, Science 357, 995 (2017)

    2017

  3. [11]

    Sch¨ afer, T

    F. Sch¨ afer, T. Fukuhara, S. Sugawa, Y. Takasu, and Y. Takahashi, Nature Reviews Physics 2, 411 (2020). 18

    2020

  4. [12]

    R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, Nature 519, 211 (2015)

    2015

  5. [13]

    M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Ne- spolo, L. Pollet, I. Bloch, and C. Gross, Science 353, 1257 (2016)

    2016

  6. [14]

    L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein, Science 353, 1260 (2016)

    2016

  7. [15]

    Mazurenko, C

    A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kan´ asz-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, Nature 545, 462 (2017)

    2017

  8. [16]

    M. Xu, L. H. Kendrick, A. Kale, Y. Gang, G. Ji, R. T. Scalettar, M. Lebrat, and M. Greiner, Nature 620, 971 (2023)

    2023

  9. [17]

    Shao, Y.-X

    H.-J. Shao, Y.-X. Wang, D.-Z. Zhu, Y.-S. Zhu, H.-N. Sun, S.-Y. Chen, C. Zhang, Z.-J. Fan, Y. Deng, X.- C. Yao, Y.-A. Chen, and J.-W. Pan, Nature 632, 267 (2024)

    2024

  10. [18]

    C. S. Chiu, G. Ji, A. Bohrdt, M. Xu, M. Knap, E. Dem- ler, F. Grusdt, M. Greiner, and D. Greif, Science 365, 251 (2019)

    2019

  11. [19]

    Bourgund, T

    D. Bourgund, T. Chalopin, P. Bojovi, H. Schlmer, S. Wang, T. Franz, S. Hirthe, A. Bohrdt, F. Grusdt, I. Bloch, and T. A. Hilker, Formation of stripes in a mixed-dimensional cold-atom fermi-hubbard system (2023), arXiv:2312.14156 [cond-mat.quant-gas]

    2023 arXiv

  12. [20]

    Sompet, S

    P. Sompet, S. Hirthe, D. Bourgund, T. Chalopin, J. Bibo, J. Koepsell, P. Bojovi´ c, R. Verresen, F. Poll- mann, G. Salomon, C. Gross, T. A. Hilker, and I. Bloch, Nature 606, 484 (2022)

    2022

  13. [21]

    Hirthe, T

    S. Hirthe, T. Chalopin, D. Bourgund, P. Bojovi´ c, A. Bohrdt, E. Demler, F. Grusdt, I. Bloch, and T. A. Hilker, Nature 613, 463 (2023)

    2023

  14. [22]

    Hartke, B

    T. Hartke, B. Oreg, C. Turnbaugh, N. Jia, and M. Zwierlein, Science 381, 82 (2023)

    2023

  15. [23]

    Schreiber, S

    M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Science 349, 842 (2015)

    2015

  16. [24]

    M. A. Nichols, L. W. Cheuk, M. Okan, T. R. Hartke, E. Mendez, T. Senthil, E. Khatami, H. Zhang, and M. W. Zwierlein, Science 363, 383 (2019)

    2019

  17. [25]

    Guardado-Sanchez, A

    E. Guardado-Sanchez, A. Morningstar, B. M. Spar, P. T. Brown, D. A. Huse, and W. S. Bakr, Phys. Rev. X 10, 011042 (2020)

    2020

  18. [26]

    Scherg, T

    S. Scherg, T. Kohlert, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidels- burger, Nature Communications 12, 4490 (2021)

    2021

  19. [27]

    M. C. Ba˜ nuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, The European P...

    2020

  20. [28]

    Aidelsburger, L

    M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. Gonz´ alez-Cuadra, P. R. Grzy- bowski, S. Hands, F. Jendrzejewski, J. J¨ unemann, G. Juzeli¯ unas, V. Kasper, A. Piga, S. J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T. V. Zache, J. Za- krzewski,...

