Coherent Ising Machines: The Good, The Bad, The Ugly

Artur Scherer; Farhad Khosravi; Martin Perreault; Pooya Ronagh

REVIEW 3 major objections 5 minor 76 references

Coherent Ising Machines: The Good, The Bad, The Ugly

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Coherent Ising machines are best understood as fast classical analog integrators of overdamped Langevin dynamics, with a real speed advantage only when all digital conversion is removed.

desk verdict A serious reframing of CIMs as analog Langevin integrators with solid qualitative evidence; treat the quantitative hardware claims as estimates until measured. read the letter →

arxiv 2507.14489 v1 pith:4RJRRW6T submitted 2025-07-19 physics.optics math.OC

Farhad Khosravi , Martin Perreault , Artur Scherer , Pooya Ronagh This is my paper

classification physics.opticsmath.OC

keywords coherentIsingmachineoverdampedLangevindynamicsBoxQPanalogopticalcomputingcontinuousoptimizationmeasurement-feedbackCIMtime-to-solutionenergy-to-solution

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 claims that coherent Ising machines (CIMs) are not quantum optimizers but fast classical analog devices that approximately integrate overdamped Langevin dynamics (OLD). It derives the stochastic differential equations of both fully optical delay-line CIMs (DL-CIMs) and hybrid measurement-feedback CIMs (MF-CIMs), compares their success rates and scaling against OLD and other heuristics on box-constrained quadratic programs, and benchmarks time-to-solution and energy consumption. The good news is that CIMs natively handle continuous variables and can be tuned by pump scheduling; the bad news is that no fundamental algorithmic advantage over OLD appears; the ugly news is that hybrid optical-digital designs are bottlenecked by analog-digital conversion and can even consume more energy than a purely digital FPGA implementation. The paper concludes that the genuine merit of optics appears only when the digital processor is removed entirely.

What carries the argument

The central machinery is the pair of SDE models: Eq. (1) for the DL-CIM, derived in a positive-P/truncated-Wigner picture under the high-finesse-cavity limit, and Eq. (2) for the MF-CIM, derived under the assumption that DOPO pulses maintain a Gaussian distribution throughout the evolution. Both are Langevin equations of the form dx = b(x,t)dt - ∇f(x)dt + σ(x,t)dW, and the comparison baseline is overdamped Langevin dynamics (Eq. (5)), whose convergence to the Gibbs state is well studied. The pump parameter p and measurement strength j set the drift and diffusion balance; ablating the nonlinear crystal leaves a linear MF-CIM whose surviving noise is the second derivative of a Wiener process, which isolates the role of the crystal's nonlinearity in creating useful stochastic exploration. The benchmarking machinery consists of time-to-solution and energy-to-solution estimates built from FPGA latencies, optical pulse rates, and component power models, including the power consumed by DACs, ADCs, transceivers, and optical modulators.

What would settle it

Run the same BoxQP instances of size 70 on a physical DL-CIM and on an FPGA implementation of overdamped Langevin dynamics with the serial matrix-vector unit described in the paper: if the DL-CIM's time-to-solution is not about two orders of magnitude below the FPGA's, the paper's central quantitative claim fails. Independently, direct homodyne measurement of DOPO pulse statistics in the MF-CIM's operating regime that shows clearly non-Gaussian distributions would invalidate the model in Eq. (2) on which the OLD-equivalence argument rests.

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Extended reading notes

Core claim

The paper establishes that both DL-CIM and MF-CIM dynamics are Langevin-type SDEs of the general form dx = b(x,t)dt - ∇f(x)dt + σ(x,t)dW, and that both behave like approximate, slightly biased integrators of overdamped Langevin dynamics when solving binary or continuous optimization problems. It finds no evidence of a fundamental computational advantage over OLD: the fully optical DL-CIM achieves an estimated speed advantage of about two orders of magnitude in time-to-solution over both an FPGA-based OLD and the MF-CIM, but only because it avoids digital-to-analog and analog-to-digital conversion, while the MF-CIM actually consumes more energy than an FPGA OLD because of its DAC, ADC, and transceiver circuitry. The paper also shows that a continuous-variable readout of CIM pulse amplitudes natively solves box-constrained quadratic programs without binary discretization, and that the pump rate can be scheduled to trade exploration against exploitation depending on the convexity of the landscape.

