{"id":"78602fe0-9c52-4929-aa8a-9e3870a02491","arxiv_id":"2508.21123","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"On small synthetic portfolio problems, noiseless QAOA fits the known ground-state energy well, but noisy QAOA fails while QITE, pretrained on noiseless simulators, still identifies the optimal portfolio on IBM hardware.","lead":"The authors benchmark two quantum optimization algorithms, QAOA and QITE, on a 9-qubit Markowitz portfolio optimization problem using noiseless simulators, noisy simulators, and IBM quantum hardware. They report QAOA converges well without noise but degrades sharply under two-qubit gate noise, while QITE keeps the optimal solution identifiable on real hardware at higher classical cost.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Concern: QITE is pretrained noiselessly then executed once, whereas QAOA is optimized under noisy cost evaluations; the noise-robustness comparison conflates training noise with execution noise. A noiseless-pretrained QAOA control is needed to support the central claim.","rationale":"This is a good-faith reading: the paper transparently describes the QITE pretraining (Appendix S4) and the modified QAOA cost (Eq. 7), so the issue is not a hidden flaw but a missing control that is essential to the comparison. The central claim ('QITE method exhibits much stronger robustness to realistic noise levels, achieving comparably optimal solutions on actual quantum hardware runs as noiseless QAOA simulated runs') is a comparative statement about noise robustness. For such a claim, both algorithms must be subjected to noise at the same stage of the pipeline. QITE's parameters are chosen to match the exact imaginary-time evolution on noiseless hardware; noise acts only when the circuit is executed. QAOA's parameters are chosen by minimizing an objective that itself is corrupted by noise; the optimization dynamics are affected, which is known to cause instability in variational algorithms. This is the weakest link in the argument. The reader's weakest_assumption identifies exactly this asymmetry, and we agree. We also note the Eg-modified cost function is a secondary issue but not as load-bearing because it affects the noiseless QAOA baseline rather than the noise comparison. A concrete control—pretraining QAOA noiselessly and then executing once under the same noise—would directly test whether the observed gap is due to algorithmic noise robustness or to the optimization protocol. Given the magnitude of the reported gap (F_Error < 1 for QITE vs >20 for noisy QAOA), it is plausible that pretrained QAOA would largely close it. The paper's other contributions—e.g., the detailed QITE embedding and the scalability results for QAOA on MPS—are not invalidated, but the headline conclusion cannot be accepted without this control.","tokens_in":18505,"tokens_out":5017,"duration_ms":50383,"concrete_test":"Re-run the 9-qubit benchmark for the same four instances: (1) optimize QAOA parameters on a noiseless simulator to convergence using the standard cost (Eq. 6) or their Eq. 11; (2) execute the optimized circuit once on the same local noisy simulator with CX error 0.007 (matching the QITE hardware noise level, Appendix S3) and compute F_Error; (3) compare to the QITE hardware F_Error in Fig. 5a. If the pretrained QAOA F_Error is comparable to QITE (e.g., <1–6) rather than >20, the robustness gap is an artifact of differing optimization conditions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that QITE is more noise-robust than QAOA is not supported because the two algorithms are not exposed to noise symmetrically. QAOA's parameters are optimized using noisy cost evaluations (Eq. 11; Fig. 3c), so noise perturbs the optimization trajectory itself and can prevent convergence. QITE's parameters are first classically optimized on a noiseless simulator to match the exact imaginary-time evolution operator (Eq. 10, Appendix S4), then executed once on noisy hardware (Fig. 5a). Thus the comparison measures QAOA's sensitivity to noise during training versus QITE's sensitivity to noise during execution only. A QAOA circuit pretrained noiselessly and then executed under the same noise would likely show far lower F_Error than the noisy-optimized QAOA in Fig. 5b; conversely, if QITE were optimized under noise, its parameters would be noisy and might lose the robustness advantage. The paper never runs either control, so the headline trade-off (Table I) conflates training noise with execution noise and cannot be concluded from the data.