A Distributed Quantum Approximate Optimization Algorithm For Unit Commitment

Ali Rajabi; Amin Kargarian; Milad Hasanzadeh

REVIEW 3 major objections 4 minor 15 references

A Distributed Quantum Approximate Optimization Algorithm For Unit Commitment

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read This paper claims that a three-block ADMM unit commitment framework can solve its binary QUBO block with distributed QAOA across multiple QPUs, and on a 15-variable five-unit case all three solver modes recover the same commitment…

desk verdict A clean, small integration study whose consistency claim is real but whose quantum solver is an unshared simulator with no reported hyperparameters; referee-worthy if the authors open the black box. read the letter →

arxiv 2608.04159 v1 pith:CMOPGTVF submitted 2026-08-04 cs.DC

Ali Rajabi , Milad Hasanzadeh , Amin Kargarian This is my paper · ORCID

classification cs.DC

keywords unitcommitmentquantumapproximateoptimizationalgorithmdistributedcomputingADMMQUBOQAOAmulti-QPUpowersystem

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

This paper tries to establish that the binary commitment step of unit commitment, isolated by a three-block ADMM decomposition, can be solved by a distributed quantum approximate optimization algorithm without changing the outer classical loop. The key move is to express the binary update as a QUBO and pass it to an interface that can enumerate exactly, run monolithic QAOA on one QPU, or run distributed QAOA across several capacity-constrained QPUs. On a five-unit, three-period case with 15 binary variables, the authors report that all three modes drive the ADMM primal residual below $10^{-3}$ and recover the same commitment bitstring, dispatch, and operating cost of $12{,}678. If true, the practical payoff is that UC instances larger than a single QPU's capacity could still be addressed by spreading logical qubits across QPUs, at the price of extra communication overhead rather than runtime gain.

What carries the argument

The load-bearing mechanism is the three-block ADMM decomposition: Block 1 solves a convex quadratic program for relaxed commitment and dispatch variables, Block 2 maps the binary commitment update into a QUBO whose coefficients depend on the current ADMM variables, and Block 3 updates the slack variable analytically. The DQAOA interface then lets Block 2 be solved by brute force, monolithic QAOA, or distributed QAOA; in distributed mode, logical data qubits are partitioned across QPUs and quadratic interactions that cross QPU boundaries are implemented through TeleGate operations with communication qubits and classically conditioned corrections. The final sampled bitstring set $S^{(k)}$ is scored against the current QUBO objective, and the best observed bitstring is returned to the ADMM loop.

What would settle it

Run the same framework on an instance where the known QUBO optimum is deliberately excluded from the sampler's candidate set at some ADMM iteration, or replace the TeleGate simulation with noisy hardware; if Eq. (17) then returns a suboptimal commitment, the recovered cost will deviate from brute force, showing that the equality is not structural.

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Extended reading notes

Core claim

The central claim is that the binary commitment block of unit commitment, isolated as a QUBO within a three-block ADMM, can be solved by distributed QAOA with the same outcome as brute-force enumeration. The paper demonstrates this on a five-unit, three-period instance with 15 logical qubits, reporting that brute force, monolithic QAOA, and distributed QAOA all converge below the primal residual tolerance and recover the same commitment matrix, the same dispatch, and the same operating cost of $12{,}678. The distributed mode achieves this by allocating the 15 logical commitment qubits across multiple capacity-constrained QPUs, while the non-distributed modes require all qubits on one QPU.

Load-bearing premise

The distributed mode's exact match with brute force assumes that the DQAOA simulator's TeleGate operations faithfully reproduce cross-QPU interactions and that the finite set of sampled bitstrings $S^{(k)}$ contains the true QUBO optimum at every ADMM iteration; if either fails, the reported zero optimality gap could be an artifact of simulation.

Editorial extensions

If this is right

In the tested case, replacing brute-force enumeration with either monolithic or distributed QAOA inside Block 2 leaves the recovered commitment bitstring, dispatch, operating cost, and ADMM convergence unchanged.
Distributed QAOA removes the requirement that all binary variables fit on one QPU, so the combined capacities of several QPUs can accommodate the same logical problem.
Because only Block 2 changes, any future improvement in binary QUBO solvers can be dropped into this ADMM framework without reformulating the UC model or the continuous updates.
The reported cost of $12{,}678 with zero optimality gap against brute force is the paper's evidence that the sampled QAOA bitstrings contained the QUBO optimum at each ADMM iteration.

