Pith. sign in

REVIEW 3 major objections 4 minor 79 references

Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read Researchers demonstrate the first experimental generation of non-Hermitian parent Hamiltonians, using single-photon interferometry to realize Hamiltonians whose left and right ground states are a prescribed matrix product pair.

desk verdict First photonic realization of non-Hermitian parent Hamiltonians; the N=2 validation is solid and the N=3 level-crossing claim is interesting but needs a convergence check for the fixed imaginary-time evolution. read the letter →

arxiv 2607.28964 v1 pith:JSQU7LXJ submitted 2026-07-31 quant-ph cond-mat.mes-hall

Yuntao Xiao , Yuchen Guo , Xiaojian Huang , Huixia Gao , Dengke Qu , Lei Xiao , Kunkun Wang , Shuo Yang
show 1 more author
Peng Xue
This is my paper · ORCID
classification quant-phcond-mat.mes-hall
keywords non-HermitianparentHamiltonianmatrixproductstatesimaginary-timeevolutionasymmetricAKLTstatesingle-photoninterferometryphasetransitionbiorthogonalquantummechanicschiralcorrelations
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 reports the first experimental construction of non-Hermitian parent Hamiltonians (NH-PHs) from a prescribed pair of matrix product states (MPSs). Using single-photon interferometry and imaginary-time evolution, the authors realize a two-site asymmetric AKLT model and measure order parameters that match the designed chiral, non-reciprocal, and antiferromagnetic correlations. Extending to a three-site model, they observe an intrinsic non-Hermitian phase transition signaled by abrupt jumps in an order parameter when the designed zero-energy state ceases to be the global ground state. The work demonstrates that non-Hermitian Hamiltonians can be reverse-engineered to have user-specified ground states, opening a route to engineered non-Hermitian phases and phase transitions.

What carries the argument

The load-bearing object is the non-Hermitian parent Hamiltonian (NH-PH), analytically constructed from a pair of MPSs that serve as the desired left and right zero-energy ground states. The experimental machinery is single-photon interferometry implementing imaginary-time evolution U_τ = e^{-Hτ} via a passive, gain-free mapping obtained by singular value decomposition: the unitary factors are realized with beam displacers and half-wave plates, while a diagonal loss matrix implements mode-selective attenuation. For the N=2 asymmetric AKLT state, the asymmetry parameter μ in the virtual bond controls non-Hermiticity; for the N=3 model, the phase φ in the local tensor drives the spectral crossi

What would settle it

Compute the excited-state population in the evolved state ρ_τ at the N=3 transition points for τ=10; if it is not exponentially small relative to the ground-state population, the observed order-parameter jumps are consistent with incomplete projection. Alternatively, repeat the experiment with τ=20 and check that the jump locations in φ remain unchanged.

Watch

Extended reading notes

Core claim

The central claim is that the non-Hermitian parent Hamiltonian method—which analytically constructs a local Hamiltonian whose left and right zero-energy ground states are a given pair of MPSs—can be implemented experimentally with single photons, and that the resulting states faithfully reproduce the designed properties. For the N=2 asymmetric AKLT chain, the measured order parameters ⟨O_AF⟩, ⟨O_left⟩, ⟨O_right⟩, and ⟨O_chiral⟩ agree with theoretical predictions across the asymmetry parameter μ. For the N=3 model, the ground-state energy and a ferromagnetic order parameter exhibit abrupt jumps at spectral crossings, providing experimental evidence of an intrinsic non-Hermitian phase transiti

Load-bearing premise

The experiment assumes that a fixed imaginary-time evolution of τ=10 fully projects the initial mixed state onto the targeted ground state for every scanned parameter, including near spectral crossings where the energy gap shrinks.

Editorial extensions

If this is right

  • The same photonic platform can construct parent Hamiltonians for arbitrary MPS pairs, enabling systematic studies of designed non-Hermitian phases beyond the AKLT and N=3 examples.
  • The order-parameter jumps observed at spectral crossings provide a direct signature of the breakdown of the non-Hermitian variational principle, which the authors connect to enhanced sensing near criticality.
  • The direct MPS-to-circuit mapping demonstrated in the cross-check offers a general recipe for preparing matrix product states on small quantum circuits.
  • The method is not limited to non-Hermitian systems: the authors note it can prepare ground states of Hermitian Hamiltonians by the same imaginary-time evolution, broadening its use as a quantum simulator.
  • The persistence of the phase transition for N=4, 6, and 10 (verified numerically) indicates the effect is not a finite-size artifact and should survive in larger implementations.