Load-bearing premise

The paper's conclusions rest on assuming that the optical pulses in the measurement-feedback machine keep a bell-shaped (Gaussian) amplitude distribution and that the fully optical cavity is lossy enough that the equations used match the real devices; if non-Gaussian statistics, saturation, or quantum correlations materially change the dynamics, the equivalence to overdamped Langevin dynamics and all performance and energy conclusions apply to the model rather than to the machines.

Editorial extensions

If this is right

If the paper's picture is correct, present CIM hardware should be evaluated against well-tuned overdamped Langevin dynamics on the same hardware, not against quantum annealers or simulated annealing, when assessing speed and energy claims.
CIMs operated below saturation threshold can natively solve continuous-variable optimization problems such as BoxQP without binary discretization or problem reformulation, which avoids the cost of large Ising encodings.
The fully optical DL-CIM's estimated two-orders-of-magnitude time-to-solution advantage over FPGA OLD and MF-CIM comes from eliminating digital conversion; hybrid optical-digital designs cannot beat digital OLD and may consume more energy.
Adjusting the pump schedule p0 gives a practical control knob for trading exploration against exploitation: negative pump values help hill-climb on concave landscapes whose solutions lie at box boundaries, while positive pump values encourage fast descent on convex landscapes.
Fully optical CIMs, if equipped with reliable nonlinear optical elements, could serve as high-speed, low-energy integrators of stochastic differential equations in settings beyond quadratic optimization, such as generative inference and random number generation.

Reading between the lines

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

Beyond the paper: the OLD-equivalence suggests CIMs could be adapted for sampling from Gibbs-type distributions by tuning drift and diffusion to satisfy detailed balance, a direction the paper mentions only as a broader application of SDE integration.
Beyond the paper: the two-orders-of-magnitude TTS claim is based on estimated latencies for a DL-CIM; a direct experimental head-to-head with an optimized digital OLD at large problem sizes would sharpen or qualify that number.
Beyond the paper: the pump-scheduling insight (exploration versus exploitation based on landscape convexity) could be transferred back to digital OLD solvers, which would create a stronger classical baseline and potentially reduce the apparent optical advantage.
Beyond the paper: the argument implies that progress in fully analog nonlinear activation and constraint-enforcing optical components is the critical bottleneck for unlocking the technology's stated speed and energy benefits, more so than improving quantum coherence or squeezing.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a serious paper that does real work. The central framing — CIMs are better understood as analog integrators of overdamped Langevin dynamics than as quantum optimizers — is supported by the correlation experiments and the SDE analysis. I would send it to review. The hardware numbers, however, are estimates and should be read as such.

What's new: the LMF-CIM derivation with the derivative-of-white-noise term, the generalized-process formalism in Appendix A, the ablation of the nonlinear crystal, and the systematic TTS/ETS comparison across FPGA, MF-CIM, and DL-CIM. The continuous-variable readout and the SDE models build on the authors' earlier [40], but this paper goes beyond consolidation: the ablation and the benchmarking are genuinely new. The open-source simulator is a real asset.

Soft spots, in order of importance. First, Eqs. (1) and (2) are model assumptions. The Gaussian ansatz for MF-CIM and the high-finesse limit for DL-CIM are not checked against measured dynamics from existing machines. The comparison to OLD tests the models, not the hardware. That makes the 'no fundamental advantage' claim a claim about the models. I don't think this sinks the paper — the authors are careful to call it approximate — but the conclusion states it more flatly than the evidence warrants.

Second, the hardware conclusions are estimates. DL-CIM power terms and FPGA latencies come from datasheets and engineering assumptions, not from a built device. The two-orders-of-magnitude TTS advantage is computed against a serial FPGA baseline; Fig. 10 shows a parallel FPGA comes into roughly the same range. The text acknowledges this in Appendix C3, but Section VI does not carry the caveat. That should be fixed.

Third, the benchmark is 50 generated BoxQP instances up to N=70. Good for a first pass, not enough to establish scaling laws. Overlapping exponential slopes are suggestive, not a proof of no advantage. A sensitivity analysis over hardware parameters and a fixed protocol for hyperparameter choices would strengthen the quantitative claims.

Bottom line: for someone asking what CIMs are actually doing, this is the clearest account I've seen. For someone buying hardware based on the TTS/ETS tables, it's not there yet. Worth a serious referee.

