{"id":"864cf8a3-ab2a-4a39-820d-95a8388e8840","arxiv_id":"2412.19590","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A Ramsey-type interferometry method that extracts the absolute ground-state energy from the frequency of oscillations between the ground state and a symmetry-adapted reference state, avoiding controlled time evolutions.","lead":"This paper introduces a quantum algorithm that estimates a ground-state energy by measuring the phase difference between the target state and a classically known reference state, without controlled time evolution. It could shorten circuits on early fault-tolerant quantum computers and quantum annealers.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Initial-state preparation in Eq. (6) is the load-bearing gap: Appendix B supplies no proof of an efficient, general preparation, and the 4-qubit demo sidesteps the issue with a trivially preparable product superposition.","rationale":"The reader's weakest assumption and my identified concern coincide: the entire interference signal rests on the availability of Eq. (6). Appendix B is the only place the paper attempts to justify this, and it is a sketch rather than a proof. It handles only Q=M, assumes rather than shows the final adiabatic step, and gives no bound on the required time T or on the achievable fidelity. The 4-qubit numerical experiment does not close this gap because the chosen initial state is a simple computational-basis superposition, preparable by a constant-depth circuit that is never described in Appendix B. Other issues noted in the paper, such as the algebraic slip in Appendix A (cos^2 x rewritten as (1+cos x)/2 instead of (1+cos 2x)/2) and the unanalyzed maximum-energy assumption for the reference state, are real but readily fixable without changing the measurement protocol. By contrast, an unproven state-preparation subroutine leaves the method without a demonstrated starting point for generic instances. The central interference idea is supported by the numerical Fourier peaks and by an independent derivation of Eq. (10), so the concern warrants a conditional verdict rather than rejection. The verdict should remain CONDITIONAL until the preparation step is either proven or replaced by an explicit circuit family.","tokens_in":12891,"tokens_out":28693,"duration_ms":268680,"concrete_test":"Simulate the full five-step sequence of Appendix B in exact time-dependent Schrodinger evolution for N=6 with the Sec. III pair-decomposed H_D, starting from the product-GHZ state indicated in step 4, and compute the fidelity F(T) of the final state with (|ground_HD>+|111111>)/sqrt(2) for T from 1/J to 100/J. If F(T) does not reach a value close to 1 for any polynomially large T, or if the step-4 input product state cannot be determined classically by reverse adiabatic passage, the preparation protocol fails. Repeating the same construction with an H_D whose ground state is not a product computational-basis state would test the claimed generality.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central measurement formula (Eq. (10)) is sound only if the initial superposition |psi_ini> of Eq. (6) can actually be prepared with high fidelity. The paper assumes this state and Appendix B, which is meant to supply it, is limited to Q=M and ends with the unsupported statement that after ASP from H_transverse to H_D 'we obtain the desired superposition state.' No gap analysis, no complexity bound, and no explicit construction for arbitrary conserved quantities or for N beyond the 4-qubit example is given. The numerical demonstration does not test the preparation: for the parameters of Sec. III, (|1100>+|1111>)/sqrt(2) is preparable by two X gates, one Hadamard, and one CNOT, so the reported Fourier peaks validate the interference part but not the claimed state-preparation subroutine. Without a polynomial-time, high-fidelity preparation protocol for general Q, the method's central claim is conditional on an unverified subroutine.