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arXiv:2511.03104

D2-UC: A Distributed-Distributed Quantum-Classical Framework for Unit Commitment

Milad Hasanzadeh, Amin Kargarian

quant-pheess.SYSubmitted Nov 5, 2025• Announced Nov 6, 2025• 0 citations
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Abstract

This paper introduces D2-UC, a quantum-ready framework for the unit commitment (UC) problem that prepares UC for near-term hybrid quantum-classical solvers by combining distributed classical decomposition with distributed quantum execution. We reformulate deterministic and stochastic UC into a three-block alternating direction method of multipliers (ADMM): (i) a convex quadratic subproblem for dispatch and reserves, (ii) a binary subproblem expressed as a quadratic unconstrained binary optimization (QUBO), and (iii) a proximal slack update for consensus. The core contributions are fivefold. First, we demonstrate how the full UC problem can be expressed as a single monolithic QUBO, establishing a direct interface to quantum solvers. Second, we decompose this large binary block into three type-specific QUBOs for commitment, startup, and shutdown, making the problem more tractable but revealing slower ADMM convergence. Third, we restore local logical couplings through per-unit-time micro-QUBOs, which accelerate convergence. Fourth, we batch micro-QUBOs into K non-overlapping block-diagonal problems, reducing many subproblems to a fixed number of solver-ready QUBOs per iteration, compatible with distributed variational quantum eigensolvers (DVQE). Fifth, we integrate an accept-if-better safeguard with DVQE to stabilize hybrid updates and prevent oscillations. Case studies confirm that the proposed methods deliver feasible schedules, faster convergence, and QUBO sizes aligned with current and near-term quantum hardware capabilities. All detailed data, codes, and parameter values are available at https://github.com/LSU-RAISE-LAB/3B-ADMM-UC-DVQE .