    2022

  21. [29]

    Di Meglio, K

    A. Di Meglio, K. Jansen, I. Tavernelli, C. Alexandrou, S. Arunachalam, C. W. Bauer, K. Borras, S. Carrazza, A. Crippa, V. Croft, R. de Putter, A. Delgado, V. Dun- jko, D. J. Egger, E. Fern´ andez-Combarro, E. Fuchs, L. Funcke, D. Gonz´ alez-Cuadra, M. Grossi, J. C. Hal- imeh, ...

    2024

  22. [30]

    G. A. Quantum, Collaborators*, F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, S. Boixo, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. Dunsworth, E. Farhi, A. Fowler, B....

    2020

  23. [31]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, A. Bengtsson, S. Boixo, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, Y. Chen, Z. Chen, Y.-A. Chen, B. Chiaro, R. Collins, S. J. Cotton, W. Courtney, S. Demura, A. Derk, A. Dunsworth, D. Ep...

    2020 arXiv

  24. [32]

    Stanisic, J

    S. Stanisic, J. L. Bosse, F. M. Gambetta, R. A. Santos, W. Mruczkiewicz, T. E. O’Brien, E. Ostby, and A. Mon- tanaro, Nature Communications 13, 5743 (2022)

    2022

  25. [33]

    R. N. Tazhigulov, S.-N. Sun, R. Haghshenas, H. Zhai, A. T. Tan, N. C. Rubin, R. Babbush, A. J. Minnich, and G. K.-L. Chan, PRX Quantum 3, 040318 (2022)

    2022

  26. [34]

    H´ emery, K

    K. H´ emery, K. Ghanem, E. Crane, S. L. Campbell, J. M. 19 Dreiling, C. Figgatt, C. Foltz, J. P. Gaebler, J. Jo- hansen, M. Mills, S. A. Moses, J. M. Pino, A. Rans- ford, M. Rowe, P. Siegfried, R. P. Stutz, H. Dreyer, A. Schuckert, and R. Nigmatullin, PRX Quantum 5, 030323 (2024)

    2024

  27. [35]

    Clinton, T

    L. Clinton, T. Cubitt, B. Flynn, F. M. Gambetta, J. Klassen, A. Montanaro, S. Piddock, R. A. Santos, and E. Sheridan, Nature Communications 15, 211 (2024)

    2024

  28. [36]

    Robledo-Moreno, M

    J. Robledo-Moreno, M. Motta, H. Haas, A. Javadi- Abhari, P. Jurcevic, W. Kirby, S. Martiel, K. Sharma, S. Sharma, T. Shirakawa, I. Sitdikov, R.-Y. Sun, K. J. Sung, M. Takita, M. C. Tran, S. Yunoki, and A. Mezza- capo, Chemistry beyond exact solutions on a quantum- centric supe...

    2024 arXiv

  29. [37]

    S. J. Evered, M. Kalinowski, A. A. Geim, T. Manovitz, D. Bluvstein, S. H. Li, N. Maskara, H. Zhou, S. Ebadi, M. Xu, J. Campo, M. Cain, S. Ostermann, S. F. Yelin, S. Sachdev, M. Greiner, V. Vuleti, and M. D. Lukin, Probing topological matter and fermion dy- namics on a neutral-...

    2025

  30. [38]

    D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997)

    1997

  31. [39]

    Ortiz, J

    G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Phys. Rev. A 64, 022319 (2001)

    2001

  32. [40]

    S. B. Bravyi and A. Y. Kitaev, Annals of Physics 298, 210 (2002)

    2002

  33. [41]

    R. C. Ball, Phys. Rev. Lett. 95, 176407 (2005)

    2005

  34. [42]

    Verstraete and J

    F. Verstraete and J. I. Cirac, Journal of Statistical Me- chanics: Theory and Experiment 2005, P09012 (2005)

    2005

  35. [43]

    J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Molecular Physics 109, 735 (2011)

    2011

  36. [44]