Reading between the lines

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

  • A testable extension is to repeat the N=3 scan with different imaginary-time evolution lengths (e.g., τ=5 and τ=20) to verify that the order-parameter jumps stay put; if they shift, the reported transition could be an artifact of incomplete projection rather than an intrinsic property.
  • The asymmetric-AKLT design suggests that longer chains built from the same tensors should exhibit a non-zero chiral order parameter in the bulk; measuring this on a photonic platform with more qubits is a natural next step.
  • Because the parent-Hamiltonian construction fixes left and right ground states independently, the scheme could be adapted to engineer transport or state-transfer channels that exploit a chosen biorthogonal pair—a direction the paper leaves implicit.
  • The demonstration that a passive loss-only operation can implement e^{-Hτ} for an arbitrary local H suggests the same optics toolbox can simulate other non-unitary processes, such as open-system dynamics, without gain.
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

3 major / 4 minor

Summary. The manuscript reports the first experimental realization of non-Hermitian parent Hamiltonians (NH-PHs) using single-photon interferometry. The authors start from a pair of matrix product states (MPSs) that serve as the designed left and right zero-energy ground states, construct the corresponding NH-PH following Ref. [48], and implement imaginary-time evolution through passive, gain-free non-unitary operations. For an N=2 asymmetric AKLT model, they reconstruct the left and right ground states by quantum state tomography and measure four order parameters (non-reciprocal, chiral, and antiferromagnetic) as a function of the asymmetry parameter μ, finding agreement with the analytic predictions. They also provide a direct MPS-preparation cross-check. For an N=3 model, they observe level crossings in the complex spectrum and abrupt jumps in a ferromagnetic order parameter, which they interpret as an intrinsic non-Hermitian phase transition. The paper claims to be the first experimental generation and characterization of NH-PHs with controllable and customizable properties.

Significance. If the results hold, the paper provides a useful proof-of-principle that the non-Hermitian parent Hamiltonian construction of Ref. [48] can be implemented in a photonic platform, enabling the reverse engineering of non-Hermitian Hamiltonians with prescribed biorthogonal ground states. The N=2 direct MPS-preparation cross-check is a particular strength, as it independently verifies that the target MPS states carry the designed correlations. The extension to N=3 and the observation of level-crossing-driven order-parameter jumps is conceptually interesting, but its interpretation as an 'intrinsic phase transition' rests on finite-system data and on the adequacy of the fixed imaginary-time evolution. The validation is largely a consistency check by construction, because the theoretical curves are computed from the same MPS states used to build the Hamiltonian; nevertheless, the experimental implementation of non-unitary evolution and the agreement with exact-diagonalization curves are nontrivial. With additional convergence and finite-size analysis, the paper would be a valuable contribution to non-Hermitian quantum simulation.