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a method to estimate the ground-state energy of a Hamiltonian without controlled time evolution. The protocol uses adiabatic state preparation (ASP) starting from a superposition of a ground state and a reference state, lets the system evolve under the problem Hamiltonian for a time τ, applies reverse ASP, and reads out the energy difference from the Fourier transform of the final projection probability. The reference-state energy is computed classically from a polynomially sized symmetry subspace, so the measured frequency directly yields the ground-state energy. The authors validate the method on a 4-qubit Heisenberg model and report good agreement with exact diagonalization, along with a numerical comparison showing shorter total runtime than conventional ASP. The main unresolved issue is the preparation of the required initial superposition state, which is assumed rather than proved in general.","tokens_in":13053,"tokens_out":6244,"duration_ms":63958,"significance":"The central measurement formula, Eq. (10), is correct, and the protocol is non-circular: the reference-state energy is obtained classically and the ground-state energy is inferred from a measured frequency difference. The numerical demonstration on the 4-qubit Heisenberg model reproduces the exact ground-state energy to a relative error of about 3.7e-5 percent and resolves additional excited-state peaks. If the initial-state preparation problem can be solved, the method is a meaningful step toward ground-state energy estimation without controlled time evolution, with potential relevance to early fault-tolerant quantum computers and quantum annealers. The paper is also useful in explicitly identifying the preparation assumption in Eq. (6). However, the current lack of a rigorous, general preparation protocol limits the strength of the claims and requires major revision.","major_comments":[{"comment":"The entire protocol hinges on the ability to prepare the superposition state |ψ_ini> of Eq. (6). Appendix B proposes an ASP-based preparation only for the special case Q = M and does not prove that the final adiabatic step from H_transverse to H_D maps the desired superposition of eigenstates onto (|ψ_g_{m,D}> + |11...1>)/√2 without level crossings or with bounded error. It also gives no complexity bound in N for arbitrary conserved quantities Q, and the numerical demonstration in Sec. III does not actually test this preparation, since the initial state (|1100> + |1111>)/√2 is preparable by elementary Clifford gates. The central claim is therefore conditional on an unverified subroutine; please either supply a rigorous preparation protocol with an accuracy and efficiency analysis, or explicitly restate the contribution as a method that assumes such a preparation is available.","section":"Sec. II, Eq. (6); Appendix B"},{"comment":"The identity used in Eq. (A1) is algebraically incorrect: cos^2(x) = (1 + cos(2x))/2, so P(τ) in Eq. (10) should be rewritten as 1/2 + 1/2 cos[(E_g - E_n)τ + θ'], not 1/2 + 1/2 cos[(E_g - E_n)τ/2 + θ'/2]. The subsequent derivation in Eq. (A3) is therefore wrong as written. The conclusion that the relative phase θ' does not affect the Fourier peak positions survives after correcting this factor, because |exp(iθ')| = 1, but the proof needs to be repaired.","section":"Appendix A, Eq. (A1)"},{"comment":"The claim that the method is robust against non-adiabatic transitions is supported by a single 4-qubit numerical example. No quantitative analysis is given for how leakage to excited states affects the amplitude of the ground-state peak, how many samples or how large τ must be to identify the ground-state peak when multiple peaks appear, or under what conditions the ground-state peak remains identifiable. Since the authors themselves note that the method fails when the ground-state population is significantly depleted, the robustness statement should be made quantitative or explicitly bounded to the regime where the ground-state peak is still visible in the Fourier spectrum.","section":"Sec. II and Sec. III, Fig. 1(c)"}],"minor_comments":[{"comment":"“An key aspect” should be “A key aspect”.","section":"Appendix C, first paragraph"},{"comment":"“byu setting T appropriately” contains a stray “u”; it should read “by setting T appropriately”.","section":"Sec. II, paragraph near Eq. (12)"},{"comment":"The phrase “relative error of 3.7 × 10^{-5}%” is technically correct but unusual; consider reporting the relative error as a dimensionless fraction (3.7 × 10^{-7}) to avoid ambiguity.","section":"Sec. III, ground-state result"},{"comment":"The phrase “By adding qubits to match the desired superposition” is vague; a concrete tensor-product construction of the desired product-state superposition would improve reproducibility.","section":"Appendix B, step 4"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The paper contains a correct and useful measurement idea, but the initial-state preparation is the main unproved subroutine and the numerical example does not exercise it. I would not support acceptance before the authors either provide a rigorous preparation analysis or substantially weaken the generality claims. The manuscript is otherwise clear and the numerical results are encouraging."