Quantum computing offers potential speedups for power system state estimation, but continuous variables like voltage angles pose challenges for quantum annealers with limited qubit resources. We introduce an iterative quantum annealing approach that progressively narrows the search space for voltage angles in DC power systems. Rather than encoding wide ranges with many qubits, our method uses few-bit encodings with dynamic range refinement across multiple annealing cycles. Testing on IEEE benchmark systems demonstrates that this approach outperforms vanilla encoding of continuous variables while reducing computational resources. This adaptive strategy addresses a fundamental challenge in quantum optimization, mapping continuous variables to discrete quantum bits, and establishes a practical pathway for quantum computing applications in power system operations.
Quantum computing offers potential speedups for power system state estimation, but continuous variables like voltage angles pose challenges for quantum annealers with limited qubit resources. We introduce an iterative quantum annealing approach that progressively narrows the search space for voltage angles in DC power systems. Rather than encoding wide ranges with many qubits, our method uses few-bit encodings with dynamic range refinement across multiple annealing cycles. Testing on IEEE benchmark systems demonstrates that this approach outperforms vanilla encoding of continuous variables while reducing computational resources. This adaptive strategy addresses a fundamental challenge in quantum optimization, mapping continuous variables to discrete quantum bits, and establishes a practical pathway for quantum computing applications in power system operations.
Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing (QA) is promising, yet its native binary nature supports only discrete variables, making accurate and efficient encodings of continuous quantities a central challenge. Existing approaches either split the coupled problem, mapping discrete decisions to QA while solving continuous fields classically, or use fixed-bit-depth encodings. The former compromises QA's global search advantages; the latter can underrepresent dynamic range or inflate the number of binary variables. We show that simply increasing bit depth can even degrade performance on current QA hardware, underscoring the need for alternative encodings. In response, we introduce an adaptive encoding strategy for continuous variables in QA that enables efficient treatment of coupled mixed-variable problems. We propose an update strategy for the representable ranges of the continuous variables and demonstrate its utility by integrating it into the minimum complementary energy formulation for structural design optimization, which provides a single, coupled constrained problem. We apply a quadratic penalty method where we update the representation of the continuous variables while targeting the full original objective, preserving QA's global search capability. On a published benchmark, the size optimization of a composite rod, our adaptive encoding improves solution quality under a fixed binary variable budget, demonstrating a superior precision-resource trade-off. Since the framework generalizes beyond structural design, it offers practical guidance for encoding continuous variables for QA and indicates that adaptive representations can enhance precision on current hardware.
Quantum annealing (QA) is a promising quantum computing paradigm for solving optimization problems. However, the performance of QA is often limited by issues such as slow convergence rates and sensitivity to parameter settings. This paper presents a novel optimization method designed to address these limitations. The approach introduces refined parameters and an adaptive strategy to enhance the algorithm's convergence speed and solution accuracy. We explore the application of this optimized QA method to complex problems, demonstrating its potential for improved performance. The core of the optimization lies in modifying the annealing schedule and incorporating a dynamic adjustment of the magnetic field strength, denoted as H(t), where t represents time. The objective function to be minimized is typically represented as E[s], where s is the state vector of the quantum annealer. We introduce a variance reduction technique, denoted as σ(t), which is dynamically adjusted based on the error estimates of the current state. The overall optimization process can be summarized as: minsE[s]subject todtdS=−β(t)E[s]−γ(t)H(t)s where β(t) is the annealing rate and γ(t) is the magnetic field strength. The adaptive strategy involves updating β(t) and γ(t) based on the error in the current solution, aiming to reduce the variance σ(t) and improve the convergence. The theoretical analysis suggests that this approach can significantly reduce the computational cost and improve the solution quality compared to traditional QA methods. Furthermore, we investigate the impact of different parameter settings on the algorithm's performance, highlighting the importance of careful tuning for optimal results. The results demonstrate a notable improvement in solution quality and convergence speed across various benchmark problems.
The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, classical global optimization algorithms outperform the quantum device. Next we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the time-evolving block decimation (TEBD) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations.
Quantum computing holds immense potential for breakthroughs across numerous fields, yet realizing this potential requires significant advancements in quantum algorithm design and hardware implementation. A crucial aspect of this journey is the efficient and accurate encoding of quantum states, which is currently limited by the capabilities of traditional classical encoding methods. This paper introduces a novel dynamic adaptive quantum state encoding strategy aimed at addressing these limitations. The proposed strategy leverages continuous monitoring of the quantum state's dynamics to dynamically adjust encoding parameters, optimizing for both computational efficiency and fidelity. We present a framework based on a feedback loop that iteratively refines the encoding process based on real-time state measurements. The core mechanism centers around adjusting the parameters of the quantum state representation to minimize error correction requirements, ultimately boosting quantum computational performance. The theoretical framework demonstrates improved performance compared to static encoding methods in a benchmark environment.
This paper investigates the use of Quantum Annealing (QA) devices for optimizing unit scheduling in renewable energy systems, addressing the challenge of energy balancing with intermittent generation. We compare two approaches for encoding inequality constraints in Quadratic Unconstrained Binary Optimization (QUBO) formulations: (a) the conventional slack-variable-based method and (b) a novel soft-encoding technique called unbalanced penalization. This first application of unbalanced penalization in the energy and power systems domain, aims to disseminate knowledge about near-term applications of quantum-computing and how to make best use of it within the community. Through computational experiments, we find thatUnbalanced Penalizationconsistently outperforms the conventional method of using slack variables by reducing the number of variables in the QUBO formulation. Despite this, its inherent nature penalizes feasible solutions unevenly, preventing the ability to handle much larger problem sizes. More broadly, we observe that both methods-like most pure quantum approaches-struggle with scalability on current QA hardware, as solution quality declines with increasing problem size. In light of these limitations, we assess the feasibility of purely quantum solutions and argue that hybrid approaches remain the most practical path forward.
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that approximates solutions to unconstrained quadratic programs via a sequence of QUBO instances. Rather than encoding real variables as binary vectors, QCQO implicitly represents them using continuous QUBO weights and iteratively refines the solution by summing sampled vectors. This allows flexible control over the number of binary variables and adapts well to hardware constraints. We prove convergence properties, introduce a step size adaptation scheme, and validate the method on linear regression. Experiments with simulated and real quantum annealers show that QCQO achieves accurate results with fewer qubits, though convergence slows on noisy hardware. Our approach enables quantum annealing to address a wider class of continuous problems.