major comments (3)
  1. [Experimental implementation; Extension to a new N=3 model] The imaginary-time evolution is performed at a single fixed value τ=10, and no convergence criterion is given. In the N=3 model the real-part gap closes at the boundaries of φ∈(π/6,π/3) and φ∈(2π/3,5π/6) (Fig. 3). At such level crossings the Hamiltonian may become defective, in which case e^{-Hτ} contains polynomial-in-τ Jordan-block factors and a fixed, large τ is not guaranteed to project onto the zero-energy MPS. Without a residual excited-state population bound or a τ-scaling test, the abrupt jumps in ⟨Õ⟩ could in principle be an artifact of incomplete projection rather than the claimed intrinsic transition. Please add: (i) the N=3 real-part gap as a function of φ; (ii) the residual population of the designated zero-energy MPS after e^{-Hτ} at τ=10; and (iii) a comparison at least for τ=5,20,50 or state fidelities to the exact ground states.
  2. [Extension to a new N=3 model] The claim that the transition is 'not a finite-size effect' is supported only by a pointer to the Supplemental Material for N=4,6,10. No gap scaling, discontinuity size, or level-crossing data are presented. Since the transition is defined by finite-system level crossings and the authors explicitly separate it from conventional thermodynamic transitions, the word 'intrinsic' and the robustness statement need quantitative support. Please include a figure or table showing, for N=3,4,6,10 (and possibly larger N), the persistence of the level crossing and the behavior of the order-parameter jump with system size.
  3. [Experimental results; Fig. 2 and Fig. 3] The theoretical curves are computed from the same MPS pair used to construct the Hamiltonian. Agreement therefore validates the state-preparation and tomography chain, but is partly a consistency check rather than an independent confirmation of the NH-PH construction. The direct MPS-preparation cross-check for N=2 is a good control. To support the 'first experimental generation' claim, I recommend reporting state fidelities F(|Ψ_s^R⟩,|R⟩) and F(|Ψ_s^L⟩,|L⟩) for both N=2 and N=3, or an equivalent quantitative closeness measure, so the reader can assess how faithfully the imaginary-time evolution reproduces the designed zero modes.
minor comments (4)
  1. [Experimental results] The definitions σ± = σx ± iσy are inconsistent with the explicit /2 in O_left and O_right and with the quoted predictions (−μ/4, −1/(4μ)) unless σ± are normalized as (σx ± iσy)/2. Please fix the notation.
  2. [Experimental implementation] Specify the energy scale: 'τ=10 in natural units' is vague without the norm of H; the reader cannot assess whether 10 is large relative to the inverse gap. A statement of the smallest real-part gap encountered in the scanned parameter range would help.
  3. [Introduction; Conclusion] The phrase 'first experimental generation/realization' appears twice. Given the consistency-check nature of the validation, a more hedged phrasing such as 'first photonic implementation' would be safer unless the absence of prior experimental work is explicitly established.
  4. [Fig. 4] Typo in caption: 'MPSs tensors' should be 'MPS tensors'. Also, the relation between the boundary conditions and the tensor elements in Eq. (7) is not fully spelled out; a brief derivation would improve reproducibility.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the NH-PH is explicitly engineered from the chosen MPS pair, so the N=2 order-parameter agreement is a designed-state consistency check rather than a fitted prediction, and the N=3 transition is a nontrivial spectral property of the constructed Hamiltonian.

full rationale

The paper's derivation chain is self-contained. The construction is explicit: Eq. (5) gives the N=2 Hamiltonian, and the N=3 Hamiltonian is built from the tensors in Eq. (6). The theoretical curves in Fig. 2 are obtained by evaluating order parameters on the designed left/right ground states ('Theoretically, evaluating these order parameters on the designed ground states yields...'), which is by construction, but the paper presents this as a validation of the photonic implementation, not as an independent prediction from the Hamiltonian. No parameters are fitted to the experimental data; the μ and φ dependencies are fixed by the MPS design. The N=3 phase transition is different: the theory curves come from exact diagonalization of the constructed Hamiltonian, and the order-parameter jumps occur where the designated zero-energy MPS ceases to be the global ground state. This is a nontrivial spectral property, not an input to the construction, and the paper checks the same transition for N=4, 6, 10. The only self-citations are Refs. [48] and [49] by coauthors Guo and Yang, which provide the NH-PH construction and the breakdown of the non-Hermitian variational principle; however, the construction is restated explicitly in the present paper and independently cross-checked by the direct MPS preparation in the End Matter, so those citations are not load-bearing in a circular way. The fixed τ=10 imaginary-time evolution is a correctness/robustness concern, not a circularity issue. No circular step is exhibited, so the circularity burden is low.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the cited NH-PH construction theorem, the biorthogonal framework, and the photonic imaginary-time evolution mapping. No new entities are postulated. The only adjustable inputs are the design parameters μ and φ, which are not fitted to data.