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper maps a Markowitz portfolio-optimization problem to a 9-qubit Ising Hamiltonian and benchmarks two variational quantum ground-state solvers—QAOA and QITE—in noiseless simulators, noisy local simulators with controlled CX error rates, and (for QITE) on IBM Quantum hardware. The authors report that QAOA converges excellently in noiseless settings, that QAOA degrades sharply under gate noise, and that QITE, despite higher classical cost, remains robust on hardware and yields return errors comparable to noiseless QAOA. They conclude that QITE is preferable for small noisy instances while QAOA offers better scalability if noise is mitigated.","tokens_in":18867,"tokens_out":5992,"duration_ms":72118,"significance":"If the comparison were sound, the paper would provide a practically useful benchmark for choosing between QAOA and QITE on near-term quantum devices for portfolio optimization. The authors have made a genuine effort to include realistic hardware data: QITE results from IBM Quantum for 50 instances, a local noise model calibrated to an IBM device, and ancillary data/code availability. The problem mapping and variational-circuit implementation are clearly described. However, the central noise-robustness comparison is asymmetrically designed, and one of the QITE cost definitions is mathematically questionable; these issues prevent the stated conclusions from being supported by the reported data.","major_comments":[{"comment":"The headline comparison is not symmetric. QAOA parameters are optimized by evaluating the cost (11) on a noisy simulator (Section III.A, Fig. 3c), so noise affects the optimization trajectory itself. By contrast, QITE parameters are pretrained on a noiseless simulator to approximate the exact unitary U_circuit built from e^{-βH} (Eq. (10), Appendix S4), and the hardware run in Fig. 5(a) is a single execution of those pretrained parameters. Thus the paper measures QAOA's sensitivity to noise during training versus QITE's sensitivity to noise during execution only. The conclusion 'QITE exhibits much stronger robustness' (abstract, Section V, Table I) is not supported without a noiseless-pretrained QAOA control or a noisy-optimized QITE control.","section":"Section III.B–IV.B, Eq. (10), Fig. 5"},{"comment":"The claimed 'excellent convergence' of noiseless QAOA is obtained with the cost C(s)=|Eg−E(s)|, where Eg is the exact ground-state energy. This is a supervised objective that presupposes the solution. Because E(s) ≥ Eg for physical states, minimizing |Eg−E(s)| is equivalent to minimizing E(s) in the ideal statevector limit, so the convergence is not fake; but as a benchmark it differs from the standard QAOA cost (6) and gives the optimizer information that a genuine QAOA user would not have. The noiseless convergence and scalability claims should either be reproduced with Eq. (6) or clearly presented as a supervised variant with the known answer used during training.","section":"Section III.A, Eq. (7), Figs. 3–4"},{"comment":"The equality C_QITE(s)=1−Tr[V†(s)U_circuit]/2^n=1−⟨ψ_h|V†(s)U_circuit|ψ_h⟩ is not correct for a general unitary A=V†U_circuit. Tr(A)/2^n is the average of the diagonal matrix elements in the computational basis, whereas ⟨ψ_h|A|ψ_h⟩ with |ψ_h⟩=Hadamard⊗n|0⟩ is the average of all matrix elements. These coincide only if the off-diagonal sum of A vanishes. Since Eq. (10) defines the training objective and the convergence threshold C_QITE<0.1, the actual optimized circuits may not target the fidelity claimed. This should be corrected or the implementation clarified.","section":"Eq. (10), Appendix S4"},{"comment":"The resource comparison is internally inconsistent. The conclusion states 'For QITE, only a single round of circuit simulation is required, equivalent to the cost of one QAOA iteration,' while Section III.C and Appendix S4 state that QITE requires between 4 and 8 variational layers and extensive classical optimization to approximate U_circuit. If the pretraining iterations are counted, QITE does not require a single circuit evaluation; if they are not counted, the comparison of 'Quantum resources' in Table I is misleading. The counting convention should be stated explicitly and applied consistently.","section":"Section V, Table I"}],"minor_comments":[{"comment":"Typo 'IWhile both methods are viable' should read 'While both methods are viable.'","section":"Section III.A"},{"comment":"The sentence '|ψ(s)⟩ =V (s)) |ψ0⟩' has an unbalanced parenthesis.","section":"Section III.C"},{"comment":"The symbol n is reused: earlier n=mw is the number of problem binary variables, while here n denotes the total number