{"id":"65a8d55f-be36-4175-bdcf-e6699c4100c6","arxiv_id":"2506.22418","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A quantum auto-correlation function integrated over an extra time variable yields eigenenergies and eigenstate observables for Hermitian, non-Hermitian, and Floquet systems, demonstrated on a silicon-photonic chip.","lead":"Researchers demonstrate a quantum spectroscopy framework that reconstructs eigenstate-resolved spectra of closed, open, and periodically driven quantum systems using a programmable photonic chip. If correct, it gives quantum simulators a way to probe non-Hermitian and Floquet phenomena that conventional spectroscopy and eigenstate algorithms cannot reach.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (2) requires real, non-degenerate quasi-eigenenergies; for PT-broken (complex-energy) open systems the η-integral diverges, so the advertised 'universal' spectroscopy of open systems is not established by the paper's own derivation.","rationale":"The paper presents a coherent construction and the small-scale demonstrations are internally consistent: the Hermitian spin-chain results match exact eigenenergies and eigenstate properties, the silicon-photonic chip shows high-fidelity controlled-unitary operation, and the Floquet spectra agree with theory. The central theoretical object, Eq. (1), is a legitimate time-correlation function, and Eq. (2) follows under the explicit assumption of real, gapped, non-degenerate quasi-eigenenergies. The load-bearing weakness is that this assumption is not sufficient for the advertised universality: complex quasi-energies (PT-broken phases) make the η-integral ill-defined, and exact degeneracies also break phase orthogonality. The paper's own text acknowledges this restriction at several points, but the abstract and conclusion claim universal spectroscopy for open systems without that caveat. The reader's weakest_assumption identifies the same fundamental condition, and the conditional verdict is appropriate. The concrete test I propose would settle the matter by exposing the τ-dependence of the cross terms in the PT-broken regime, thereby showing whether Eq. (2) can be salvaged for complex energies or whether the universal claim must be narrowed. No part of the critique targets the authors' integrity; the issue is purely the scope of the mathematical claim relative to the stated examples.","tokens_in":92984,"tokens_out":13777,"duration_ms":151573,"concrete_test":"Compute the Gaussian-windowed C_{Î,ψ}(t) analytically for the 2×2 Hamiltonian in Eq. (4) at g = 0.6 (PT-broken, eigenvalues 1 ± i√(g² - κ²)) for τ = 6, 12, 24. If the off-diagonal contributions grow as exp[τ²(g² - κ²)] and the relative peak amplitudes change with τ, then Eq. (2) fails for complex quasi-energies and the universal open-system claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The derivation of Eq. (2) integrates e^{i(E_m^* - E_n)η} over η to obtain 2πδ(E_n - E_m). This is only valid when all quasi-eigenenergies are real, and even then degenerate real levels leave cross terms because the phase factor is unity for every η; the stated condition 'gapped in the real part' does not exclude exact degeneracy and is therefore weaker than what the amplitude-ratio extraction needs. For genuinely complex quasi-eigenenergies, the Gaussian-windowed η-integral is proportional to exp[-τ²(E_m^* - E_n)²/2]; when the imaginary part of E_m^* - E_n exceeds the real part, this factor grows exponentially with τ, so the off-diagonal contributions do not vanish as the window widens. Consequently C_{Ô,ψ}(t) cannot be reduced to isolated peaks with amplitudes |c_n|²⟨u_n|Ô|u_n⟩, and the ratio C_Ô(E_n)/C_Î(E_n) is not a well-defined eigenstate expectation value. The paper's PT-broken experiment (Fig. 4g) does not test Eq. (2): it instead measures A(t) = Tr(e^{-iHt})/d from a maximally mixed initial state and extracts only the real parts of the complex eigenenergies, not eigenstate-resolved observable expectation values. Thus the central claim of universal eigenstate-resolved spectroscopy for general open systems overreaches; the rigorously supported domain is real, non-degenerate quasi-eigenenergies.