free parameters (2)
  • μ (asymmetry parameter)
    Asymmetry parameter in the AKLT MPS tensor, scanned over 1/3 to 3; chosen by hand, not fitted to data. It tunes the designed chirality/non-Hermiticity.
  • φ (phase parameter)
    Phase parameter in the N=3 MPS tensor, scanned over [0,2π); chosen by hand, not fitted. It tunes the location of the level-crossing transition.
assumptions (4)
  • domain assumption Existence of NH-PH for a given MPS pair.
    Construction theorem invoked from Ref [48]; the paper's Hamiltonians H (Eq. 5) and H̃ are accepted as parent Hamiltonians without re-derivation.
  • domain assumption Imaginary-time evolution e^{-Hτ} projects onto the ground state with smallest real-part eigenvalue.
    Used in Experimental implementation to extract left/right ground states; assumes non-zero overlap and a spectral gap; no convergence check.
  • standard math Rescaled passive operation Ũτ = Uτ e^{-Λ(τ)} shares eigenstates with Uτ.
    SVD-based mapping from Ref [67] to avoid gain in photonic implementation; relies on global scale not changing eigenstates.
  • ad hoc to paper Choice |L⟩ = P|R⟩ (N=2) and |L̃⟩ = K|R̃⟩ (N=3) yield the intended left zero-energy modes.
    These choices define the left states and are part of the design, not independently justified; central claims about left-ground-state properties depend on them.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems." pith.science (2026). https://pith.science/paper/JSQU7LXJ

@misc{pith2026260728964,
  author       = {Pith},
  title        = {Pith review of: Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JSQU7LXJ}},
  note         = {Machine review of arXiv:2607.28964}
}
read the original abstract

Non-Hermitian systems host phenomena absent in Hermitian physics, but realizing Hamiltonians with intrinsic non-Hermitian properties remains challenging. The theoretical method of non-Hermitian parent Hamiltonian (NH-PH) enables the construction of a non-Hermitian system from a pair of matrix product states (MPSs) with tailored properties. Here, we report the first experimental generation of NH-PHs. This generation starts from MPSs that represent asymmetric Affleck--Kennedy--Lieb--Tasaki (AKLT) states. The construction is validated with single photons via imaginary-time evolution of the generated NH-PH to obtain its left and right ground states. We then characterize the properties of the system by measuring four different order parameters that probe non-reciprocal correlations, chiral imbalance, and conventional antiferromagnetic correlations. Furthermore, extending the framework to a larger system with a different model, we observe an intrinsic non-Hermitian phase transition, manifested by abrupt jumps of an order parameter when the designated zero-energy modes cease to be the globally lowest-energy states. Our work provides the first experimental realization and characterization of non-Hermitian Hamiltonians with controllable and customizable properties, opening new avenues for exploring intrinsic non-Hermitian phenomena across diverse physical platforms.

Figures

Figures reproduced from arXiv: 2607.28964 by the authors.

Figure 1
Figure 1. FIG. 1. Experimental setup. A heralded single photon is created via type-II spontaneous parametric down-conversion via a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The expectation values of order parameters [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Real (a) and imaginary (b) parts of the ground-state [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The mapping from MPSs tensors to unitary op [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The expectation values of order parameters [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

79 extracted references

  1. [48]

    R. Shen, Y. Guo, and S. Yang, Construction of non- Hermitian parent Hamiltonian from matrix product states, Phys. Rev. Lett.130, 220401 (2023)

    2023

  2. [1]

    Hatano and D

    N. Hatano and D. R. Nelson, Localization transitions in non-Hermitian quantum mechanics, Phys. Rev. Lett.77, 570 (1996)

    1996

  3. [2]

    C. M. Bender, Making sense of non-Hermitian Hamilto- nians, Rep. Prog. Phys.70, 947 (2007)

    2007

  4. [3]

    Lieu, Topological phases in the non-Hermitian Su- Schrieffer-Heeger model, Phys

    S. Lieu, Topological phases in the non-Hermitian Su- Schrieffer-Heeger model, Phys. Rev. B97, 045106 (2018)

    2018

  5. [4]

    Ashida, Z

    Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys.69, 249 (2020). 6

    2020

  6. [5]