of qubits including the ancilla. This should be disambiguated.","section":"Eq. (10)"},{"comment":"Typo: 'Higher noise levels lead to a increase in errors' should be 'an increase in errors.'","section":"Fig. 5 caption"},{"comment":"The notation '010100100 (101011011 under little-endian qubit ordering)' is confusing; the correspondence between the bitstring and the qubit ordering should be defined explicitly.","section":"Section II.B"},{"comment":"The appendix numbering starts at S13; this appears to be an artifact and should be renumbered consistently.","section":"Appendix S1"}],"recommendation":"major_revision","confidential_remarks":"The central comparison is interesting and the hardware data are valuable, but the asymmetric training/execution protocol is a load-bearing design flaw. I recommend major revision rather than rejection because the missing controls—noiseless-pretrained QAOA and/or noisy-optimized QITE—are feasible within the manuscript's scope. The Eq. (10) trace/Hadamard identity also needs correction before the QITE results can be considered reliable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper does one genuinely new thing: it puts QITE and QAOA head-to-head on the same 9-qubit Markowitz instances, including QITE runs on IBM hardware at ~0.007 ECR error and 50 additional hardware instances. The data and code are on Zenodo, and the authors are transparent about their modifications to the QAOA cost function (Eq. 7) and about QITE's heavy classical overhead. Those are real assets.\n\nThe central claim, however, is not supported. The comparison is apples-to-oranges. QAOA's parameters are optimized using noisy cost evaluations, so noise corrupts the optimization trajectory itself. QITE's parameters are first classically pretrained on a noiseless simulator to match the exact imaginary-time evolution operator, then executed once on noisy hardware. That measures QAOA's sensitivity to noise during training against QITE's sensitivity to noise during execution only. It does not measure algorithm robustness. A noiseless-pretrained QAOA control would very likely show far smaller return errors under the same execution noise, and noisy QITE training might lose its apparent edge. The paper runs neither control, so the abstract's claim that \"QITE exhibits much stronger robustness to realistic noise levels\" is an overstatement.\n\nThe use of the exact ground-state energy Eg in Eq. 7 is a second soft spot, though less damaging because the authors disclose it and also confirm the final bitstring peaks. Still, it means the noiseless QAOA convergence is partly a fit to a known answer, not a solution of the optimization problem. A standard cost function without Eg should be the baseline.\n\nMinor issues: the local noise model only includes CX errors, omitting single-qubit and readout errors (usually secondary, so not fatal), and the QITE hardware runs lack error bars, even though Fig. 5b reports them for QAOA. Also, the data are synthetic, but that is acceptable for a controlled benchmark.\n\nThe reader's rejection is fair in spirit. This is not a desk-reject paper, though; it is a serious empirical effort with transparent methods and a fixable flaw. The right move is to send it to peer review with a request for the missing controls: noiseless-pretrained QAOA run under noise, QITE optimized with noisy cost evaluations, a standard QAOA without Eg, and error bars on hardware runs. If those controls do not change the qualitative conclusion, the paper will be solid. As it stands, the headline trade-off in Table I is premature.","headline":"A useful empirical benchmark with a real hardware QITE demonstration, but the central QAOA-vs-QITE robustness claim rests on an asymmetric comparison that does not hold up as stated.","tokens_in":19312,"tokens_out":1932,"would_cite":false,"duration_ms":23705,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P68","91G10"],"pacs":["03.67.Ac"],"model":"deepseek-v4-flash","headline":"Under realistic two-qubit gate noise, quantum imaginary-time evolution still identifies the optimal Markowitz portfolio where QAOA fails to converge.","keywords":["QAOA","quantum imaginary-time evolution","Markowitz portfolio optimization","Ising Hamiltonian","QUBO","noisy quantum simulation","variational quantum circuits","NISQ devices"],"falsifier":"Run a matched protocol on the same hardware: pretrain a QAOA circuit noiselessly, execute it once, and compare the probability of the optimal bitstring and the return error against the paper's QITE hardware runs. If the pretrained QAOA peak is sharp, the robustness ordering is an