Reading between the lines

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

A natural next test is whether the consistency survives larger UC instances, where the sampled set $S^{(k)}$ may miss the true QUBO optimum and QAOA parameter optimization becomes harder.
The reported equality with brute force is only as strong as the simulator's TeleGate fidelity; on real hardware, communication qubit errors and classical correction overhead would likely break the exact cost match.
The same DQAOA interface could be applied to other mixed-binary power-system problems, such as optimal transmission switching or expansion planning, because the outer ADMM structure is problem-agnostic.
The paper does not claim runtime advantage; a fair comparison would need wall-clock or circuit-depth accounting for cross-QPU TeleGate overhead.

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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

Punchline: this is a small but honest integration study. The new bit is that the authors' DQAOA package, with its distributed TeleGate machinery, is plugged into the binary block of their three-block ADMM formulation and tested on one 15-variable instance. Brute-force enumeration gives the same $12,678 schedule, so the final optimum is anchored. That is genuine, if modest, evidence.

What's good: The paper is clearly written, the ADMM/QUBO derivation is standard, and the comparison is fair in the sense that all three modes share the same UC data, ADMM parameters, and stopping tolerance. Using brute force as a reference on a small instance is the right way to check a quantum/classical hybrid pipeline. The convergence plots show the primal residual dropping below 1e-3 for both QAOA modes, and the commitment/dispatch tables match.

Soft spots: The load-bearing part is unverified. The DQAOA simulator is only described by reference to the authors' own preprint [15]; no source, no independent benchmark, no noise model. The paper never reports QAOA depth p, Adam iterations, learning rate, final shot count, or the number of independent runs. With 15 variables the sample set can easily miss the optimum, so the 'zero optimality gap' is a statement about the sampled outcomes of this particular simulator, not about distributed QAOA as a method. The reader's stress-test is right on this. I also note Eq. (9) has a 1/2 factor on the dual update, which is non-standard; it may be harmless if the slack variable absorbs it, but it deserves a sentence of justification.

One thing I'd push back on: the stress-test says the equality with brute force is 'not established.' I'd soften that. The brute-force mode uses the same ADMM loop and the same Eq. (9), so the final $12,678 optimum is real for this instance. What is not established is that the QAOA/DQAOA modes found it through the quantum circuit as claimed, as opposed to the optimizer effectively solving a small QUBO by classical means or by luck. That distinction matters for the paper's significance, but it doesn't undo the consistency result.

Bottom line: worth a serious referee, but only if the authors are pressed to release the simulator or benchmark it against an external QAOA implementation, report all hyperparameters and shots, run multiple seeds, and justify Eq. (9). As is, it's a case study, not a validated method. I would not cite it yet; I'd bring it to reading group as an example of how to anchor hybrid quantum-classical results with brute force.

Referee Report

3 major / 4 minor

Summary. The paper integrates a distributed QAOA (DQAOA) package as the binary commitment solver within a three-block ADMM framework for unit commitment. The first block solves a continuous QP for relaxed commitments and dispatches, the second block solves a QUBO encoding the binary commitment decisions, and the third block updates a slack variable. The binary QUBO can be solved by brute-force enumeration, monolithic QAOA, or distributed QAOA, with all other ADMM steps identical. On a five-unit, three-period instance with 15 binary variables, the authors report that all three modes converge below a primal residual tolerance of 10^-3 and recover the same commitment schedule, dispatch, and operating cost of $12,678, which they describe as a zero optimality gap relative to brute force. The paper claims that the distributed mode achieves this while distributing the 15 logical qubits across multiple capacity-constrained QPUs.

Significance. If the consistency and multi-QPU capacity claims are established, the work would provide a useful template for hybrid quantum-classical decomposition of mixed-integer power-system problems, since the binary block can be swapped among classical and quantum solvers without altering the ADMM machinery. The paper makes a strong, falsifiable prediction: all three modes recover exactly the same commitment/dispatch solution on the tested instance. It also has a sensible design virtue in that the brute-force mode provides an internal reference point for the final recovered optimum. However, the evidence presented is currently insufficient to support the central claim, because the quantum-mode results depend on unreported hyperparameters and sampling details, and on an unverified, self-cited simulator. The significance is therefore contingent on the authors supplying the missing experimental and verification information.

major comments (3)