    L. Pan, X. Chen, Y. Chen, and H. Zhai, Non-Hermitian linear response theory, Nat. Phys.16, 767 (2020)

    2020

  7. [6]

    Müller and I

    M. Müller and I. Rotter, Exceptional points in open quantum systems, J. Phys. A: Math. Theor.41, 244018 (2008)

    2008

  8. [7]

    Miri and A

    M.-A. Miri and A. Alù, Exceptional points in optics and photonics, Science363, eaar7709 (2019)

    2019

Show all 79 references
  1. [8]

    Ghatak, M

    A. Ghatak, M. Brandenbourger, J. van Wezel, and C. Coulais, Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial, Proc. Natl. Acad. Sci. USA117, 29561 (2020)

    2020

  2. [9]

    K. Ding, C. Fang, and G. Ma, Non-Hermitian topology and exceptional-point geometries, Nat. Rev. Phys.4, 745 (2022)

    2022

  3. [10]

    W. Mao, Z. Fu, Y. Li, F. Li, and L. Yang, Exceptional- point-enhanced phase sensing, Sci. Adv.10, eadl5037 (2024)

    2024

  4. [11]

    Xue, Essay: Topological phases and exceptional points in non-Hermitian systems, Phys

    P. Xue, Essay: Topological phases and exceptional points in non-Hermitian systems, Phys. Rev. Lett.136, 170001 (2026)

    2026

  5. [12]

    T. E. Lee, Anomalous edge state in a non-Hermitian lat- tice, Phys. Rev. Lett.116, 133903 (2016)

    2016

  6. [13]

    S. Yao, F. Song, and Z. Wang, Non-Hermitian Chern bands, Phys. Rev. Lett.121, 136802 (2018)

    2018

  7. [14]

    F. Song, S. Yao, and Z. Wang, Non-Hermitian skin effect and chiral damping in open quantum systems, Phys. Rev. Lett.123, 170401 (2019)

    2019

  8. [15]

    L. Li, C. H. Lee, S. Mu, and J. Gong, Critical non- Hermitian skin effect, Nat. Commun.11, 5491 (2020)

    2020

  9. [16]

    Zhang, Y

    X. Zhang, Y. Tian, J.-H. Jiang, M.-H. Lu, and Y.- F. Chen, Observation of higher-order non-Hermitian skin effect, Nat. Commun.12, 5377 (2021)

    2021

  10. [17]

    L. Xiao, Y. Chu, Q. Lin, H. Lin, W. Yi, J. Cai, and P. Xue, Non-Hermitian sensing in the absence of excep- tional points, Phys. Rev. Lett.133, 180801 (2024)

    2024

  11. [18]

    Li, X.-W

    Z. Li, X.-W. Luo, D. Lin, A. Gharajeh, J. Moon, J. Hou, C. Zhang, and Q. Gu, Topological microlaser with a non- Hermitian topological bulk, Phys. Rev. Lett.131, 023202 (2023)

    2023

  12. [19]

    del Pino, J

    J. del Pino, J. J. Slim, and E. Verhagen, Non- Hermitian chiral phononics through optomechanically in- duced squeezing, Nature606, 82–87 (2022)

    2022

  13. [20]

    Khandelwal, W

    S. Khandelwal, W. Chen, K. W. Murch, and G. Haack, Chiral Bell-State transfer via dissipative Liouvillian dy- namics, Phys. Rev. Lett.133, 070403 (2024)

    2024

  14. [21]

    H. Gao, K. Sun, D. Qu, K. Wang, L. Xiao, W. Yi, and P. Xue, Photonic chiral state transfer near the Liouvillian exceptional point, Phys. Rev. Lett.134, 146602 (2025)

    2025

  15. [22]

    Z.-Z. Li, W. Chen, M. Abbasi, K. W. Murch, and K. B. Whaley, Speeding up entanglement generation by proximity to higher-order exceptional points, Phys. Rev. Lett.131, 100202 (2023)

    2023

  16. [23]

    L. Xiao, X. Zhan, Z.-H. Bian, K.-K. Wang, X. Zhang, X.-P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, and P. Xue, Observa- tion of topological edge states in parity-time-symmetric quantum walks, Nat. Phys.13, 1117 (2017)