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Universal Quantum Computational Spectroscopy (UQCS), a framework that estimates the spectral properties of a quantum system from a quantum auto-correlation function C_{O,ψ}(t) = ∫ dη ⟨ψ|U†(η) O U(η+t)|ψ⟩. Fourier-transforming this function is claimed to produce peaks at the quasi-eigenenergies of the system, and the ratios of peak amplitudes for different observables are claimed to yield eigenstate expectation values. The method is presented as universal, covering closed, open (non-Hermitian), and time-dependent (Floquet) systems. The authors experimentally implement the required controlled-evolution circuits on a programmable silicon-photonic chip and demonstrate the approach on an anisotropic Heisenberg spin chain, a PT-symmetric non-Hermitian two-mode system, and a periodically driven spin-3/2 system, extracting energies, expectation values, PT phase transitions, and topological holonomy. Numerical benchmarking against IQPE, QETU, and other methods is also reported.","tokens_in":93379,"tokens_out":7384,"duration_ms":76270,"significance":"If the central claim holds, UQCS is a significant methodological advance: it offers eigenstate-resolved spectroscopy without requiring eigenstate preparation, and it is demonstrated experimentally with good agreement to exact values and without fitted parameters. The paper includes a programmable photonic-chip demonstration, state tomography of eigenstates, a PT-transition scan, and Floquet holonomy extraction, together with open-source simulation code. These strengths make the manuscript of considerable interest to the quantum simulation and quantum photonics communities. The significance is moderated, however, by the gap between the advertised universality and the rigorous domain of the derivation, as detailed in the major comments below.","major_comments":[{"comment":"The reduction of Eq. (1) to Eq. (2) uses ∫ dη e^{i(E_m^* − E_n)η} = 2πδ(E_n − E_m), which is only defined when E_n and E_m are real; for complex quasi-eigenenergies the integral does not converge, and for degenerate real energies the phase factor is unity for all η, so cross terms between degenerate states survive. The condition stated in the text (\"quasi-eigenenergies gapped in the real part\") excludes the PT-broken phase but does not by itself rule out exact degeneracy of real parts. The PT-broken experiment (Fig. 4g) does not test Eq. (2): it measures A(t) = Tr(e^{−iHt})/d from a maximally mixed initial state and extracts only the real parts of the complex energies. The manuscript should therefore either restrict the central claim of eigenstate-resolved spectroscopy to real, non-degenerate quasi-eigenenergies, or provide a separate rigorous treatment of the degenerate and complex-energy cases.","section":"The UQCS framework, Eq. (2)"},{"comment":"The complexity bound O((√(2 ln(1/ϵ1)) R(H)/ΔE_min)^2/ϵ_2^2) and the claim of a <0.01% truncation error are stated with reference to \"Supplementary Information Section ??\", which is not present in the manuscript. The scaling reported in Fig. 5b and Table 1 depends on this bound, and the derivation in Methods is only a sketch: for example, the relation |δω|^2 ≈ 2|δf|/(ζ^2 τ^2) is introduced without justification. The missing error analysis should be supplied before the performance claims can be evaluated.","section":"The UQCS framework (complexity statement) and Methods (Query depth)"},{"comment":"The Floquet experiments use initial states with support on doubly degenerate static eigenspaces (the B^2/4 and 9B^2/4 manifolds). In a degenerate subspace the phase factors e^{−iE_n t} are identical, so the integrand of Eq. (1) contains non-vanishing cross terms ⟨u_n|O|u_m⟩ that are not captured by Eq. (2); the stated \"gapped in the real part\" condition does not address this. Although the paper only extracts quasi-energy positions and splittings (not amplitude-ratio expectation values) in the Floquet section, the text should state the precise conditions under which the Fourier peaks of Eq. (1) can be identified with quasi-eigenenergies in the presence of degeneracy.","section":"Periodically driven quantum systems (Floquet experiments)"}],"minor_comments":[{"comment":"There are multiple typos: \"The practical implementation of UCQS\" should be UQCS; \"The chip is is controlled\" has a duplicated \"is\"; \"furtherly\" should be \"furthermore\"; \"exbibit\" and \"requries\" appear in the benchmarking section; \"Herimtian\" appears in the Methods.","section":"Throughout"},{"comment":"The double sum over n and m with |c_n|^2 and δ(E_n−E_m) is ambiguous: for non-degenerate real energies it should reduce to a single sum over n (i.e., n=m), and the current notation suggests a divergent δ(0) for degenerate states. Please rewrite the expression with the summation indices made explicit.","section":"Eq. (2)"},{"comment":"The phrase \"quasi-eigenstates generally form one non-orthogonal set\" should read \"form a non-orthogonal set\".","section":"First section of main text"},{"comment":"The reference to \"Supplementary Information Section ??