    J. D. Whitfield, V. c. v. Havl ´ ıˇ cek, and M. Troyer, Phys. Rev. A 94, 030301 (2016)

    2016

  37. [45]

    Preskill, Quantum 2, 79 (2018)

    J. Preskill, Quantum 2, 79 (2018)

    2018

  38. [46]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pear- son, M. Troyer, and P. Zoller, Nature 607, 667 (2022)

    2022

  39. [47]

    Flannigan, N

    S. Flannigan, N. Pearson, G. H. Low, A. Buyskikh, I. Bloch, P. Zoller, M. Troyer, and A. J. Daley, Quantum Science and Technology 7, 045025 (2022)

    2022

  40. [48]

    Trivedi, A

    R. Trivedi, A. Franco Rubio, and J. I. Cirac, Nature Communications 15, 6507 (2024)

    2024

  41. [49]

    B. F. Schiffer, A. F. Rubio, R. Trivedi, and J. I. Cirac, The quantum adiabatic algorithm suppresses the prolif- eration of errors (2024), arXiv:2404.15397 [quant-ph]

    2024 arXiv

  42. [50]

    Kashyap, G

    V. Kashyap, G. Styliaris, S. Mouradian, J. I. Cirac, and R. Trivedi, Accuracy guarantees and quantum advan- tage in analogue open quantum simulation with and without noise (2024), arXiv:2404.11081 [quant-ph]

    2024 arXiv

  43. [51]

    M. Qin, T. Schfer, S. Andergassen, P. Corboz, and E. Gull, Annual Review of Condensed Matter Physics 13, 275 (2022)

    2022

  44. [53]

    Xu, C.-M

    H. Xu, C.-M. Chung, M. Qin, U. Schollw¨ ock, S. R. White, and S. Zhang, Science 384, eadh7691 (2024)

    2024

  45. [54]

    H.-N. Dai, B. Yang, A. Reingruber, X.-F. Xu, X. Jiang, Y.-A. Chen, Z.-S. Yuan, and J.-W. Pan, Nature Physics 12, 783 (2016)

    2016

  46. [55]

    X. Qiu, J. Zou, X. Qi, and X. Li, npj Quantum Infor- mation 6, 87 (2020)

    2020

  47. [56]

    B. Yang, H. Sun, R. Ott, H. Y. Wang, T. V. Zache, J. C. Halimeh, Z. S. Yuan, P. Hauke, and J. W. Pan, Nature 587, 392 (2020)

    2020

  48. [57]

    B. Yang, H. Sun, C.-J. Huang, H.-Y. Wang, Y. Deng, H.-N. Dai, Z.-S. Yuan, and J.-W. Pan, Science 369, 550 (2020)

    2020

  49. [58]

    Zhang, M.-G

    W.-Y. Zhang, M.-G. He, H. Sun, Y.-G. Zheng, Y. Liu, A. Luo, H.-Y. Wang, Z.-H. Zhu, P.-Y. Qiu, Y.-C. Shen, X.-K. Wang, W. Lin, S.-T. Yu, B.-C. Li, B. Xiao, M.-D. Li, Y.-M. Yang, X. Jiang, H.-N. Dai, Y. Zhou, X. Ma, Z.-S. Yuan, and J.-W. Pan, Phys. Rev. Lett. 131, 073401 (2023)

    2023

  50. [59]

    Chalopin, P

    T. Chalopin, P. Bojovi´ c, D. Bourgund, S. Wang, T. Franz, I. Bloch, and T. Hilker, Phys. Rev. Lett. 134, 053402 (2025)

    2025

  51. [60]

    D. Wei, D. Adler, K. Srakaew, S. Agrawal, P. Weckesser, I. Bloch, and J. Zeiher, Phys. Rev. X 13, 021042 (2023)

    2023

  52. [61]

    Impertro, S

    A. Impertro, S. Karch, J. F. Wienand, S. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Phys. Rev. Lett. 133, 063401 (2024)

    2024

  53. [62]