    2017

  17. [24]

    W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an op- tical microcavity, Nature548, 192 (2017)

    2017

  18. [25]

    Reisenbauer, H

    M. Reisenbauer, H. Rudolph, L. Egyed, K. Hornberger, A. V. Zasedatelev, M. Abuzarli, B. A. Stickler, and U. Delić, Non-Hermitian dynamics and non-reciprocity of optically coupled nanoparticles, Nat. Phys.20, 1629 (2024)

    2024

  19. [26]

    T. Dai, Y. Ao, J. Mao, Y. Yang, Y. Zheng, C. Zhai, Y. Li, J. Yuan, B. Tang, Z. Li, J. Luo, W. Wang, X. Hu, Q. Gong, and J. Wang, Non-Hermitian topological phase transitions controlled by nonlinearity, Nat. Phys.20, 101 (2024)

    2024

  20. [27]

    K. Wang, L. Xiao, H. Lin, W. Yi, E. J. Bergholtz, and P. Xue, Experimental simulation of symmetry-protected higher-order exceptional points with single photons, Sci. Adv.9, eadi0732 (2023)

    2023

  21. [28]

    L. Xiao, K. Wang, D. Qu, H. Gao, Q. Lin, Z. Bian, X. Zhan, and P. Xue, Non-Hermitian physics in photonic systems, Photonics Insights4, R09 (2025)

    2025

  22. [29]

    H. Gao, H. Xue, Z. Gu, T. Liu, J. Zhu, and B. Zhang, Non-Hermitian route to higher-order topology in an acoustic crystal, Nat. Commun.12, 1888 (2021)

    2021

  23. [30]

    Zhang, Y

    L. Zhang, Y. Yang, Y. Ge, Y.-J. Guan, Q. Chen, Q. Yan, F. Chen, R. Xi, Y. Li, D. Jia, S.-Q. Yuan, H.-X. Sun, H. Chen, and B. Zhang, Acoustic non-Hermitian skin effect from twisted winding topology, Nat. Commun.12, 6297 (2021)

    2021

  24. [31]

    J. Wu, R. Zheng, J. Liang, M. Ke, J. Lu, W. Deng, X. Huang, and Z. Liu, Spin-dependent localization of helical edge states in a non-Hermitian phononic crystal, Phys. Rev. Lett.133, 126601 (2024)

    2024

  25. [32]

    W. Chen, M. Abbasi, Y. N. Joglekar, and K. W. Murch, Quantum jumps in the non-Hermitian dynamics of a superconducting qubit, Phys. Rev. Lett.127, 140504 (2021)

    2021

  26. [33]

    Helbig, T

    T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L.-W. Molenkamp, C.-H. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys.16, 747 (2020)

    2020

  27. [34]

    S. Liu, R. Shao, S. Ma, L. Zhang, O. You, H. Wu, Y. J. Xiang, T.-J. Cui, and S. Zhang, Non-Hermitian skin effect in a non-Hermitian electrical circuit, Research 2021, 5608038 (2021)

    2021

  28. [35]

    T. Gao, E. Estrecho, K. Y. Bliokh, T. C. H. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, Observation of non-Hermitian degeneracies in a chaotic exciton-polariton bill...

    2015

  29. [36]

    Yao and Z

    S. Yao and Z. Wang, Edge states and topological invari- ants of non-Hermitian systems, Phys. Rev. Lett.121, 086803 (2018)

    2018

  30. [37]

    Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Hi- gashikawa, and M. Ueda, Topological phases of non- Hermitian systems, Phys. Rev. X8, 031079 (2018)

    2018

  31. [38]

    D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Non- Hermitian boundary modes and topology, Phys. Rev. Lett.124, 056802 (2020)

    2020

  32. [39]

    F. K. Kunst, E. Edvardsson, J. C. Budich, and E. J. Bergholtz, Biorthogonal bulk-boundary correspon- dence in non-Hermitian systems, Phys. Rev. Lett.121, 026808 (2018)

    2018

  33. [40]

    Affleck, T

    I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rig- orous results on valence-bond ground states in antiferro- magnets, Phys. Rev. Lett.59, 799 (1987)