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This paper introduces D2-UC, a quantum-ready framework for the unit commitment (UC) problem that prepares UC for near-term hybrid quantum-classical solvers by combining distributed classical decomposition with distributed quantum execution. We reformulate deterministic and stochastic UC into a three-block alternating direction method of multipliers (ADMM): (i) a convex quadratic subproblem for dispatch and reserves, (ii) a binary subproblem expressed as a quadratic unconstrained binary optimization (QUBO), and (iii) a proximal slack update for consensus. The core contributions are fivefold. First, we demonstrate how the full UC problem can be expressed as a single monolithic QUBO, establishing a direct interface to quantum solvers. Second, we decompose this large binary block into three type-specific QUBOs for commitment, startup, and shutdown, making the problem more tractable but revealing slower ADMM convergence. Third, we restore local logical couplings through per-unit-time micro-QUBOs, which accelerate convergence. Fourth, we batch micro-QUBOs into K non-overlapping block-diagonal problems, reducing many subproblems to a fixed number of solver-ready QUBOs per iteration, compatible with distributed variational quantum eigensolvers (DVQE). Fifth, we integrate an accept-if-better safeguard with DVQE to stabilize hybrid updates and prevent oscillations. Case studies confirm that the proposed methods deliver feasible schedules, faster convergence, and QUBO sizes aligned with current and near-term quantum hardware capabilities. All detailed data, codes, and parameter values are available at https://github.com/LSU-RAISE-LAB/3B-ADMM-UC-DVQE .
We present a distributed hybrid quantum-classical algorithm for solving unit commitment (UC) in quantum computing settings. The proposed algorithm embeds a distributed variational quantum eigensolver (DVQE) inside a three-block alternating direction method of multipliers (ADMM) structure. The ADMM split enables a distributed formulation by decomposing UC into three blocks, which are (i) a convex quadratic program for relaxed commitments and dispatch, (ii) a quadratic unconstrained binary optimization (QUBO) to determine unit commitment on/off binary variables, and (iii) a linear optimization based on proximal slack variables to enforce UC feasibility. This enables a distributed layout where Blocks 1, 2 and 3 are solved sequentially. Within each ADMM iteration, DVQE is implemented to solve the QUBO problem in a distributed manner. DVQE receives the coefficients in the QUBO cost function, and updates parameters using a classical optimizer, and returns the bitstring used for the binary update. We apply an accept-if-better safeguard that only accepts a new bitstring if it reduces the current linear QUBO cost. Case studies on a 5-unit single-period and a multi-period variant show that DVQE with the accept-if-better safeguard matches brute-force accuracy, while being faster than brute-force.
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.
This paper proposes a hybrid quantum-classical algorithm to solve a fundamental power system problem called unit commitment (UC). The UC problem is decomposed into a quadratic subproblem, a quadratic unconstrained binary optimization (QUBO) subproblem, and an unconstrained quadratic subproblem. A classical optimization solver solves the first and third subproblems, while the QUBO subproblem is solved by a quantum algorithm called quantum approximate optimization algorithm (QAOA). The three subproblems are then coordinated iteratively using a three-block alternating direction method of multipliers algorithm. Using Qiskit on the IBM Q system as the simulation environment, simulation results demonstrate the validity of the proposed algorithm to solve the UC problem.
The penetration of distributed energy resources (DERs) within the microgrids (MGs) increases the complexity of Unit Commitment (UC) problem. In this paper, the idea of quantum computing (QC) is introduced in power system distributed optimization to solve the combinatorially complex UC problem. To take advantage of QC, the quantum-amenable model of UC problem is innovatively developed. Then, by using the hybrid nature of quantum-inspired alternate direction method of multipliers (ADMM) and by exploiting the superposition and entanglement of quantum bits (qubits), the classical ADMM coordinates the subproblems to obtain feasible solutions. Additionally, this paper uses a decomposition and coordination-supported framework for quantum optimization, which allows to solve problems larger that currently available quantum computers are capable of solving. The quantum distributed UC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing,
The unit commitment (UC) problem stands as a critical optimization challenge in the electrical power industry. It is classified as NP-hard, placing it among the most intractable problems to solve. This paper introduces a novel hybrid quantum-classical algorithm designed to efficiently (approximately) solve the UC problem in polynomial time. In this approach, the UC problem is decomposed into two subproblems: a QUBO (Quadratic Unconstrained Binary Optimization) problem and a quadratic optimization problem. The algorithm employs the Quantum Approximate Optimization Algorithm (QAOA) to identify the optimal unit combination and classical methods to determine individual unit powers. The proposed hybrid algorithm is the first to include both the spinning reserve constraint (thus improving its applicability to real-world scenarios) and to explore QAOA warm-start optimization in this context. The effectiveness of this optimization was illustrated for specific instances of the UC problem, not only in terms of solution accuracy but also by reducing the number of iterations required for QAOA convergence. Hybrid solutions achieved using a single-layer warm-start QAOA (p=1) are within a 5.1 % margin of the reference (approximate) classical solution, while guaranteeing polynomial time complexity on the number of power generation units and time intervals.
A series of hybrid quantum-classical generalized Benders decomposition (GBD) algorithms are proposed to address unit commitment (UC) problems under centralized, distributed, and partially distributed frameworks. In the centralized approach, the quantum GBD transforms the master problem (MP) into a quadratic unconstrained binary optimization form suitable for quantum computing. For distributed systems, the distributed consensus quantum GBD employs an average consensus strategy to reformulate subproblems into local subproblems. By leveraging the dual information, local cutting planes are constructed to decompose the MP into local master problems (LMPs). This approach reduces the qubit overhead and addresses the partitioning requirements. The consensus-inspired quantum GBD (CIQGBD) and its partially distributed variant, D-CIQGBD are proposed based on optimizing the allocation of relaxation variables directly, the algorithms construct more rational cutting planes, thereby enhancing the minimum eigenenergy gap of the system Hamiltonian during quantum annealing and improving the computational efficiency. Extensive experiments under various UC scenarios validate the performance of the above-mentioned hybrid algorithms. Compared to the classical solver Gurobi, D-CIQGBD demonstrates a speed advantage in solving the security-constrained UC problem on the IEEE-RTS 24-bus system. These results provide new perspectives on leveraging quantum computing for the distributed optimization of power systems.