artifact of when noise enters the pipeline; if the peak remains broad, QITE's advantage is genuine.","tokens_in":18347,"feed_emoji":"📈","tokens_out":9549,"duration_ms":90086,"temperature":0.7,"pith_summary":"This paper benchmarks two quantum solvers, QAOA and quantum imaginary-time evolution (QITE), on the same Markowitz portfolio-selection problems encoded as Ising Hamiltonian ground states. In noiseless simulation, QAOA converges cleanly to the optimal investment bitstring for 9-, 20-, and 30-qubit instances. Once two-qubit gate errors at rates typical of current hardware are introduced, QAOA's cost landscape becomes unstable, its portfolio returns degrade toward random unoptimized levels, and it no longer peaks on the optimal bitstring. QITE, whose variational circuit is pretrained to mimic imaginary-time evolution and then executed once, still returns the optimal bitstring on real quantum hardware with small return errors. The paper's message is that for small noise-dominated instances QITE is the more reliable choice, while QAOA retains the scalability advantage if noise is mitigated.","feed_headline":"Quantum imaginary-time evolution beats QAOA on real hardware","feed_subtitle":"Imaginary-time evolution keeps the optimal bitstring under realistic noise; QAOA only converges with none.","key_machinery":"The load-bearing objects are two variational circuits built from the same layer: parameterized U3 single-qubit rotations plus entangling ECR/CX gates. QAOA uses the circuit to minimize the energy gap |E_g - E(s)|, evaluating the Hamiltonian expectation every iteration; noise entering each evaluation scatters the optimizer across a rugged landscape. QITE instead constructs the non-unitary operator e^{-βH}, embeds it as a larger unitary U through singular-value and QR decompositions, trains a variational circuit V to approximate U by maximizing overlap (C_QITE ≈ 0), and then implements U once, post-selecting an ancilla qubit in |0⟩. The comparison that carries the paper's argument is therefore","core_discovery":"The central claim is an empirical ordering of two solvers on one problem class. For Ising-encoded Markowitz portfolio optimization at 9 qubits, QITE is markedly more tolerant of realistic two-qubit gate noise than QAOA. With a two-qubit error rate near 0.007, QITE executed on quantum hardware produced return errors between roughly 1 and 6, and the optimal portfolio bitstring remained the most probable measured outcome. QAOA optimized through noisy cost evaluations under the same error scale produced return errors above 20, failed to converge, and showed no peak on the optimal bitstring. In noise-free conditions QAOA converged to the exact ground state within hundreds of iterations and, in te","pith_inferences":["The paper compares QITE pretrained without noise against QAOA optimized through noisy cost evaluations; if QAOA were also pretrained noiselessly and then executed once under the same noise, its measured peak on the optimal bitstring might be substantially sharper than the paper's noisy-QAOA results show.","The claimed QITE advantage is benchmarked at one investor-preference setting (θ1=0.8, θ2=0.1, θ3=0.1); re-running the comparison across a spread of θ values would test whether noise robustness survives changes in how heavily risk and budget deviation are penalized.","A practical follow-up is to measure QITE's ancilla post-selection success probability; as system size grows, the accepted-branch probability decays, and that overhead will determine whether QITE's noise advantage survives beyond 9 qubits.","Applying standard error-mitigation techniques to QAOA on real hardware would directly test whether the paper's simulated QAOA noise sensitivity overstates what mitigated QAOA can achieve today."],"forward_implications":["On near-term hardware with two-qubit error rates around 10^-2, QITE can solve 9-qubit Markowitz instances without error mitigation; the optimal allocation is identifiable from the measured state histogram.","QAOA at the same error scale yields portfolios whose return errors rival unoptimized random states, so its use on noisy devices requires effective error mitigation before it adds value.","QITE's practical ceiling is set by classical pretraining cost and circuit depth (4-8 layers for 9 qubits), not by noise, so scaling QITE to larger instances is limited classically.","QAOA remains the scalable route: 20- and 30-qubit noiseless tensor-network simulations converge to reasonable energies, suggesting larger instances are feasible once hardware noise is suppressed.","Because the same Ising/QUBO encoding covers