[§III.C and §IV.B] The central claim that monolithic QAOA and DQAOA recover the same optimum as brute force requires that, at every ADMM iteration, the sampled set S(k) in Eq. (17) contains a bitstring achieving the true QUBO minimum or at least one that steers ADMM to the same fixed point. The paper does not report the QAOA depth p in Eq. (14), the Adam optimizer's iteration count or learning rate, the number of final shots, or the number of independent runs. With 15 binary variables there are 32,768 candidate bitstrings, so a finite sample can easily miss the optimum. Please report these quantities and provide evidence, such as the distribution of recovered costs over repeated runs, the probability that the sampled set contains the optimum at each ADMM iteration, or a comparison against an exhaustive-search check of the QUBO minima at selected iterations.
[§III.B and §IV.B] The distributed-QAOA results rely entirely on the authors' DQAOA simulator described only by reference to [15]. The TeleGate mechanism for cross-QPU interactions is not described in the manuscript, and no independent verification, noise model, or release of the simulator is provided. Since the observed equality with brute force in the distributed mode depends on this simulator faithfully implementing the cross-QPU Z_j Z_m terms, please provide a concrete verification of the TeleGate implementation (e.g., statevector comparison on small instances), release the simulator code, or benchmark it against an independent distributed-QAOA implementation. Without this, the distributed result is a claim about an unverified simulation rather than a demonstrated property of the method.
[§II.B, Eq. (9)] The dual variable update in Eq. (9) uses a factor of 1/2 on the residual, λ(k) = λ(k−1) + (ρ/2)(y(k) − z(k) + r(k)), whereas the standard ADMM gradient ascent update for the consensus constraint would be λ(k) = λ(k−1) + ρ(y(k) − z(k) + r(k)). This non-standard scaling is not discussed or justified in the paper. Since the fixed point and convergence behavior of the ADMM scheme depend on the dual update, please either justify the ρ/2 scaling or replace it with the standard update and re-run the experiments.

minor comments (4)

[Eq. (3)] The notation ρ/2 ∥y_i,t − z_i,t + r_i,t∥_2^2 uses a vector norm on scalar quantities; it should be written as (ρ/2)(y_i,t − z_i,t + r_i,t)^2 for clarity.
[§IV.B and Fig. 3] Figure 3 shows convergence curves only for the two quantum modes, but the text says 'Fig. 3 indicates the ADMM primal residual for the solver quantum modes'; adding the brute-force curve would directly support the consistency claim and make the comparison complete.
[Table II and text] Table II reports the cost as 12678.45, while the text states $12,678; please reconcile the rounding so that the table and the narrative agree.
[References] Reference [15] is a self-cited preprint described as providing the DQAOA interface; given that the present paper's central result depends on this package, please clarify its availability or peer-review status in the manuscript text.

Circularity Check

1 steps flagged · score 4.0 of 10

The distributed-QAOA leg of the consistency claim rests on the authors' own unverified DQAOA simulator [15], while the ADMM/QUBO derivation itself and the brute-force reference are independent; circularity is partial, not definitional.

self citation load bearing [Section III-B (Capacity-Constrained Distributed QAOA); also Section I and Ref. [15].]
"If they are assigned to different QPUs, the corresponding operation is realized through the TeleGate-based mechanism of the DQAOA package [15]. TeleGate uses communication qubits, intermediate measurements, and classically conditioned corrections to reproduce the required cross-QPU interaction while preserving the logical data qubits."

The paper's central demonstration that distributed QAOA recovers the same commitment schedule and operating cost as brute force depends on the correctness of the cross-QPU TeleGate operations. That correctness is not derived or verified within the present paper; it is imported from Ref. [15], a same-author preprint that is not machine-checked, code-released, or benchmarked against any independent quantum device or simulator. Thus the load-bearing support for the distributed-mode result reduces to an unverified self-citation rather than to an external test. The brute-force leg is an independent reference, so the overall consistency claim is not circular by construction, but the distributed claim is not independently evidenced.

full rationale

The ADMM derivation is self-contained: Block 1 solves the continuous QP, Block 2 constructs the QUBO and selects the best sampled bitstring via Eq. (17), Block 3 updates the slack variable in closed form, and the dual update is standard. The brute-force mode provides an exact reference for the 15-bit QUBO. If the QAOA and DQAOA simulator outputs match that reference, that is an empirical consistency claim, not a conclusion forced by definition. There is no equation in the paper that makes the quantum modes equal to brute force by construction. The QUBO coefficients depend on the ADMM variables, and the final cost is evaluated from the recovered schedule and dispatch, so the reported $12,678 figure is not obtained by renaming a fitted parameter. The main circularity-adjacent issue is the reliance on the authors' own DQAOA simulator [15] for the distributed TeleGate mechanism; no formal verification, external benchmark, or code release is provided for that simulator, and the paper gives no QAOA depth, shot counts, or optimizer details. This is a load-bearing self-citation for the distributed result, raising the score to 4, but the independent brute-force leg and the self-contained ADMM formulation prevent a higher circularity score.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim does not fit any measured constants, but it depends on several hand-chosen algorithm parameters and on the correctness of the authors' own unreleased simulator. The brute-force mode provides an independent anchor for the final binary optimum.