    Gonzlez-Cuadra, D

    D. Gonzlez-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermer- sch, J. Ye, and P. Zoller, Proceedings of the National Academy of Sciences 120, e2304294120 (2023)

    2023

  54. [63]

    T. V. Zache, D. Gonz´ alez-Cuadra, and P. Zoller, Quan- tum 7, 1140 (2023)

    2023

  55. [64]

    Gkritsis, D

    F. Gkritsis, D. Dux, J. Zhang, N. Jain, C. Gogolin, and P. M. Preiss, Simulating chemistry with fermionic optical superlattices (2024), arXiv:2409.05663 [cond- mat.quant-gas]

    2024 arXiv

  56. [65]

    Schuckert, E

    A. Schuckert, E. Crane, A. V. Gorshkov, M. Hafezi, and M. J. Gullans, Fermion-qubit fault-tolerant quan- tum computing (2024), arXiv:2411.08955 [quant-ph]

    2024 arXiv

  57. [66]

    R. Ott, D. Gonzlez-Cuadra, T. V. Zache, P. Zoller, A. M. Kaufman, and H. Pichler, Error-corrected fermionic quantum processors with neutral atoms (2024), arXiv:2412.16081 [quant-ph]

    2024 arXiv

  58. [67]

    Kokail, C

    C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller, Nature 569, 355 (2019)

    2019

  59. [68]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Rev. Mod. Phys. 93, 025001 (2021)

    2021

  60. [69]

    Joshi, F

    C. Joshi, F. Yang, and M. Mirhosseini, Phys. Rev. X 13, 021039 (2023)

    2023

  61. [70]

    Labuhn, D

    H. Labuhn, D. Barredo, S. Ravets, S. de L´ es´ eleuc, T. Macr ` ı, T. Lahaye, and A. Browaeys, Nature 534, 667 (2016)

    2016

  62. [71]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 551, 579 (2017)

    2017

  63. [72]

    Keesling, A

    A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pich- ler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 568, 207 (2019)

    2019

  64. [73]

    de L´ es´ eleuc, V

    S. de L´ es´ eleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Science 365, 775 (2019)

    2019

  65. [74]

    Ebadi, T

    S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, 20 V. Vuleti´ c, and M. D. Lukin, Nature595, 227 (2021)

    2021

  66. [75]

    Scholl, M

    P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. L¨ auchli, and A. Browaeys, Nature 595, 233 (2021)

    2021

  67. [76]

    Bluvstein, A

    D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Se- meghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Science371, 1355 (2021)

    2021

  68. [77]

    Semeghini, H

    G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kali- nowski, R. Samajdar, A. Omran, S. Sachdev, A. Vish- wanath, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Sci- ence 374, 1242 (2021)

    2021

  69. [78]

    Scholl, H

    P. Scholl, H. J. Williams, G. Bornet, F. Wallner, D. Barredo, L. Henriet, A. Signoles, C. Hainaut, T. Franz, S. Geier, A. Tebben, A. Salzinger, G. Z¨ urn, T. Lahaye, M. Weidem¨ uller, and A. Browaeys, PRX Quantum 3, 020303 (2022)

    2022

  70. [79]

    Manovitz, S

    T. Manovitz, S. H. Li, S. Ebadi, R. Samajdar, A. A. Geim, S. J. Evered, D. Bluvstein, H. Zhou, N. U. Ky- lolu, J. Feldmeier, P. E. Dolgirev, N. Maskara, M. Kali- nowski, S. Sachdev, D. A. Huse, M. Greiner, V. Vuleti, and M. D. Lukin, Quantum coarsening and collec- tive dynamic...