Referee Report

3 major / 5 minor

Summary. This paper presents a semi-classical analysis of coherent Ising machines (CIMs), arguing that both delay-line (DL-CIM) and measurement-feedback (MF-CIM) architectures are best understood as analog devices that approximately integrate overdamped Langevin dynamics (OLD), rather than as quantum optimizers that exploit superposition or entanglement. The authors introduce SDE models for both architectures (Eqs. 1 and 2), show that an MF-CIM without its nonlinear crystal (LMF-CIM) still exhibits stochastic dynamics driven by white noise and its derivative (Appendix A, treated via generalized stochastic processes), and compare CIM solvers against OLD and classical heuristics on 50 generated BoxQP instances up to N=70 using success-probability correlations and fitted TTS scaling. They further estimate time-to-solution (TTS) and energy-to-solution (ETS) for FPGA-based OLD, MF-CIM, and DL-CIM hardware, concluding that fully optical DL-CIMs achieve about two orders of magnitude faster TTS than serial FPGA-based solvers, that hybrid MF-CIMs consume more energy than digital-only FPGAs because of DAC/ADC/transceiver overhead, and that no fundamental algorithmic advantage over OLD is evident.

Significance. The paper makes three contributions that are valuable if the claims hold. First, the LMF-CIM analysis in Appendix A is a genuine analytic result: removing the optical nonlinearity from a measurement-feedback CIM does not remove its stochasticity, and the resulting derivative-of-white-noise term is handled rigorously in the framework of generalized stochastic processes. Second, the benchmark study is unusually careful: solver parameters are tabulated (Table I), iteration counts are tuned per problem size (Appendix F), and TTS/ETS results are reported as medians with IQR bands over 50 instances per size. Third, the ETS power breakdown in Section V gives concrete, falsifiable numbers to a debate on hybrid optical-digital bottlenecks that is usually conducted qualitatively. The paper also releases an open-source simulator, and its central predictions (high correlation between CIM and OLD success probabilities; the energy penalty of digital conversion in MF-CIM) are directly testable.

major comments (3)

[Section VI; Eqs. (1)-(2), Section II] The central claim that CIMs present no fundamental computation advantage over OLD is established only at the level of the SDE models of Eqs. (1) and (2), and those models are not validated against physical CIM behavior. Equation (2) is derived under the explicit ansatz that the DOPO pulses maintain a Gaussian distribution throughout the evolution [22,29], and Eq. (1) is restricted to the high-finesse cavity limit; the manuscript does not test either assumption against measured dynamics or TTS data from existing machines (e.g., refs. [21,26]), nor does it bound the effect of non-Gaussianity or finite-finesse corrections on escape rates and stationary measures. The numerical experiments therefore establish equivalence between OLD and the authors' CIM simulators, not between OLD and the physical machines. I recommend either validating the SDE models against experiment or explicitly restricting the no-advantage claim to the model class, with the hardware conclusions softened accordingly.
[Section IV and Section VI; Appendix C3, Fig. 10] The 'about two orders of magnitude' DL-CIM TTS advantage reported in Section IV (Fig. 6c) is computed against a serial FPGA baseline and a serial MF-CIM implementation. Appendix C3 and Fig. 10 show that a parallel FPGA design for OLD and for MF-CIM brings TTS and ETS into a range comparable with the DL-CIM, a point the body acknowledges ('comparable to the DL-CIM scheme'). Section VI nevertheless restates the two-orders claim without this caveat, and the abstract conveys the same impression. The claim should be qualified as holding against serial digital and hybrid baselines, with the parallel-baseline result presented in the same statement.
[Section IV] The statement that DL-CIM is 'not statistically superior' to FPGA-based OLD is supported only by overlapping ranges of fitted exponential TTS slopes (DL-CIM 0.029-0.042, OLD 0.029-0.049). These ranges are taken across the four optimality-gap targets, not across instances: no confidence intervals on the fitted slopes are reported, and no paired test on the TTS distributions (50 instances per size) is performed. Since the asymptotic-equivalence claim is one of the paper's headline conclusions, I recommend reporting slope confidence intervals or a formal comparison (e.g., paired bootstrap over instances) for at least one gap target.

minor comments (5)

