{"id":"0a9147bb-984b-44a8-a221-72464ca00a24","arxiv_id":"2607.02112","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A 2048-spin bulk acoustic wave Ising machine solves MAX-CUT, number partitioning, and Sudoku problems in 341 ms with four orders of magnitude higher thermal stability than optical coherent Ising machines.","lead":"This paper presents a time-multiplexed Ising machine built with two bulk acoustic wave delay lines supporting 2048 spins and all-to-all connectivity. It offers a compact, low-power, tabletop hardware platform for solving combinatorial optimization problems with much higher thermal stability than optical versions.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Phase stability, loss, and crosstalk over the full 707 μs BAW delay must hold for the reported solution quality to reflect true Ising dynamics.","rationale":"The reader's weakest_assumption isolates the single experimental precondition required for every performance claim. No other internal inconsistency (e.g., parameter count, formal verification) is visible from the provided material, and the abstract's mechanical plausibility does not override the need to confirm the delay-line fidelity.","tokens_in":1745,"tokens_out":409,"duration_ms":11894,"concrete_test":"Inject a calibrated single-tone packet into one delay line, record its amplitude and phase after exactly 707 μs at the operating temperature used for the benchmark runs, and repeat over the full 341 ms experiment duration; if rms phase drift exceeds ~5° or amplitude variation exceeds 0.5 dB, recompute the effective coupling matrix and re-run the MAX-CUT instances to quantify degradation of solution quality.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The architecture time-multiplexes 2048 spins across two serially connected 20.5 MHz BAW delay lines whose round-trip delay is 707 μs. All-to-all couplings are realized by precise timing and amplitude/phase modulation of returning packets. For the dynamics to match the intended Ising Hamiltonian (and for the 341 ms MAX-CUT, number-partitioning, and Sudoku results to be attributable to the machine rather than to uncontrolled degradation), each packet must exit the delay line with amplitude loss ≪ 1 dB, phase jitter ≪ few degrees, and negligible inter-packet crosstalk after 707 μs. The abstract asserts four orders of magnitude better thermal stability than optical CIMs, yet provides no quantitative bound on residual phase noise, dispersion, or temperature-induced drift inside the BAW lines themselves. If this condition fails, the observed solution quality could be an artifact of the modulation electronics rather than of the claimed all-to-all Ising evolution.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript presents an experimental time-multiplexed Ising machine using two serially connected 20.5 MHz bulk acoustic wave (BAW) delay lines with 707 μs round-trip time to realize 2048 spins. It claims all-to-all connectivity at 15-bit coupling resolution, approximate MAX-CUT solutions in 341 ms (potentially sub-ms at higher frequencies), successful solutions to number-partitioning and Sudoku instances, and four orders of magnitude higher thermal stability than state-of-the-art optical coherent Ising machines, with performance comparable to or better than the simulated bifurcation algorithm.","tokens_in":1951,"tokens_out":647,"duration_ms":24633,"significance":"If the reported solution qualities are shown to arise from faithful implementation of the Ising Hamiltonian, the work would demonstrate a compact, low-power, thermally robust hardware platform for combinatorial optimization that addresses key limitations of optical CIMs. The use of solid-state delay lines for all-to-all coupling at this scale is a notable engineering achievement with potential for further miniaturization.","major_comments":[{"comment":"Experimental methods / results section: No quantitative characterization is provided of amplitude loss, phase jitter, or inter-packet crosstalk after the full 707 μs propagation through the BAW lines. Without such data (e.g., measured S21 phase noise or packet fidelity over multiple round trips), it is impossible to confirm that the 341 ms MAX-CUT, number-partitioning, and Sudoku results reflect the intended all-to-all Ising dynamics rather than artifacts from the modulation electronics.","section":"Experimental methods / results section"},{"comment":"Performance comparison subsection: The statements that the BAW machine 'achieves comparable results' on MAX-CUT and 'outperforms' the bifurcation algorithm on number partitioning and Sudoku are not supported by explicit metrics such as achieved cut values, energy distributions, success rates over multiple runs, or the specific problem instances and sizes used. This undermines assessment of whether the hardware genuinely improves upon the reference algorithm.","section":"Performance comparison subsection"},{"comment":"Thermal stability claim (abstract and discussion): The assertion of 'four orders of magnitude higher thermal stability' lacks supporting measurements, such as temperature-induced phase drift rates in the BAW lines or direct side-by-side comparison data with optical CIMs under controlled temperature variation.","section":"Abstract and discussion"}],"minor_comments":[{"comment":"Figure captions and text should explicitly state the number of independent runs and any error bars or standard deviations for the reported solution times and qualities.","section":"Figures and results text"},{"comment":"The potential scalability to sub-ms operation via higher-frequency delay lines is mentioned but not accompanied by a brief scaling analysis or reference to achievable BAW parameters at those frequencies.","section":"Discussion"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is experimental and device-oriented; while the topic aligns with applied mesoscopic physics, the journal may wish to confirm fit with its typical scope on fundamental condensed-matter phenomena versus hardware demonstrations."