    2024 arXiv

  71. [80]

    Lukin, B

    A. Lukin, B. F. Schiffer, B. Braverman, S. H. Cantu, F. Huber, A. Bylinskii, J. Amato-Grill, N. Maskara, M. Cain, D. S. Wild, R. Samajdar, and M. D. Lukin, Quantum quench dynamics as a shortcut to adiabaticity (2024), arXiv:2405.21019 [quant-ph]

    2024 arXiv

  72. [81]

    Gonzalez-Cuadra, M

    D. Gonzalez-Cuadra, M. Hamdan, T. V. Zache, B. Braverman, M. Kornjaca, A. Lukin, S. H. Cantu, F. Liu, S.-T. Wang, A. Keesling, M. D. Lukin, P. Zoller, and A. Bylinskii, Observation of string break- ing on a (2 + 1)d rydberg quantum simulator (2024), arXiv:2410.16558 [quant-ph]

    2024 arXiv

  73. [82]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Nat. Phys. Rev.3, 625 (2021)

    2021

  74. [83]

    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, Nat. Commun. 5, 4213 (2014)

    2014

  75. [84]

    I. D. Kivlichan, J. McClean, N. Wiebe, C. Gidney, A. Aspuru-Guzik, G. K. L. Chan, and R. Babbush, Phys. Rev. Lett. 120, 110501 (2018)

    2018

  76. [85]

    H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, Nat. Commun. 10, 1 (2019)

    2019

  77. [86]

    H. L. Tang, V. O. Shkolnikov, G. S. Barron, H. R. Grim- sley, N. J. Mayhall, E. Barnes, and S. E. Economou, PRX Quantum 2, 020310 (2021)

    2021

  78. [87]

    Takeshita, N

    T. Takeshita, N. C. Rubin, Z. Jiang, E. Lee, R. Babbush, and J. R. McClean, Phys. Rev. X 10, 10.1103/PhysRevX.10.011004 (2020)

    2020 doi

  79. [88]

    W. J. Huggins, J. R. McClean, N. C. Rubin, Z. Jiang, N. Wiebe, K. B. Whaley, and R. Babbush, npj Quantum Information 7, 10.1038/s41534-020-00341-7 (2021)

    2021 doi

  80. [89]

    Motta, C

    M. Motta, C. Sun, A. T. Tan, M. J. ORourke, E. Ye, A. J. Minnich, F. G. Brandao, and G. K.-L. Chan, Na- ture Physics 16, 205 (2020)

    2020

  81. [90]

    McArdle, T

    S. McArdle, T. Jones, S. Endo, Y. Li, S. C. Benjamin, and X. Yuan, npj Quantum Information 5, 75 (2019)

    2019

  82. [91]

    X. Yuan, S. Endo, Q. Zhao, Y. Li, and S. C. Benjamin, Quantum 3, 191 (2019)

    2019

  83. [92]

    Gacon, J

    J. Gacon, J. Nys, R. Rossi, S. Woerner, and G. Carleo, Phys. Rev. Res. 6, 013143 (2024)

    2024

  84. [93]

    A. M. Kaufman and K.-K. Ni, Nature Physics 17, 1324 (2021)

    2021

  85. [94]

    A. W. Young, W. J. Eckner, N. Schine, A. M. Childs, and A. M. Kaufman, Science 377, 885 (2022)

    2022

  86. [95]

    Z. Z. Yan, B. M. Spar, M. L. Prichard, S. Chi, H.-T. Wei, E. Ibarra-Garc ´ ıa-Padilla, K. R. A. Hazzard, and W. S. Bakr, Phys. Rev. Lett. 129, 123201 (2022)

    2022

  87. [96]

    R. Tao, M. Ammenwerth, F. Gyger, I. Bloch, and J. Zei- her, Phys. Rev. Lett. 133, 013401 (2024)

    2024

  88. [97]

    P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003)

    2003

  89. [98]

    Griessner, A

    A. Griessner, A. J. Daley, S. R. Clark, D. Jaksch, and P. Zoller, New Journal of Physics 9, 44 (2007)

    2007

  90. [99]

    Popp, J.-J

    M. Popp, J.-J. Garcia-Ripoll, K. G. Vollbrecht, and J. I. Cirac, Phys. Rev. A 74, 013622 (2006)

    2006

  91. [100]