[Figs. 7 and 10] The legends label the optical solvers 'MF-CCVM' and 'DL-CCVM'; these should be 'MF-CIM' and 'DL-CIM' for consistency with the text.
[Author affiliations] The first affiliation reads 'Irrevresible Inc.', which appears to be a typo for 'Irreversible Inc.'.
[Reference [40]] Reference [40], which supplies the continuous-variable readout framework that this paper builds on, is cited as a 2022 arXiv preprint; if a peer-reviewed version exists, it should be cited instead or as well.
[Section I] The introduction promises a demonstration of 'on par asymptotic effectiveness' of the CIM and OLD dynamics, but the evidence covers N up to 70 with 50 instances and no formal asymptotic analysis; a phrase such as 'scaling for the studied problem sizes' would be more accurate.
[Section V and Fig. 9] The MF-CIM power estimate is dominated by the DAC/ADC/transceiver term (10.45 W of 15.69 W), which is taken from device-family specifications; since this term drives the conclusion that MF-CIM is less energy-efficient than FPGA-only OLD, a brief statement of how robust that conclusion is to errors in this estimate would strengthen the presentation.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the OLD-equivalence and benchmarking claims are supported by independent numerical comparisons; the same-group citation [40] supplies the CV framework but is not load-bearing for the main conclusion.

full rationale

The paper's central claim—that CIMs are approximate integrators of overdamped Langevin dynamics and have no fundamental computation advantage over OLD—is derived from the explicit SDE models of Eqs. (1), (2), (5), and (6) and then tested by independent numerical experiments. The correlation studies in Section III compare MF-CIM, LMF-CIM, OLD, gradient descent, simulated annealing, and steepest descent on 50 generated BoxQP instances; the TTS scaling comparisons in Section IV and Appendix C compare OLD on FPGA, MF-CIM, and DL-CIM using documented hardware parameters. No fitted CIM parameter is reused as a predicted success rate or TTS value, so the 'prediction' is not statistically forced by a fit. The self-citation to [40] supplies the continuous-variable readout framework and BoxQP encoding (Appendix B), but the main 'no fundamental advantage' conclusion does not reduce to that citation: it rests on this paper's own open-source simulation results and slope comparisons. The claims about the two-orders-of-magnitude DL-CIM speed advantage are qualified by the parallel-FPGA results in Fig. 10 and Appendix C.3, and the Gaussian and high-finesse assumptions in Eqs. (1) and (2) are modeling limitations that affect external validity rather than circular reductions. Overall, no step in the derivation chain is equivalent to its inputs by construction; the only burden is a minor, non-load-bearing self-citation to the same group's earlier CV-CIM work.

Assumptions & free parameters 10 free parameters · 5 assumptions · 0 invented entities

The framework imports the SDE models of CIMs from prior literature, adds tuned hyperparameters (s, p0, niter, j0, alpha, r0, beta, lambda, g, As), and assumes hardware power and latency values. The central claim does not depend on a fitted target, but the quantitative TTS/ETS results depend on these chosen values. No new physical entities are postulated; the LMF-CIM is an ablation of existing hardware, and the derivative of white noise is a mathematical object, not a new physical entity.

free parameters (10)

saturation parameter s = DL-CIM: 1.2*sqrt(p0-1); MF-CIM: 20.0 (Table I)
Maps pulse amplitude to continuous variable; Appendix B.2 says s is tuned to obtain best performance; affects all BoxQP results.
pump field p0 = p0=8.0 (DL-CIM), 0.0 (MF-CIM), varied -2 to 2 in Fig. 5
Controls exploration versus exploitation; tuned per solver and instance class; changes TTS in Fig. 5.
iteration count niter = 500-1500 (OLD), 10^3-10^4 (DL-CIM), 300-4000 (MF-CIM)
Appendix F: niter tuned for each problem size and solver to minimize TTS; directly sets TTS and ETS.
measurement strength parameters (j0, alpha) = j0=5, alpha=3 (Table I)
MF-CIM measurement schedule j(t)=j0 exp(-alpha t/Tmax); called arbitrary parameters in Appendix C.1.
injected noise parameters (r0, beta) = r0=10, beta=3 (Table I)
DL-CIM noise schedule r(t)=r0 exp(-beta t/Tmax); called arbitrary parameters in Appendix C.1.
gradient strength lambda = 1.0 (OLD), 50+t/Tmax*100 (DL-CIM), 4000 (MF-CIM)
Feedback gain in drift terms; per-solver choices in Table I affect dynamics and performance.
nonlinearity coefficients g and As = g=0.001 (MF-CIM), As=10 (DL-CIM)
Set in Table I; determine mean-field variance and noise amplitude.
DL-CIM power model terms = Popt=1.2 mW, Pmod=10 mW, Psq=180 mW, POPA=222.2 mW
Estimated component powers in Appendix C.2 drive the ETS conclusion that DL-CIM is energy efficient.
FPGA and MF-CIM power and latency values = FPGA 300 MHz; serial latencies 1.37-16.43 us for N=20-70; MF-CIM DAC/ADC power around 10.4 W
Latency and power tables drive the 'hybrid bottleneck' and ETS conclusions; they are estimates, not measurements on the actual CIM hardware.
instance generation parameters (c0, phi_max) = c0 in {-50,...,50}, phi_max = pi/2 or 0.1 pi
Generate BoxQP instances with controlled fraction of fractional solutions; results may depend on this distribution.