free parameters (6)

ADMM penalty coefficient rho = not reported
Controls the augmented Lagrangian and dual update in Eqs. (3) and (9). No value is given, and the dual update uses a non-standard rho/2 scaling.
Regularization coefficient beta = not reported
Controls slack-variable regularization in Block 3, Eq. (8). The value is not reported.
QAOA depth p = not reported
Number of alternating cost and mixer layers in Eq. (14). The value is not specified.
QAOA optimizer settings = not reported
Adam learning rate, number of optimization iterations, and convergence criteria for the variational parameters are not specified.
Final shot count = not reported
Number of final circuit samples used to build the set S(k) in Eq. (17). The paper only says 'a certain number of final shots'.
QPU capacity configuration = not reported
Capacities c_m and the number of QPUs in the distributed mode are not reported, despite being inputs to the allocation constraint in Eq. (16).

assumptions (4)

domain assumption The three-block ADMM converges to a good unit commitment solution for the tested settings.
ADMM for mixed-binary problems is heuristic; convergence is only shown on one small instance.
standard math The binary-to-Ising mapping and QAOA cost Hamiltonian construction are standard.
The mapping bz=(I-Z)/2 and the cost Hamiltonian in Eq. (12) are standard literature results.
ad hoc to paper The DQAOA simulator faithfully emulates distributed quantum execution with cross-QPU TeleGate operations.
The simulator comes from the authors' own preprint [15] and is not independently verified or released.
domain assumption The finite set of sampled bitstrings S(k) contains the true QUBO optimum at every ADMM iteration.
The method selects the best observed sample in Eq. (17). Without sufficient shots, the true optimum can be missed.

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Cite this review

Pith. "Pith review of A Distributed Quantum Approximate Optimization Algorithm For Unit Commitment." pith.science (2026). https://pith.science/paper/CMOPGTVF

@misc{pith2026260804159,
  author       = {Pith},
  title        = {Pith review of: A Distributed Quantum Approximate Optimization Algorithm For Unit Commitment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CMOPGTVF}},
  note         = {Machine review of arXiv:2608.04159}
}

read the original abstract

This paper presents a distributed quantum approximate optimization algorithm (DQAOA)-enabled three-block alternating direction method of multipliers (ADMM) framework for unit commitment (UC). The relaxed commitment and dispatch variables are solved in a continuous quadratic programming block, while the binary commitment block is formulated as a quadratic unconstrained binary optimization (QUBO) problem. The DQAOA interface allows this QUBO to be solved using brute-force enumeration, monolithic QAOA, or distributed QAOA, while the remaining ADMM updates are kept unchanged. In the distributed mode, the logical commitment qubits are allocated across multiple capacity-constrained quantum processing units (QPU), avoiding the requirement that the complete binary problem fits on a single device. The framework is evaluated on a five-unit UC instance containing 15 binary variables. All three solver modes reduce the ADMM primal residual below a certain tolerance and recover the same commitment schedule, dispatch, and operating cost. The results demonstrate solution consistency across the three solver modes and the multi-QPU capacity accommodation provided by the distributed QAOA method.

Figures

Figures reproduced from arXiv: 2608.04159 by the authors.

**Figure 2.** Integration of the DQAOA package as the selectable [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** ADMM primal residual convergence for the five-unit, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

15 extracted references · 6 canonical work pages

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [15]

A Distributed Quantum Approximate Optimization Algorithm Simulator for Engineering Design Optimization

A. Rajabi, M. Hasanzadeh, and A. Kargarian, “A distributed quantum approximate optimization algorithm simulator for engineering design optimization,”arXiv preprint arXiv:2606.26297, 2026

work page Pith review arXiv 2026

[2] [1]

Unit commitment—a bibliographical survey,

N. P. Padhy, “Unit commitment—a bibliographical survey,”IEEE Transactions on Power Systems, vol. 19, no. 2, pp. 1196–1205, 2004

work page 2004

[3] [2]

A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem,

M. Carri ´on and J. M. Arroyo, “A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem,”IEEE Transactions on power systems, vol. 21, no. 3, pp. 1371–1378, 2006

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[4] [3]

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M. Hasanzadeh, A. Rajabi, and A. Kargarian, “A survey on applications of quantum computing for unit commitment,”arXiv preprint arXiv:2601.01777, 2026

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Multiblock admm heuristics for mixed-binary optimization on classical and quantum computers,

C. Gambella and A. Simonetto, “Multiblock admm heuristics for mixed-binary optimization on classical and quantum computers,”IEEE Transactions on Quantum Engineering, vol. 1, pp. 1–22, 2020

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