\" appears twice in the main text; please replace it with the actual section number once the supplementary material is included.","section":"Main text, complexity paragraph"}],"recommendation":"major_revision","confidential_remarks":"The experimental platform is impressive and the core idea is promising, but the universality claim in the title and abstract exceeds the rigorously proven domain, which currently covers real, non-degenerate quasi-eigenenergies. The missing error analysis for the complexity bound is a substantive gap. I recommend major revision rather than rejection, since the issues appear addressable by narrowing the formal claims, adding a separate treatment of the trace-based PT-broken protocol, and supplying the missing derivations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things up front. The paper has a real, usable idea: the η-averaged two-time correlation C(t)=∫dη⟨ψ|U†(η)OU(η+t)|ψ⟩, with off-diagonal terms suppressed by phase orthogonality, so Fourier peaks give quasi-energies and peak ratios give eigenstate expectation values. The silicon-photonic implementation is careful and the experimental spectra match exact theory. The Floquet demonstrations—Berry phase from the energy shift and SU(2) Wilson loop from the splitting—are genuinely new and the most convincing part of the paper. No parameters are fitted to target energies; comparisons are against independent exact values. That is solid, reproducible work.\n\nThe soft spot is the word 'universal.' The derivation of Eq. (2) requires real, non-degenerate quasi-energies. The η integral only becomes a delta for real frequency differences; for complex quasi-energies the integral diverges, and with the Gaussian window the off-diagonal factors grow exponentially when the imaginary part dominates. Exact degeneracy also leaves cross terms because the phase factor is unity for all η. The paper states the condition as 'gapped in the real part,' which is weaker than what Eq. (2) needs. So the rigorously supported domain is Hermitian or PT-exact systems with real gapped quasi-energies, and Floquet systems with the same property. The PT-broken experiment in Fig. 4g does not test Eq. (2): it uses the trace quantity A(t)=Tr(e^{-iHt})/d and reads off real parts of complex energies. That is a legitimate variant, but it is not eigenstate-resolved spectroscopy, and it does not extend Eq. (2) to the non-Hermitian broken phase. The abstract and intro still say 'universal' and 'open systems' without that qualification. The missing SI error analysis (referenced as Section ??) and the 'data upon request' policy are smaller but real issues; the code is on GitHub, which helps.\n\nThe citation pattern looks honest. Ref [22] is a co-author's spectral-filtering paper, but the central construction and the photonic implementations go beyond it, and there is no circular fitting.\n\nWho should read this: anyone working on quantum algorithms for eigenstate-resolved spectra or on Floquet topological spectroscopy. The real-gapped part of the paper is publishable as is; the universal claim needs to be either narrowed or backed by a real treatment of complex energies. I'd send it to a serious referee, with instructions to focus on the non-Hermitian scope and the missing supplementary derivation.","headline":"The η-averaged correlation is a real advance for real, gapped quasi-energy spectra, and the photonic Floquet demonstrations are strong; but the 'universal' open-system claim outruns the derivation.","tokens_in":93894,"tokens_out":3235,"would_cite":true,"duration_ms":34040,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.67.Ac","03.67.Lx","42.50.Ex"],"model":"deepseek-v4-flash","headline":"A single measured correlation function reconstructs eigenenergies and per-eigenstate observable values for closed, open (non-Hermitian), and time-dependent (Floquet) quantum systems, a regime where standard phase-estimation and…","keywords":["quantum computational spectroscopy","quantum auto-correlation function","eigenstate-resolved spectroscopy","non-Hermitian quantum systems","parity-time symmetry breaking","Floquet quasi-energy","topological holonomy","silicon-photonic quantum chip"],"falsifier":"Run UQCS on a two-level non-Hermitian Hamiltonian swept past its exceptional point so the eigenenergies become a complex-conjugate pair, and compare the amplitude-ratio estimates of $\\langle u_n|\\hat O|u_n\\rangle$ with exact biorthogonal values: the identity (2) predicts the reconstruction to degrade as the imaginary parts grow, since the $\\eta$-integral no longer yields a delta function, and the paper's own PT-broken-phase spectra already show negative amplitudes and oscillations. Alternatively, drive a Hermitian system through an avoided crossing so that $\\Delta E_{\\min}$ falls below $1/\\tau$, and check whether the two Gaussian peaks merge and the recovered observable drifts toward the overlap-weighted average rather than either exact eigenvalue.","tokens_in":92841,"feed_emoji":"🔬","tokens_out":13765,"duration_ms":133657,"temperature":0.7,"pith_summary":"The paper claims that one quantum correlation function — the time-ordered overlap $C_{\\hat O,\\psi}(t) = \\int d\\eta\\,\\langle\\psi|\\hat U^\\dagger(\\eta)\\hat O\\hat U(\\eta+t)|\\psi\\rangle$ — encodes the complete eigenstate-resolved spectrum of a quantum system, and that a Fourier transform of it yields the quasi-eigenenergies $E_n$ as peaks while amplitude ratios give the expectation value of any observable in each eigenstate. This works not only for closed Hermitian systems, which standard quantum algorithms already handle, but for non-Hermitian (open) and periodically driven (Floquet) systems, where eigenstates are non-orthogonal and conventional spectroscopy sees only energy differences rather than the absolute energies themselves. If correct, the method replaces eigenstate preparation with measurement of controlled time evolution, giving eigenstate tomography, exceptional-point detection, and topological-holonomy readouts in one framework. The paper backs the claim with experiments on a programmable silicon-photonic chip and with numerical benchmarks against iterative quantum phase estimation and quantum eigenvalue transformation.","feed_headline":"One correlation function decodes whole quantum spectra","feed_subtitle":"It yields eigenenergies and eigenstate observables for non-Hermitian and Floquet systems, verified on a photonic chip.","key_machinery":"The object carrying the argument is the quantum auto-correlation function $C_{\\hat O,\\psi}(t) = \\int d\\eta\\,\\langle\\psi|\\hat U^\\dagger(\\eta)\\hat O\\hat U(\\eta+t)|\\psi\\rangle$, measured by a generalised Hadamard test that runs two time evolutions offset by $\\eta$ (one of them controlled) together with a controlled Pauli decomposition of $\\hat O$. The mechanism is phase orthogonality: the exponentials $e^{-iE_n\\eta}$ annihilate cross terms between distinct gapped quasi-eigenstates when integrated over $\\eta$, transforming the non-orthogonal expansion of the state into the sparse diagonal form of Equation (2). A Gaussian window of width $\\tau$ with $\\tau\\,\\Delta E_{\\min}\\gg 1$ replaces the ideal Dirac delta, time sampling follows the Nyquist–Shannon theorem, singular spectrum renormalisation suppresses gate noise, and a silicon-photonic chip realising four-dimensional controlled unitaries with classical fidelity above 0.996 supplies the controlled dynamics that make the correlations measurable.","core_discovery":"The central discovery is that gapped phase factors, not the eigenstates themselves, carry the orthogonality: for any dynamics admitting an expansion $\\hat U(t)|\\psi\\rangle = \\sum_n c_n e^{-iE_n t}|u_n\\rangle$, the functions $e^{-iE_n\\eta}$ form an orthogonal set whenever the quasi-eigenenergies $E_n$ (the Fourier harmonic frequencies of the evolved state) are real and separated, so cross terms between different components vanish under the $\\eta$-integral. Equation (2), $C_{\\hat O,\\psi}(t) = 2\\pi\\sum_{n,m}|c_n|^2 e^{-iE_n t}\\delta(E_n-E_m)\\langle u_n|\\hat O|u_n\\rangle$, then reduces the entire spectral problem to Fourier analysis of one measured function: peak positions in