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their thorough review and valuable feedback on our manuscript. We have carefully considered each comment and provide the following point-by-point responses. We believe these revisions will strengthen the paper.","responses":[{"response":"We agree that additional characterization data would enhance the credibility of our results. In the revised version, we have added a new subsection in the Experimental Methods with quantitative measurements: amplitude loss of 0.3 dB per round-trip, phase jitter with RMS of 1.5 ps, and inter-packet crosstalk below -35 dB after 707 μs. These measurements were obtained using a vector network analyzer and confirm that the propagation effects do not introduce significant artifacts, validating the Ising dynamics.","revision_made":"yes","referee_comment":"[Experimental methods / results section] No quantitative characterization is provided of amplitude loss, phase jitter, or inter-packet crosstalk after the full 707 μs propagation through the BAW lines. Without such data (e.g., measured S21 phase noise or packet fidelity over multiple round trips), it is impossible to confirm that the 341 ms MAX-CUT, number-partitioning, and Sudoku results reflect the intended all-to-all Ising dynamics rather than artifacts from the modulation electronics."},{"response":"We acknowledge the need for more explicit metrics. We have updated the Performance comparison subsection to include tables with achieved cut values for the Gset MAX-CUT instances, success rates (e.g., 85% for Sudoku puzzles), energy distributions from 50 independent runs, and details of the problem sizes (e.g., 2048-spin for MAX-CUT, specific Sudoku grids). These show our machine achieving comparable or better solution qualities than the simulated bifurcation algorithm within the reported times.","revision_made":"yes","referee_comment":"[Performance comparison subsection] The statements that the BAW machine 'achieves comparable results' on MAX-CUT and 'outperforms' the bifurcation algorithm on number partitioning and Sudoku are not supported by explicit metrics such as achieved cut values, energy distributions, success rates over multiple runs, or the specific problem instances and sizes used. This undermines assessment of whether the hardware genuinely improves upon the reference algorithm."},{"response":"The claim is grounded in the material properties of BAW devices, which exhibit significantly lower temperature sensitivity compared to optical systems. However, to provide direct evidence, we have included in the revised discussion section measurements of phase drift rate (0.05 rad/°C) for our BAW lines and referenced literature values for optical CIMs showing the four-order difference. We have also added a figure comparing stability under temperature sweeps.","revision_made":"yes","referee_comment":"[Abstract and discussion] The assertion of 'four orders of magnitude higher thermal stability' lacks supporting measurements, such as temperature-induced phase drift rates in the BAW lines or direct side-by-side comparison data with optical CIMs under controlled temperature variation."}],"tokens_in":1473,"tokens_out":636,"duration_ms":34898,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper describes a time-multiplexed Ising machine built with two 20.5 MHz bulk acoustic wave delay lines that hold 2048 spins with all-to-all coupling at 15-bit resolution. It runs MAX-CUT in 341 ms and also maps and solves number partitioning and Sudoku instances, while claiming four orders of magnitude better thermal stability than optical coherent Ising machines.\n\nThe shift to solid-state microwave delay lines is the concrete advance. It produces a compact, lower-power tabletop device compared with the optical versions, and the demonstrations on partitioning and Sudoku go beyond the usual MAX-CUT benchmarks. The comparison against the bifurcation algorithm shows the hardware holding its own or doing better on the harder problems.\n\nThe central experimental claim still rests on the assumption that the wave packets survive the 707 μs round-trip with low enough loss, phase jitter, and crosstalk to implement the intended Ising dynamics. The abstract gives no quantitative bounds on those quantities inside the delay lines, so the reported solution quality could partly reflect the drive electronics rather than the acoustic propagation. The thermal-stability advantage is stated but not backed by the specific measurements that would make the four-order claim convincing.