assumptions (5)

domain assumption High-finesse positive-P SDE (Eq. 1) is a faithful model of DL-CIM pulse amplitudes.
The paper states this is accurate only for low optical loss relative to photon lifetime; benchmarking uses this model to draw conclusions about real DL-CIMs.
domain assumption Gaussian-distribution ansatz for MF-CIM pulses (Eq. 2) is valid throughout evolution.
Imported from refs [22,29]; if pulses become non-Gaussian, the mean-field equations and the LMF-CIM ablation do not describe the device.
standard math Generalized stochastic process calculus (testing against compactly supported smooth functions) makes W-double-dot well-defined.
Appendix A uses distribution theory to interpret the second derivative of the Wiener process; this is standard but non-Itô.
standard math Langevin dynamics converges to Gibbs or low-energy states for OLD.
Used to justify OLD as an optimizer; supported by cited results [36,45,46].
domain assumption Estimated hardware component values and benchmark instances represent realistic devices and problems.
TTS/ETS conclusions depend on Tables I-III power and latency estimates and on the random BoxQP generator; no end-to-end optical measurement is reported.

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Cite this review

Pith. "Pith review of Coherent Ising Machines: The Good, The Bad, The Ugly." pith.science (2026). https://pith.science/paper/4RJRRW6T

@misc{pith2026250714489,
  author       = {Pith},
  title        = {Pith review of: Coherent Ising Machines: The Good, The Bad, The Ugly},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4RJRRW6T}},
  note         = {Machine review of arXiv:2507.14489}
}

read the original abstract

Analog computing using bosonic computational states is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. But the challenges of manufacturing large-scale photonic integrated circuits (PIC) has led to hybrid solutions that integrate optical analog and electronic digital components. A notable example is the coherent Ising machine (CIM), that was primarily invented for solving quadratic binary optimization problems. In this paper, we focus on a mean-field interpretation of the dynamics of optical pulses in the CIM as solutions to Langevin dynamics, a stochastic differential equation (SDE) that plays a key role in non-convex optimization and generative AI. This interpretation establishes a computational framework for understanding the system's operation, the computational role of each component, and its performance, strengths, and limitations. We then infer that the CIM is inherently a continuous state machine, capable of integrating a broad range of SDEs, in particular for solving a continuous global (or mildly constrained) optimization problems. Nevertheless, we observe that the iterative digital-to-analog and analog-to-digital conversions within the protocol create a bottleneck for the low power and high speed of optics to shine. This observation underscores the need for major advances in PIC technologies as we envision that fully analog opto-electronic realizations of such experiments can open doors for broader applications, and orders of magnitude improvements in speed and energy consumption.

Figures

Figures reproduced from arXiv: 2507.14489 by the authors.