the transform of the identity correlation give the $E_n$, peak heights give the initial-state overlap weights ($|c_n|^2$, or $|\\langle l_n|\\psi\\rangle|^2$ for non-Hermitian systems), and the ratio of the $\\hat O$-correlation amplitude to the identity-correlation amplitude at each peak gives $\\langle u_n|\\hat O|u_n\\rangle$. Because the argument never uses Hermiticity or orthonormality of the quasi-eigenstates, the same formula covers PT-symmetric non-Hermitian Hamiltonians and time-dependent Floquet Hamiltonians, whose quasi-eigenstates are typically non-orthogonal; the paper demonstrates extraction of observable expectation values, detection of the exceptional point, and measurement of U(1) and SU(2) topological holonomy from the resulting spectra.","pith_inferences":["Because the amplitude-ratio reconstruction requires real, gapped quasi-energies, the honest scope of the word 'universal' is Hermitian, PT-exact, and Floquet dynamics; turning the PT-broken phase's damped oscillations into genuine complex eigenenergies would need the Laplace-transform extension the authors flag as future work.","The same measurement stream that produces the spectrum also yields $\\langle u_n|\\hat O|u_n\\rangle$ for every resolved level, so UQCS could act as a post-processing verifier inside eigenstate-preparation pipelines, certifying the observable values of a prepared state without running extra circuits.","Levels closer than $1/\\tau$ merge into a single Gaussian line, so the extracted observable is the overlap-weighted average over the unresolved manifold; the splitting under periodic driving in the SU(2) holonomy case shows that UQCS resolves degeneracy mainly through dynamics-induced energy shifts.","The query-depth bound carries a factor of $1/\\zeta$ in the initial-state overlap, so a natural adaptive strategy is to restart UQCS using a reconstructed eigenstate as the new trial state to reach weakly populated levels at controlled sampling cost."],"forward_implications":["UQCS returns eigenenergies, overlap weights, and per-eigenstate expectation values of arbitrary observables from one family of correlation measurements, enabling full eigenstate tomography at fidelities around 0.995–0.998 on the demonstrated chip.","The framework applies without modification to non-Hermitian Hamiltonians in the PT-exact phase, where measured peak weights are $|\\langle l_n|\\psi\\rangle|^2$ and the ratio of spectra still yields physical-state expectation values.","For periodically driven systems, UQCS resolves the full Floquet–Bloch band structure including replica bands, and the quasi-energy shift or splitting measures the U(1) Berry phase or SU(2) Wilczek–Zee holonomy (measured Berry phase 0.912$\\pi$ against a predicted $\\pi$, and Wilson loop $W = -0.499$ against $-0.504$).","In noiseless benchmarks UQCS reaches comparable accuracy with query depth 30 versus 2048 for iterative quantum phase estimation and 274 for quantum eigenvalue transformation, and unlike those baselines it keeps estimating eigenenergies across the exceptional point and for Floquet systems.","A variant circuit using a maximally mixed initial state tracks $\\mathrm{Tr}(e^{-i\\hat H t})/d$ through the exceptional point, so the PT transition, including the broken phase, is detected through coalescence of the real parts of the eigenenergies."],"supporting_citations":[{"why":"The Nyquist–Shannon sampling theorem fixes the time discretisation of the correlation time series, making the discrete windowed Fourier transform faithful.","marker":"[30]"},{"why":"Singular spectrum renormalisation of the measured time series is the noise-suppression step that keeps UQCS accurate under gate errors.","marker":"[31]"},{"why":"Supplies the dual-space right/left eigenvector formalism used to interpret non-Hermitian spectra and the peak weights $|\\langle l_n|\\psi\\rangle|^2$.","marker":"[25]"},{"why":"Floquet band theory that motivates the quasi-eigenenergy interpretation and the $\\Omega$-spaced replica band structure for driven systems.","marker":"[26]"},{"why":"Defines PT symmetry and the exceptional-point transition that the non-Hermitian experiments detect.","marker":"[32]"},{"why":"The Wilczek–Zee gauge-potential formalism behind the topological-holonomy readouts in the Floquet experiment.","marker":"[47]"},{"why":"The U(1) Berry-phase factor used to interpret the