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.
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 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 .
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,
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.
The advent of quantum computing can potentially revolutionize how complex problems are solved. This paper proposes a two-loop quantum-classical solution algorithm for generation scheduling by infusing quantum computing, machine learning, and distributed optimization. The aim is to facilitate employing noisy near-term quantum machines with a limited number of qubits to solve practical power system optimization problems such as generation scheduling. The outer loop is a 3-block quantum alternative direction method of multipliers (QADMM) algorithm that decomposes the generation scheduling problem into three subproblems, including one quadratically unconstrained binary optimization (QUBO) and two non-QUBOs. The inner loop is a trainable quantum approximate optimization algorithm (T-QAOA) for solving QUBO on a quantum computer. The proposed T-QAOA translates interactions of quantum-classical machines as sequential information and uses a recurrent neural network to estimate variational parameters of the quantum circuit with a proper sampling technique. T-QAOA determines the QUBO solution in a few quantum-learner iterations instead of hundreds of iterations needed for a quantum-classical solver. The outer 3-block ADMM coordinates QUBO and non-QUBO solutions to obtain the solution to the original problem. The conditions under which the proposed QADMM is guaranteed to converge are discussed. Two mathematical and three generation scheduling cases are studied. Analyses performed on quantum simulators and classical computers show the effectiveness of the proposed algorithm. The advantages of T-QAOA are discussed and numerically compared with QAOA which uses a stochastic gradient descent-based optimizer.