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper does something real. Prior Ramsey-ASP work estimated energy gaps; this one uses a symmetry-protected reference state with a classically known eigenvalue as the second arm of the interferometer, so the Fourier peak lands on an absolute ground-state energy. The central formula, Eq. (10), is correct, the 4-qubit Heisenberg numerics reproduce the exact ground energy to 3.7e-5%, and Appendix C shows the subspace-sweep works without knowing which subspace holds the true ground state. The non-adiabatic-robustness point is also honestly made: unwanted excitations show up as extra peaks rather than silently corrupting one number, and the authors state the limit where ground-state population is lost.\n\nWhat is soft, in order of severity.\n\nFirst, the initial-state preparation in Eq. (6) is the load-bearing subroutine, and it is not actually delivered. Appendix B is explicitly for Q = M, uses a GHZ-state route, and ends with an adiabatic step that has no gap analysis or complexity bound. Generalizing to arbitrary conserved Q and large N is non-trivial, because the ground state of the driving Hamiltonian in a subspace is itself the kind of object that usually requires an adiabatic schedule to prepare. The 4-qubit demonstration does not test this: (|1100>+|1111>)/sqrt(2) is a simple product-state superposition, so the simulation validates the interference readout, not the preparation subroutine. That said, this is a gap in the paper, not a contradiction of the method; a referee should ask for either a provably efficient construction for a useful class of Q, or an explicit statement that the method is conditional on a preparable initial superposition.\n\nSecond, Appendix A has an algebraic error. From Eq. (10), P(tau) should expand to 1/2 + 1/2 cos(Delta E tau + theta'), not 1/2 + 1/2 cos(Delta E tau/2 + theta'/2). As written, the Fourier analysis would put the peak at Delta E/2, contradicting the main text. The final conclusion (the relative phase drops out) is still right, but the exhibited identity is wrong and should be fixed.\n\nThird, the maximum-energy-reference assumption is a real caveat. The suggested fix, adding -lambda(Q-q)^2, does not change the spectrum within a fixed Q sector, but it does alter the global ground state across sectors, so it is not a free lunch. For quantum chemistry the |1...1> state is plausibly the top state, but the paper should be more precise about when this holds.\n\nThe central idea is sound; the weaknesses are in the presentation and the preparation subroutine rather than in the main interference mechanism. People working on early fault-tolerant energy estimation or annealing readout protocols will get value from this. I would send it to peer review: the referee should push on the preparation subroutine and the Appendix A algebra. I would cite it for the absolute-energy Ramsey idea.","headline":"A genuinely useful variant of Ramsey-ASP that estimates absolute ground-state energies; the interference part is sound, but the initial-state preparation is assumed more than proven.","tokens_in":13592,"tokens_out":4432,"would_cite":true,"duration_ms":43653,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper shows that the ground-state energy can be estimated accurately without controlled time evolution by combining adiabatic state preparation, a classically known reference state, and a Ramsey-type measurement whose Fourier peak…","keywords":["ground-state energy","adiabatic state preparation","Ramsey-type measurement","reference state","conserved quantity","phase estimation","quantum annealing","Heisenberg model"],"falsifier":"A concrete test: implement the full sequence on a small device for a Hamiltonian with a known ground-state energy, using the GHZ-based preparation sketched in Appendix B, and check whether the Fourier peak of $P(\\tau)$ reproduces that energy to the precision set by the sampling time. A theoretical falsifier is to show that for some conserved quantity satisfying the paper's assumptions, the spectral gap of the state-preparation Hamiltonian closes faster than polynomially with system size, making the initial-state preparation impossible in polynomial time; that would invalidate the scalability claim while leaving the central identity