    1987

  34. [41]

    Pérez-García, F

    D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quan- tum Inf. Comput.7, 401 (2007). 7

    2007

  35. [42]

    Verstraete, V

    F. Verstraete, V. Murg, and J. I. Cirac, Matrix prod- uct states, projected entangled pair states, and varia- tional renormalization group methods for quantum spin systems, Adv. Phys.57, 143 (2008)

    2008

  36. [43]

    Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann

    U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011)

    2011

  37. [44]

    Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann

    R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys.349, 117 (2014)

    2014

  38. [45]

    J. I. Cirac, D. Pérez-García, N. Schuch, and F. Ver- straete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys.93, 045003 (2021)

    2021

  39. [46]

    Greiter, D

    M. Greiter, D. F. Schroeter, and R. Thomale, Parent Hamiltonian for the non-Abelian chiral spin liquid, Phys. Rev. B89, 165125 (2014)

    2014

  40. [47]

    Haegeman, K

    J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac, and F. Verstraete, Gauging quantum states: From global to local symmetries in many-body systems, Phys. Rev. X 5, 011024 (2015)

    2015

  41. [49]

    Y. Guo, R. Shen, and S. Yang, Composite quantum phases in non-Hermitian systems, Phys. Rev. Research 5, 033181 (2023)

    2023

  42. [50]

    Maekawa and H

    D. Maekawa and H. Tasaki, The asymmetric valence- bond-solid states in quantum spin chains: The difference between odd and even spins, J. Math. Phys.64, 031901 (2023)

    2023

  43. [51]

    D. C. Brody, Biorthogonal quantum mechanics, J. Phys. A: Math. Theor.47, 035305 (2014)

    2014

  44. [52]

    See Supplemental Material at [ ] for details on the con- struction of non-Hermitian parent Hamiltonians, quan- tum state and process tomography, experimental imple- mentationsofimaginary-timeevolutionandquantumcir- cuits, and numerical results for larger systems, which in- clu...

  45. [53]

    Raussendorf and H

    R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett.86, 5188 (2001)

    2001

  46. [54]

    Toninelli, B

    E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, Concepts in quantum state tomography and classical im- plementation with intense light: A tutorial, Adv. Opt. Photon.11, 67 (2019)

    2019

  47. [55]

    M. F. Z. Arruda, W. C. Soares, S. P. Walborn, D. S. Tasca, A. Kanaan, R. Medeiros de Araújo, and P. H. Souto Ribeiro, Klyshko’s advanced-wave picture in stimulated parametric down-conversion with a spatially structured pump beam, Phys. Rev. A98, 023850 (2018)

    2018

  48. [56]

    M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, Cambridge University Press, Cambridge (2000)

    2000

  49. [57]

    I. L. Chuang and M. A. Nielsen, Prescription for ex- perimental determination of the dynamics of a quantum black box, J. Mod. Opt.44, 2455 (1997)

    1997

  50. [58]

    X.Wang, C.-S.Yu, andX.X.Yi, Analternativequantum fidelity for mixed states of qudits, Phys. Lett. A373, 58 (2008)

    2008

  51. [59]

    Zhang, G

    W.-H. Zhang, G. Chen, X.-X. Peng, X.-J. Ye, P. Yin, Y. Xiao, Z.-B. Hou, Z.-D. Cheng, Y.-C. Wu, J.-S. Xu, C.- F. Li, and G.-C. Guo, Experimentally robust self-testing for bipartite and tripartite entangled states, Phys. Rev. Lett.121, 240402 (2018)

    2018

  52. [60]

    M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Experimental realization of any discrete unitary opera- tor, Phys. Rev. Lett.73, 58 (1994)

    1994

  53. [61]

    L. Xiao, D. Qu, K. Wang, H.-W. Li, J.-Y. Dai, B. Dóra, M.Heyl, R.Moessner, W.Yi, andP.Xue, Non-Hermitian Kibble-Zurek mechanism with tunable complexity in single-photon interferometry, PRX Quantum2, 020313 (2021)

    2021

  54. [62]

    T.-C. Wei, R. Raussendorf, and I. Affleck, Some aspects of Affleck–Kennedy–Lieb–Tasaki models: Tensor net- work, physical properties, spectral gap, deformation, and quantum computation, in entanglement in spin chains: From theory to quantum technology applications, edited by A...