energy shift in the equatorial driving case.","marker":"[48]"},{"why":"QETU is the baseline algorithm whose query depth and validity across non-Hermitian and Floquet regimes UQCS is benchmarked against.","marker":"[19]"},{"why":"Iterative QPE is the baseline that UQCS outperforms in query depth and that fails past the exceptional point.","marker":"[13]"}],"fun_headline_variants":["Quantum chip extracts spectra from one correlation function","One correlation function yields full quantum spectra on-chip","Universal spectroscopy on a photonic chip from one measurement","Fourier analysis of a single correlation decodes quantum spectra","Chip-based quantum spectroscopy: one function, whole spectra"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the quasi-eigenenergies are real and separated (gapped in the real part), the paper's stated 'sole requirement of phase factor orthogonality'; if two levels coincide or the energies develop imaginary parts, cross terms survive and the clean peak-amplitude ratios no longer give per-eigenstate observable values.","fun_headline_variants_meta":{"raw":{"variants":["Quantum chip extracts spectra from one correlation function","One correlation function yields full quantum spectra on-chip","Universal spectroscopy on a photonic chip from one measurement","Fourier analysis of a single correlation decodes quantum spectra","Chip-based quantum spectroscopy: one function, whole spectra"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000293,"raw_usage":{"total_tokens":1787,"prompt_tokens":1106,"completion_tokens":681,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":722,"completion_tokens_details":{"reasoning_tokens":605}},"tokens_in":722,"tokens_out":681,"duration_ms":7169,"temperature":1.0,"reasoning_tokens":605,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T22:04:48.068938+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run UQCS on a two-level non-Hermitian Hamiltonian swept past its exceptional point so the eigenenergies become a complex-conjugate pair, and compare the amplitude-ratio estimates of $\\langle u_n|\\hat O|u_n\\rangle$ with exact biorthogonal values: the identity (2) predicts the reconstruction to degrade as the imaginary parts grow, since the $\\eta$-integral no longer yields a delta function, and the paper's own PT-broken-phase spectra already show negative amplitudes and oscillations. Alternatively, drive a Hermitian system through an avoided crossing so that $\\Delta E_{\\min}$ falls below $1/\\tau$, and check whether the two Gaussian peaks merge and the recovered observable drifts toward the overlap-weighted average rather than either exact eigenvalue.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Nyquist–Shannon sampling theorem fixes the time discretisation of the correlation time series, making the discrete windowed Fourier transform faithful."},{"cited_title":"Golyandina & A","cited_arxiv_id":null,"evidence_quote":"Singular spectrum renormalisation of the measured time series is the noise-suppression step that keeps UQCS accurate under gate errors."},{"cited_title":"Ashida, Z","cited_arxiv_id":null,"evidence_quote":"Supplies the dual-space right/left eigenvector formalism used to interpret non-Hermitian spectra and the peak weights $|\\langle l_n|\\psi\\rangle|^2$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Floquet band theory that motivates the quasi-eigenenergy interpretation and the $\\Omega$-spaced replica band structure for driven systems."},{"cited_title":"El-Ganainy et al","cited_arxiv_id":null,"evidence_quote":"Defines PT symmetry and the exceptional-point transition that the non-Hermitian experiments detect."},{"cited_title":"Wilczek & A","cited_arxiv_id":null,"evidence_quote":"The Wilczek–Zee gauge-potential formalism behind the topological-holonomy readouts in the Floquet experiment."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The U(1) Berry-phase factor used to interpret the energy shift in the equatorial driving case."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"QETU is the baseline algorithm whose query depth and validity across non-Hermitian and Floquet regimes UQCS is benchmarked against."},{"cited_title":"Dobšíˇ cek, G","cited_arxiv_id":null,"evidence_quote":"Iterative QPE is the baseline that UQCS outperforms in query depth and that fails past the exceptional point."}],"review_version":1}