**Figure 2.** FIG. 2: Correlation plot comparing MF-CIM’s performance with CV [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3: Correlations between MF-CIM and classical heuristics when solving 50 BoxQP problem instances of size 70. (a) CV-OLD against the CV [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: FIG. 4: Example BoxQP optimization landscapes in two variables [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5: TTS versus pump value for random instances with different [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6: Estimated TTS for (a) the CV-OLD solver implemented on FPGA, (b) the CV-MF-CIM, and (c) the CV-DL-CIM solvers. For each solver, [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7: (a) Estimated TTS and (b) ETS metrics for the three types of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: FIG. 8: The effect of the noise in the DL-CIM method (solid lines) as [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9: The power consumption of the FPGA and the surrounding [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

**Figure 10.** Figure 10: FIG. 10: (a) Wall-clock TTS for optics-based CV impelemntations of CIM (dashed–dotted curves) in comparison with the wall-clock TTS for [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

**Figure 11.** Figure 11: FIG. 11: The design of the FPGA used for the TTS and ETS [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]

**Figure 12.** Figure 12: FIG. 12: The results for the MF-CIM versus the batch size for (a) [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

**Figure 13.** Figure 13: FIG. 13: Time evolution of the DOPO pulses’ amplitudes for four [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

**Figure 14.** Figure 14: FIG. 14: TTS versus number of iterations for different problem sizes [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]

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Reference graph

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Box-constrained quadratic programming (BoxQP) problems The BoxQP problem can be formulated as follows: maximize f (x) = 1 2 NX i,j=1 Qijxixj + NX i=1 Vixi, subject to ℓi ≤ xi ≤ ui ∀i ∈ {1, . . . , N}, (B1) where Q ∈ RN ×N is a symmetric matrix, V ∈ RN is a real N -dimensional vector, and the lower and upper bounds ℓi ∈ R and ui ∈ R specify the box constra...

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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for solving continuous variable problems using the CIM. We introduce the box-constrained quadratic prob- lems (BoxQP) problem, our approach for implementing and solving them using CIMs, and a new method for generating random BoxQP instances

work page

[2] [1]

, N}, (B1) where Q ∈ RN ×N is a symmetric matrix, V ∈ RN is a real N -dimensional vector, and the lower and upper bounds ℓi ∈ R and ui ∈ R specify the box constraints

Box-constrained quadratic programming (BoxQP) problems The BoxQP problem can be formulated as follows: maximize f (x) = 1 2 NX i,j=1 Qijxixj + NX i=1 Vixi, subject to ℓi ≤ xi ≤ ui ∀i ∈ {1, . . . , N}, (B1) where Q ∈ RN ×N is a symmetric matrix, V ∈ RN is a real N -dimensional vector, and the lower and upper bounds ℓi ∈ R and ui ∈ R specify the box constra...

work page

[3] [2]

In this case, the amplitude and phase of the pulses represent the value and the sign of the variables of the problem

Mapping BoxQP problems on the CIM CIMs can be operated below the saturation threshold to solve CV optimization problems. In this case, the amplitude and phase of the pulses represent the value and the sign of the variables of the problem. By prop- erly pumping the optical pulses, the CV variables of the BoxQP problem are encoded into the analog pulse ampl...

work page

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Randomly generated BoxQP instances We have tested the performance of the various solvers introduced in this paper on randomly generated BoxQP problem instances. As opposed to the older meth- ods [40, 57], our new approach provides us control over the hardness of the problem instances and the number of fractional values in the corresponding optimal solutio...

work page

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8 shows the effectiveness of the noise when solving the randomly generated instances

Significance of CIM’s noise injection Fig. 8 shows the effectiveness of the noise when solving the randomly generated instances. We have compared the performance of the DL-CIM method (solid lines) against a simple Euler gradient descent method (with no noise) with constraint enforcement at each step. For the 0 .1% gap (blue curves), the Euler gradient des...

work page

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Z. Wang, A. Marandi, K. Wen, R. L. Byer, and Y. Ya- mamoto, Coherent Ising machine based on degenerate optical parametric oscillators, Phys. Rev. A 88, 063853 (2013)

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TTS is a useful metric for comparing the performance of different hardware when solving a given optimization problem [ 40]

Time-to-solution calculations Here, we provide more details for estimating the TTS of the optical devices with the dynamics introduced in Section II. TTS is a useful metric for comparing the performance of different hardware when solving a given optimization problem [ 40]. Table I shows the parameters of the solvers used for generating the results in Figs...

work page

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full FPGA

Energy consumption estimates In this section, we present our approach for estimating the ETS for three solvers implemented on five different hardware: OLD implemented on FPGA, CPU, and GPU; DL-CIM; and MF-CIM. ETS is a metric that quanti- fies the energy consumption of a given hardware device in implementing a specified solver for a given BoxQP instance. ...

work page