many NP problems, the robustness ordering is a candidate general guide for ground-state optimization on noisy digital quantum processors."],"supporting_citations":[{"why":"Introduces QAOA, the variational algorithm benchmarked throughout the paper.","marker":"[35]"},{"why":"Introduces quantum imaginary-time evolution as a ground-state preparation method that QITE benchmarks.","marker":"[51]"},{"why":"Provides the variational-ansatz formulation of imaginary-time evolution used to build the QITE circuit.","marker":"[52]"},{"why":"Supplies the Markowitz portfolio objective and its mapping to an Ising Hamiltonian that generates the problem instances.","marker":"[43]"},{"why":"Earlier QAOA portfolio-optimization benchmark whose noiseless results this work extends to noisy settings.","marker":"[47]"},{"why":"Supplies the classical optimization routines used to train the variational parameters.","marker":"[83]"},{"why":"Provides the real/imaginary-time evolution circuit construction (SVD embedding) used to implement e^{-βH} unitarily in QITE.","marker":"[96]"},{"why":"Provides the simulation and hardware-access software stack used to run the local noisy simulations and device executions.","marker":"[95]"}],"fun_headline_variants":["QITE beats QAOA under realistic noise in quantum portfolio optimization","Noisy quantum computing: QITE more robust than QAOA for finance","Quantum portfolio: imaginary-time evolution resists noise better than QAOA","Under gate noise, QITE outperforms QAOA on quantum finance benchmark","QITE shows noise resilience over QAOA in Ising portfolio optimization"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The noise comparison is asymmetrical: QITE is pretrained on a noiseless simulator and then executed once under hardware noise, whereas QAOA is optimized through hundreds of noisy cost evaluations; if QAOA were pretrained the same way and then executed once, or if QITE parameters were optimized under noise, the reported robustness gap could shrink or reverse.","fun_headline_variants_meta":{"raw":{"variants":["QITE beats QAOA under realistic noise in quantum portfolio optimization","Noisy quantum computing: QITE more robust than QAOA for finance","Quantum portfolio: imaginary-time evolution resists noise better than QAOA","Under gate noise, QITE outperforms QAOA on quantum finance benchmark","QITE shows noise resilience over QAOA in Ising portfolio optimization"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000159,"raw_usage":{"total_tokens":1036,"prompt_tokens":682,"completion_tokens":354,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":426,"completion_tokens_details":{"reasoning_tokens":262}},"tokens_in":426,"tokens_out":354,"duration_ms":4428,"temperature":1.0,"reasoning_tokens":262,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T14:34:25.761474+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a matched protocol on the same hardware: pretrain a QAOA circuit noiselessly, execute it once, and compare the probability of the optimal bitstring and the return error against the paper's QITE hardware runs. If the pretrained QAOA peak is sharp, the robustness ordering is an artifact of when noise enters the pipeline; if the peak remains broad, QITE's advantage is genuine.","supporting_citations":[{"cited_title":"Gunjan and S","cited_arxiv_id":null,"evidence_quote":"Introduces quantum imaginary-time evolution as a ground-state preparation method that QITE benchmarks."},{"cited_title":"Brandhofer, D","cited_arxiv_id":null,"evidence_quote":"Provides the variational-ansatz formulation of imaginary-time evolution used to build the QITE circuit."},{"cited_title":"Au-Yeung, N","cited_arxiv_id":null,"evidence_quote":"Supplies the Markowitz portfolio objective and its mapping to an Ising Hamiltonian that generates the problem instances."},{"cited_title":"Huang, Mean–variance models for portfolio selection subject to experts’ estimations, Expert Systems with Ap- plications 39, 5887 (2012)","cited_arxiv_id":null,"evidence_quote":"Supplies the classical optimization routines used to train the variational parameters."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the real/imaginary-time evolution circuit construction (SVD embedding) used to implement e^{-βH} unitarily in QITE."},{"cited_title":"Marzec, Portfolio optimization: Applications in quan- tum computing, Handbook of High-Frequency Trading and Modeling in Finance , 73 (2016)","cited_arxiv_id":null,"evidence_quote":"Provides the simulation and hardware-access software stack used to run the local noisy simulations and device executions."}],"review_version":1}