intact.","tokens_in":12676,"feed_emoji":"⚛️","tokens_out":9164,"duration_ms":78141,"temperature":0.7,"pith_summary":"The paper proposes a method to estimate the ground-state energy of a quantum Hamiltonian without ever implementing controlled time evolution, which is a major practical bottleneck in phase-estimation algorithms. The trick is to prepare a superposition of the ground state of a simple driving Hamiltonian and a \"reference state\" whose energy is known classically, then let the system evolve under the target Hamiltonian for a variable time, reverse the adiabatic sweep, and measure the probability of returning to the starting state. That probability oscillates at a frequency equal to the difference between the target ground-state energy and the reference energy, so a Fourier transform of the measured signal directly yields the ground-state energy. The authors show numerically on a four-qubit Heisenberg model that the estimate matches exact diagonalization to within $3.7\\times10^{-5}\\%$ relative error, and they argue that the scheme is robust against non-adiabatic transitions because such transitions produce extra spectral peaks rather than corrupting the main one. If correct, the method would shorten quantum circuits on early fault-tolerant devices and make ground-state estimation feasible on quantum-annealing hardware.","feed_headline":"Read out ground-state energy without controlled time evolution","feed_subtitle":"A known-energy reference state and a Ramsey measurement yield the energy directly from a Fourier peak.","key_machinery":"The central object is the conserved quantity $\\hat{Q}$, which block-diagonalizes both the driving and the problem Hamiltonians, together with a reference state chosen from a classically solvable sector of $\\hat{Q}$. The machine that carries the argument is the three-stage time-dependent Hamiltonian $H(t)=F(t)\\hat{H}_D + [1-F(t)]\\hat{H}_P$ with $F(t)$ linear during forward adiabatic preparation, zero during the free-evolution (Ramsey) period $\\tau$, and linear again during reverse preparation. Because the state is a superposition of two eigenstates that live in different $\\hat{Q}$ sectors, and $\\hat{Q}$ is conserved, each component evolves independently and acquires a relative phase proportional to the energy difference; the return probability $P(\\tau)$ is the cosine of that phase. The discrete Fourier transform $f(\\omega)=\\sum_n P(\\tau_n)e^{-i\\omega\\tau_n}$ converts the oscillating signal into a peak at $\\omega = E^g_{q',P}-E^n_{q,P}$. Non-adiabatic transitions during forward preparation add extra Fourier peaks at the energies of excited states, which is why the method is robust and does not require fine-tuning the adiabatic time $T$.","core_discovery":"The central claim is that a classically computable eigenstate, called a reference state, can serve as a phase reference for Ramsey-type energy estimation, eliminating the need for controlled time evolution. Suppose the driving and problem Hamiltonians share a conserved quantity $\\hat{Q}$ with polynomial-size eigenspaces. The initial state is a superposition $|\\psi_\\mathrm{ini}\\rangle = (|\\psi^g_{q',D}\\rangle + |\\psi_{q,D}\\rangle_n)/\\sqrt{2}$ of the driving-Hamiltonian ground state in sector $q'$ and a known reference state in sector $q$. After adiabatic state preparation, free evolution under $\\hat{H}_P$ for a time $\\tau$, and reverse adiabatic state preparation, the probability of projecting back onto $|\\psi_\\mathrm{ini}\\rangle$ is $P(\\tau) = \\cos^2[(E^g_{q',P} - E^n_{q,P})\\tau/2 + \\theta'/2]$, and its discrete Fourier transform peaks at the energy difference $E^g_{q',P} - E^n_{q,P}$. Since the reference energy $E^n_{q,P}$ is obtained classically, the ground-state energy in the sector $q'$ is read off directly. The paper demonstrates this on a four-qubit Heisenberg model with total magnetization as the conserved quantity, recovering the ground-state energy with a relative error of $3.7\\times10^{-5}\\%$ and estimating several excited-state energies from the same data.","pith_inferences":["A natural extension would be to use the same reference-state interference trick to estimate energy gaps at avoided crossings or to probe symmetry-breaking transitions, by choosing reference states from different $\\hat{Q}$ sectors.","The choice of a maximum-energy reference state (as in the numerical example) means the ground-state peak is the largest frequency component, suggesting a blind readout that does not require prior spectral knowledge.","The