    W. S. Bakr, P. M. Preiss, M. E. Tai, R. Ma, J. Simon, and M. Greiner, Nature 480, 500 (2011)

    2011

  92. [101]

    M. Xu, L. H. Kendrick, A. Kale, Y. Gang, C. Feng, S. Zhang, A. W. Young, M. Lebrat, and M. Greiner, A neutral-atom hubbard quantum simulator in the cryo- genic regime (2025), arXiv:2502.00095 [cond-mat.quant- gas]

    2025 arXiv

  93. [102]

    Trebst, U

    S. Trebst, U. Schollw¨ ock, M. Troyer, and P. Zoller, Phys. Rev. Lett. 96, 250402 (2006)

    2006

  94. [103]

    W. S. Bakr, J. I. Gillen, A. Peng, S. F¨ olling, and M. Greiner, Nature 462, 74 (2009)

    2009

  95. [104]

    J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Nature 467, 68 (2010)

    2010

  96. [105]

    Gross and W

    C. Gross and W. S. Bakr, Nature Physics 17, 1316 (2021)

    2021

  97. [106]

    D. K. Mark, H.-Y. Hu, J. Kwan, C. Kokail, S. Choi, and S. F. Yelin, Efficiently measuring d-wave pair- ing and beyond in quantum gas microscopes (2024), arXiv:2412.13186 [cond-mat.quant-gas]

    2024

  98. [107]

    Zheng, C.-M

    B.-X. Zheng, C.-M. Chung, P. Corboz, G. Ehlers, M.-P. Qin, R. M. Noack, H. Shi, S. R. White, S. Zhang, and G. K.-L. Chan, Science 358, 1155 (2017)

    2017

  99. [108]

    Qin, C.-M

    M. Qin, C.-M. Chung, H. Shi, E. Vitali, C. Hubig, U. Schollw¨ ock, S. R. White, and S. Zhang (Simons Col- laboration on the Many-Electron Problem), Phys. Rev. X 10, 031016 (2020)

    2020

  100. [109]

    Jiang and T

    H.-C. Jiang and T. P. Devereaux, Science 365, 1424 (2019)

    2019

  101. [110]

    M. F. Parsons, A. Mazurenko, C. S. Chiu, G. Ji, D. Greif, and M. Greiner, Science 353, 1253 (2016)

    2016

  102. [111]

    Koepsell, J

    J. Koepsell, J. Vijayan, P. Sompet, F. Grusdt, T. A. Hilker, E. Demler, G. Salomon, I. Bloch, and C. Gross, Nature 572, 358 (2019)

    2019

  103. [112]

    Ponsioen, S

    B. Ponsioen, S. S. Chung, and P. Corboz, Phys. Rev. B 100, 195141 (2019)

    2019

  104. [113]

    Motta, W

    M. Motta, W. Kirby, I. Liepuoniute, K. J. Sung, J. Cohn, A. Mezzacapo, K. Klymko, N. Nguyen, N. Yoshioka, and J. E. Rice, Electronic Structure 6, 013001 (2024)

    2024

  105. [114]

    Y. Yang, A. Christianen, M. C. Ba˜ nuls, D. S. Wild, and J. I. Cirac, Phys. Rev. Lett. 132, 220601 (2024)

    2024

  106. [115]

    Poulin and P

    D. Poulin and P. Wocjan, Phys. Rev. Lett. 102, 130503 (2009)

    2009

  107. [116]

    Y. Ge, J. Tura, and J. I. Cirac, Journal of Mathematical Physics 60, 022202 (2019)

    2019

  108. [117]

    Lin and Y

    L. Lin and Y. Tong, Quantum 4, 372 (2020)

    2020

  109. [118]

    S. Lu, M. C. Ba˜ nuls, and J. I. Cirac, PRX Quantum 2, 21 020321 (2021)

    2021

  110. [119]

