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 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.
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 Qiskit-compatible distributed quantum approximate optimization algorithm (DQAOA) simulator for quadratic unconstrained binary optimization (QUBO) problems arising in engineering design and decision applications. The open-source simulator is available through the RAISE LAB website and GitHub repository, with README documentation for installation, input formatting, configurable parameters, and example workflows. The package addresses the need for a reusable simulator that can solve and compare QUBO instances across different QAOA execution modes. It supports monolithic QAOA on a single quantum processing unit (QPU) and distributed QAOA across a user-specified number of QPUs with configurable capacities. The workflow canonicalizes the QUBO model, maps it to a cost Hamiltonian, allocates variables across QPUs, identifies local and cross-QPU couplings, and constructs the corresponding circuits. Runtime optimizations, including parameterized circuit reuse, objective reuse at fixed depth, batched evaluations, and parallel multi-start execution, reduce repeated overhead. A Streamlit graphical user interface is also provided for entering or uploading QUBO instances, configuring solver settings, running selected modes, and visualizing solution-quality metrics without editing Python scripts. The package is demonstrated on standalone QUBO benchmarks and a power generation unit commitment application. In the unit commitment case, brute force, monolithic QAOA, and distributed QAOA recover the same commitment bitstring and operating cost. Across multiple case studies, the simulator produces results consistent with classical monolithic QAOA references in terms of optimal bitstrings and costs. Staged runtime analysis shows substantial runtime reduction across implementation stages, while distributed QAOA remains more demanding because cross-QPU couplings require remote operations.
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 .
Abstract The unit commitment problem (UCP) is a non‐convex mixed‐integer programming issue that is crucial in the power system. The quantum alternating direction method of multipliers (QADMM) decompose the UCP into quadratic binary optimization (QBO) subproblems and continuous optimization subproblems. Relaxing constraints reformulate the QBO into a quadratic unconstrainted binary optimization (QUBO) problem, which can be addressed using quantum algorithms. Nevertheless, this approach lacks precision for hard constraints and requires more qubits, limiting the UCP scale addressed within QADMM. To confront the aforementioned challenges, this study introduces the consensus constraint‐encoded divide‐and‐conquer QADMM (CCDC‐QADMM). As a scalable fully distributed algorithm, CCDC‐QADMM decomposes the UCP into two subproblems: Subproblem 1, a QUBO problem embedded with minimum up/down constraints, and Subproblem 2, a UC problem without minimum up/down constraints. By employing variable duplication for decoupling and leveraging the principles of average consensus, CCDC‐QADMM achieves fully distributed computation. Specifically, in the QUBO subproblem 1, this algorithm encodes minimum up/down constraints into a hard constraint form within the mixing Hamiltonian. Simultaneously, it employs a divide‐and‐conquer strategy to accommodate the current constraints posed by the limited qubit resources. The effectiveness and scalability of this algorithm are substantiated through practical validation within real‐world UCP scenarios.
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.
Widely used quantum optimization algorithms such as quantum annealing and quantum approximate optimization algorithm (QAOA) for quadratically unconstrained binary optimization (QUBO) problems cannot systematically and efficiently handle constraints and mixed discrete and continuous decision variables. To address this, we present a novel hybrid classicalquantum approach which combines classical alternating direction method of multipliers (ADMM) with QAOA. Compared to conventional penalty-based method, this approach avoids quantization of continuous variables, eliminates the need for additional qubits to capture constraints on a quantum device and leads to reduced QAOA circuit depth suitable for near term implementation. We illustrate the efficacy of our approach on several constrained mixed integer optimization problems.