method's practicality hinges on the reference-state preparation of Appendix B; scaling the GHZ-based protocol to larger $N$ and general conserved quantities is the step most likely to limit real-world applicability.","One could test robustness experimentally on quantum-annealing hardware, where controlled time evolution is unavailable, by comparing the Fourier-derived energy against annealing results."],"forward_implications":["The method removes the need for controlled time evolution, shortening the circuits required for ground-state energy estimation on early fault-tolerant quantum computers.","Because non-adiabatic transitions appear as extra peaks in the Fourier spectrum rather than as errors in the ground-state peak, the adiabatic sweep time $T$ does not need to be fine-tuned in advance.","Excited-state energies can be extracted from the same measurement data, since every peak corresponds to an energy difference between the reference state and an eigenstate of the problem Hamiltonian.","If the subspace containing the true ground state is unknown, applying the procedure across all $\\hat{Q}$ sectors and comparing the recovered energies identifies it, as demonstrated numerically for a Heisenberg ring."],"supporting_citations":[{"why":"Prior methods that estimate energy gaps without controlled time evolution using ASP and Ramsey measurements; this paper extends them to direct eigenvalue estimation.","marker":"[29, 30]"},{"why":"Briefly mentions using a trivial eigenstate superposition with ASP for quantum chemistry; this paper generalizes and details the approach.","marker":"[35]"},{"why":"Introduces reverse adiabatic state preparation (RASP), the stage that returns the system to the measurement basis.","marker":"[31–34]"},{"why":"Gives the adiabatic condition that conventional ASP-based energy estimation must satisfy; the paper contrasts its robustness against these constraints.","marker":"[36–39]"},{"why":"Supplies the GHZ-state preparation techniques used in Appendix B to build the required initial superposition.","marker":"[45–51]"}],"fun_headline_variants":["No controlled evolution: energy from a Ramsey peak","Symmetry and Ramsey: energy without controlled time evolution","Adiabatic Ramsey: ground-state energy from a reference state","Ground-state energy via reference-state Ramsey, no controlled evolution","Use known eigenstate as phase reference for energy estimation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire protocol rests on being able to prepare the initial superposition of the driving Hamiltonian's ground state and the reference state efficiently and with high fidelity; if that preparation cannot be done for a given Hamiltonian or system size, the measurement cannot be run even though the interference formula remains correct.","fun_headline_variants_meta":{"raw":{"variants":["No controlled evolution: energy from a Ramsey peak","Symmetry and Ramsey: energy without controlled time evolution","Adiabatic Ramsey: ground-state energy from a reference state","Ground-state energy via reference-state Ramsey, no controlled evolution","Use known eigenstate as phase reference for energy estimation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000258,"raw_usage":{"total_tokens":1584,"prompt_tokens":950,"completion_tokens":634,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":566,"completion_tokens_details":{"reasoning_tokens":556}},"tokens_in":566,"tokens_out":634,"duration_ms":6468,"temperature":1.0,"reasoning_tokens":556,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T00:11:10.967428+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete test: implement the full sequence on a small device for a Hamiltonian with a known ground-state energy, using the GHZ-based preparation sketched in Appendix B, and check whether the Fourier peak of $P(\\tau)$ reproduces that energy to the precision set by the sampling time. A theoretical falsifier is to show that for some conserved quantity satisfying the paper's assumptions, the spectral gap of the state-preparation Hamiltonian closes faster than polynomially with system size, making the initial-state preparation impossible in polynomial time; that would invalidate the scalability claim while leaving the central identity intact.","supporting_citations":[{"cited_title":"Sci.12, 2121 (2021)","cited_arxiv_id":null,"evidence_quote":"Briefly mentions using a trivial eigenstate superposition with ASP for quantum chemistry; this paper generalizes and details the approach."}],"review_version":1}