    R. D. Somma, New Journal of Physics 21, 123025 (2019)

    2019

  111. [120]

    T. E. OBrien, B. Tarasinski, and B. M. Terhal, New Journal of Physics 21, 023022 (2019)

    2019

  112. [121]

    Lin and Y

    L. Lin and Y. Tong, PRX Quantum 3, 010318 (2022)

    2022

  113. [122]

    Ding and L

    Z. Ding and L. Lin, PRX Quantum 4, 020331 (2023)

    2023

  114. [123]

    G. Wang, D. S. Frana, R. Zhang, S. Zhu, and P. D. Johnson, Quantum 7, 1167 (2023)

    2023

  115. [124]

    Chalopin, P

    T. Chalopin, P. Bojovi´ c, S. Wang, T. Franz, A. Sinha, Z. Wang, D. Bourgund, J. Obermeyer, F. Grusdt, A. Bohrdt, et al. , arXiv:2412.17801 (2024)

    2024

  116. [125]

    L. Su, A. Douglas, M. Szurek, A. H. H´ ebert, A. Krahn, R. Groth, G. A. Phelps, O. Markovi´ c, and M. Greiner, Nature Communications 16, 1017 (2025)

    2025

  117. [126]

    Naldesi, A

    P. Naldesi, A. Elben, A. Minguzzi, D. Cl´ ement, P. Zoller, and B. Vermersch, Phys. Rev. Lett. 131, 060601 (2023)

    2023

  118. [127]

    Gluza and J

    M. Gluza and J. Eisert, Phys. Rev. Lett. 127, 090503 (2021)

    2021

  119. [128]

    A. Zhao, N. C. Rubin, and A. Miyake, Phys. Rev. Lett. 127, 110504 (2021)

    2021

  120. [129]

    G. H. Low, Classical shadows of fermions with particle number symmetry (2024), arXiv:2208.08964 [quant-ph]

    2024 arXiv

  121. [130]

    Denzler, A

    J. Denzler, A. A. Mele, E. Derbyshire, T. Guaita, and J. Eisert, Learning fermionic correlations by evolv- ing with random translationally invariant hamiltonians (2023), arXiv:2309.12933 [quant-ph]

    2023 arXiv

  122. [131]

    M. C. Tran, D. K. Mark, W. W. Ho, and S. Choi, Phys. Rev. X 13, 011049 (2023)

    2023

  123. [132]

    Aidelsburger, S

    M. Aidelsburger, S. Nascimbene, and N. Goldman, Comptes Rendus Physique 19, 394 (2018), quantum simulation / Simulation quantique

    2018

  124. [133]

    Chomaz, I

    L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe- Tolra, B. L. Lev, and T. Pfau, Reports on Progress in Physics 86, 026401 (2022)

    2022

  125. [134]

    Arg¨ uello-Luengo, A

    J. Arg¨ uello-Luengo, A. Gonz´ alez-Tudela, and D. Gonz´ alez-Cuadra, Phys. Rev. Lett. 129, 083401 (2022)

    2022

  126. [135]

    L´ eonard, S

    J. L´ eonard, S. Kim, J. Kwan, P. Segura, F. Grusdt, C. Repellin, N. Goldman, and M. Greiner, Nature 619, 495 (2023)

    2023

  127. [136]

    Tabares, A

    C. Tabares, A. Mu˜ noz de las Heras, L. Tagliacozzo, D. Porras, and A. Gonz´ alez-Tudela, Phys. Rev. Lett. 131, 073602 (2023)

    2023

  128. [137]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, Sci- Post Phys. Codebases , 4 (2022)

    2022

  129. [138]

    Havl ´ ıˇ cek, M

    V. Havl ´ ıˇ cek, M. Troyer, and J. D. Whitfield, Phys. Rev. A 95, 032332 (2017)

    2017

  130. [139]

    Childs and N

    A. Childs and N. Wiebe, Quantum Information and Computation 12, 10.26421/qic12.11-12 (2012)

    2012 doi

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.