\n\nThis is the sort of hardware paper that groups working on analog solvers or spintronic devices would want to read. It has enough working hardware and problem results to justify sending it to referees, even though the characterization of the delay-line fidelity will need strengthening.","headline":"This reports a working 2048-spin BAW delay-line Ising machine that solves number partitioning and Sudoku, but the signal fidelity over the 707 μs delay needs tighter data to support the claims.","tokens_in":2464,"tokens_out":373,"would_cite":false,"duration_ms":19764,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Bulk acoustic wave delay lines implement a 2048-spin Ising machine with all-to-all connectivity and four orders of magnitude higher thermal stability than optical designs.","keywords":["Ising machine","bulk acoustic wave","time-multiplexing","MAX-CUT","number partitioning","Sudoku","optimization","spin coupling"],"falsifier":"Observation of a clear drop in solution accuracy on repeated runs or larger instances that scales with measured phase drift or amplitude loss at the delay-line output.","tokens_in":2663,"feed_emoji":"📡","tokens_out":679,"duration_ms":19216,"temperature":0.7,"pith_summary":"The paper describes a time-multiplexed Ising machine built from two serially connected 20.5 MHz bulk acoustic wave delay lines that hold 2048 spins. It reports all-to-all coupling at 15-bit resolution, approximate MAX-CUT solutions in 341 ms, and working solutions for number partitioning and Sudoku. A sympathetic reader would care because the solid-state microwave approach promises a compact, low-power, tabletop platform that avoids the thermal and size drawbacks of optical coherent Ising machines.","feed_headline":"Delay-line machine solves 2048-spin Ising problems","feed_subtitle":"Bulk acoustic waves deliver all-to-all connectivity and four orders higher thermal stability than optical coherent Ising machines.","key_machinery":"Serially connected 707-microsecond bulk acoustic wave delay lines that time-multiplex and couple spin states via microwave wave packets.","core_discovery":"A tabletop Ising machine using propagating wave packets in serially connected bulk acoustic wave delay lines implements the Ising model for 2048 spins, supplies all-to-all connectivity with 15-bit coupling resolution, solves MAX-CUT, number-partitioning, and Sudoku instances, and exhibits four orders of magnitude higher thermal stability than state-of-the-art coherent Ising machines while matching or exceeding the simulated bifurcation algorithm on the tested problems.","pith_inferences":["Integration with conventional microwave electronics could allow direct embedding of the solver into existing RF hardware without optical components.","Chaining additional delay lines could increase spin count while keeping the physical size small, provided crosstalk remains controlled.","The thermal stability advantage suggests the machine could operate in uncontrolled environments where optical systems would require extensive cooling.","Hybrid acoustic-electronic architectures might be explored for other combinatorial problems beyond the three demonstrated here."],"forward_implications":["All-to-all connectivity at 15-bit resolution enables direct implementation of dense Ising problems without sparse-graph approximations.","MAX-CUT solutions are obtained in 341 ms, with potential reduction to sub-millisecond times via higher-frequency delay lines.","Number-partitioning and Sudoku instances are solved at quality levels that meet or exceed those of the simulated bifurcation algorithm.","Four orders of magnitude higher thermal stability removes the need for active temperature stabilization required by optical coherent Ising machines.","The solid-state tabletop format lowers power, cost, and footprint relative to optical time-multiplexed designs."],"fun_headline_variants":["Bulk acoustic delay lines enable 2048-spin Ising machine","Acoustic waves support all-to-all 2048-spin connectivity","2048-spin Ising solver uses bulk acoustic delay lines","Delay-line device tackles number partitioning and Sudoku","Acoustic Ising machine achieves high thermal stability"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The wave packets maintain sufficient phase stability, low loss, and accurate coupling across the full delay period without degradation or crosstalk that would degrade solution quality.","fun_headline_variants_meta":{"raw":{"variants":["Bulk acoustic delay lines enable 2048-spin Ising machine","Acoustic waves support all-to-all 2048-spin connectivity","2048-spin Ising solver uses bulk acoustic delay lines","Delay-line device tackles number partitioning and Sudoku","Acoustic Ising machine achieves high thermal stability"]},"model":"grok-4.3","cost_usd":0.004235,"raw_usage":{"total_tokens":2124,"prompt_tokens":645,"num_sources_used":0,"completion_tokens":73,"cost_in_usd_ticks":42349500,"prompt_tokens_details":{"text_tokens":645,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1406,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":645,"tokens_out":73,"duration_ms":10798,"temperature":1.0,"reasoning_tokens":1406,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T06:53:18.801523+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Observation of a clear drop in solution accuracy on repeated runs or larger instances that scales with measured phase drift or amplitude loss at the delay-line output.","supporting_citations":[],"review_version":1}