    2022

  55. [63]

    K. C. Smith, E. Crane, N. Wiebe, and S. M. Girvin, Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements, PRX Quantum4, 020315 (2023)

    2023

  56. [64]

    McArdle, T

    S. McArdle, T. Jones, S. Endo, Y. Li, S. C. Benjamin, and X. Yuan, Variational ansatz-based quantum simula- tion of imaginary time evolution, npj Quantum Inf.5, 75 (2019)

    2019

  57. [65]

    Motta, C

    M. Motta, C. Sun, A. T. K. Tan, M. J. O’Rourke, E. Ye, A. J. Minnich, F. G. S. L. Brandão, and G. K.-L. Chan, Determining eigenstates and thermal states on a quan- tum computer using quantum imaginary time evolution, Nat. Phys.16, 205 (2020)

    2020

  58. [66]

    K. Wang, L. Xiao, J. C. Budich, W. Yi, and P. Xue, Sim- ulating exceptional non-Hermitian metals with single- photon interferometry, Phys. Rev. Lett.127, 026404 (2021)

    2021

  59. [67]

    Tischler, C

    N. Tischler, C. Rockstuhl, and K. Słowik, Quantum opti- cal realization of arbitrary linear transformations allow- ing for loss and gain, Phys. Rev. X8, 021017 (2018)

    2018

  60. [68]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quantum sim- ulation, Rev. Mod. Phys.86, 153 (2014)

    2014

  61. [69]

    A. A. Houck, H. E. Türeci, and J. Koch, On-chip quan- tumsimulationwithsuperconductingcircuits, Nat.Phys. 8, 292–299 (2012)

    2012

  62. [70]

    Gerritsma, G

    R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, Quantum simulation of the Dirac equation, Nature463, 68–71 (2010)

    2010

  63. [71]

    P. J. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jef- frey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley, C. Neill, C. Quin...

    2016

  64. [72]

    Pérez-García, M

    D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac, String order and symmetries in quantum spin lattices, Phys. Rev. Lett.100, 167202 (2008)

    2008

  65. [73]

    Pollmann, A

    F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one di- mension, Phys. Rev. B81, 064439 (2010)

    2010

  66. [74]

    B. Song, S. Dutta, S. Bhave, J.-C. Yu, Jr., E. Carter, N. Cooper, and U. Schneider, Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice, Nat. Phys.18, 259–264 (2022). 8

    2022

  67. [75]

    Beaulieu, F

    G. Beaulieu, F. Minganti, S. Frasca, V. Savona, S. Fe- licetti, R. Di Candia, and P. Scarlino, Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator, Nat. Commun.16, 1954 (2025)

    1954

  68. [76]

    Cai, Z.-D

    M.-L. Cai, Z.-D. Liu, W.-D. Zhao, Y.-K. Wu, Q.-X. Mei, Y. Jiang, L. He, X. Zhang, Z.-C. Zhou, and L.-M. Duan, Observation of a quantum phase transition in the quan- tumRabimodelwithasingletrappedion, Nat.Commun. 12, 1126 (2021)

    2021

  69. [77]

    Alushi, W

    U. Alushi, W. Górecki, S. Felicetti, and R. Di Candia, Optimality and noise resilience of critical quantum sens- ing, Phys. Rev. Lett.133, 040801 (2024)

    2024

  70. [78]

    Hotter, H

    C. Hotter, H. Ritsch, and K. Gietka, Combining critical and quantum metrology, Phys. Rev. Lett.132, 060801 (2024)

    2024

  71. [79]

    Barratt, J

    F. Barratt, J. Dborin, M. Bal, V. Stojevic, F. Pollmann, and A. G. Green, Parallel quantum simulation of large systems on small NISQ computers, npj Quantum Inf.7, 79 (2021). End Matter Direct MPS preparation forN= 2.— As an independent cross-check, we directly generate the tar...

    2021

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.