Abstract One of the major problems of quantum computing applications is that the required number of qubits to solve a practical problem is much larger than that of today's quantum hardware. In this work, we introduce the large-system sampling approximation (LSSA) algorithm to solve Ising problems with sizes up to Ngb2Ngb by an Ngb-qubit gate-based quantum computer, and problems with sizes up to Nan2Ngb by a hybrid computational architecture of an Nan-qubit quantum annealer and an Ngb-qubit gate-based quantum computer. By dividing the full-system problem into smaller subsystem problems, the LSSA algorithm then solves the subsystem problems by either gate-based quantum computers or quantum annealers, and optimizes the amplitude contributions of the solutions of the different subsystems with the full-problem Hamiltonian by the variational quantum eigensolver (VQE) on a gate-based quantum computer to determine the approximated ground-state configuration. LSSA has polynomial time complexity and can be further extended to a deeper level of approximation with computational overhead that grows linearly with the problem size. The effects of different subsystem sizes, numbers of subsystems, and full problem sizes on the performance of LSSA are investigated on both simulators and real hardware. The completely new computational concept of the hybrid gate-based and annealing quantum computing architecture opens a promising possibility to investigate large-size Ising problems and combinatorial optimization problems, making practical applications by quantum computing possible in the near future.
Abstract One of the major problems of quantum computing applications is that the required number of qubits to solve a practical problem is much larger than that of today's quantum hardware. In this work, we introduce the large-system sampling approximation (LSSA) algorithm to solve Ising problems with sizes up to Ngb2Ngb by an Ngb-qubit gate-based quantum computer, and problems with sizes up to Nan2Ngb by a hybrid computational architecture of an Nan-qubit quantum annealer and an Ngb-qubit gate-based quantum computer. By dividing the full-system problem into smaller subsystem problems, the LSSA algorithm then solves the subsystem problems by either gate-based quantum computers or quantum annealers, and optimizes the amplitude contributions of the solutions of the different subsystems with the full-problem Hamiltonian by the variational quantum eigensolver (VQE) on a gate-based quantum computer to determine the approximated ground-state configuration. LSSA has polynomial time complexity and can be further extended to a deeper level of approximation with computational overhead that grows linearly with the problem size. The effects of different subsystem sizes, numbers of subsystems, and full problem sizes on the performance of LSSA are investigated on both simulators and real hardware. The completely new computational concept of the hybrid gate-based and annealing quantum computing architecture opens a promising possibility to investigate large-size Ising problems and combinatorial optimization problems, making practical applications by quantum computing possible in the near future.
Portfolio optimization is one of the most studied problems for demonstrating the near-term applications of quantum computing. However, large-scale problems cannot be solved on today's quantum hardware. In this work, we extend upon a study to use the best of both quantum annealing and gate-based quantum computing systems to enable solving large-scale optimization problems efficiently on the available hardware. The existing work uses a method called Large System Sampling Approximation (LSSA) that involves dividing the large problem into several smaller problems and then combining the multiple solutions to approximate the solution to the original problem. This paper introduces a novel technique to modify the sampling step of LSSA. We divide the portfolio optimization problem into sub-systems of smaller sizes by selecting a diverse set of assets that act as representatives of the entire market and capture the highest correlations among assets. We conduct tests on real-world stock data from the Indian stock market on up to 64 assets. Our experimentation shows that the hybrid approach performs at par with the traditional classical optimization methods with a good approximation ratio. We also demonstrate the effectiveness of our approach on a range of portfolio optimization problems of different sizes. We present the effects of different parameters on the proposed method and compare its performance with the earlier work. Our findings suggest that hybrid annealer-gate quantum computing can be a valuable tool for portfolio managers seeking to optimize their investment portfolios in the near future.
Portfolio optimization is a well-established problem in the field of finance and has recently gained attention in the context of quantum computing. The hardware limitations of quantum computers prevent the direct application of quantum algorithms to large-scale problems. We propose a novel two-stage approach that combines the strengths of both quantum annealing and gate-based quantum computing to efficiently solve large-scale portfolio optimization problems. Building upon the existing Large System Sampling Approximation (LSSA) approach, our work introduces a novel modification to the decomposition and aggregation steps of LSSA. We divide the problem into sub-problems of smaller sizes by solving the Maximum Independent Set (MIS) of the market graph and use a Parameterized Quantum Circuit (PQC) to aggregate the sub-problem solutions. We conduct extensive experiments on real-world data from the US stock market on up to 128 assets on simulators. Our results demonstrate that the proposed approach performs better with the same hardware resources. The outcomes of our research suggest that hybrid annealer-gate quantum computing can provide a practical and scalable solution to large-scale portfolio optimization problems, bridging the gap between theoretical advancements in quantum computing and real-world applications in finance.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
Quantum computing has emerged as a transformative paradigm, leveraging principles of quantum mechanics to tackle computationally intractable problems. This manuscript explores the potential of quantum computing for solving complex engineering problems—specifically optimization, simulation, and data analysis tasks—using technologies and methodologies available up to 2022. We examine both gate-based and quantum annealing approaches, outline experimental frameworks, and compare performance against classical counterparts. Results from simulated benchmark problems demonstrate promising speedups in select cases, though practical adoption is constrained by hardware limitations such as qubit coherence times and noise. The study concludes by highlighting avenues for integrating hybrid quantum-classical workflows in engineering, along with a discussion of current constraints and future directions. Over the past decade, research efforts have focused on understanding how quantum phenomena like superposition and entanglement can be harnessed to realize computational advantages for specific problem classes. In particular, combinatorial optimization problems—ubiquitous in engineering design and logistics—offer fertile ground for quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing. Additionally, quantum simulation techniques, including the Variational Quantum Eigensolver (VQE), promise to accelerate the modeling of physical systems at the molecular and materials level, potentially informing the design of next-generation structural and functional materials. Beyond raw algorithmic performance, this paper carefully assesses the end‑to‑end workflow, accounting for overheads in problem encoding, error mitigation, and classical post‑processing. We also present a detailed analysis of resource utilization—quantified by qubit counts, circuit depths, and annealing schedules—highlighting trade‑offs between solution quality and execution time. Ultimately, our findings underscore that, while pure quantum speedups remain rare in 2022, hybrid approaches harnessing both quantum and classical resources can yield practical benefits for small‑to‑medium scale engineering tasks. This expanded evaluation provides a roadmap for researchers and practitioners interested in applying quantum computing to real‑world engineering challenges.
Codon optimization is a challenging combinatorial optimization problem with important applications in synthetic biology, protein expression, and biotechnology. While quantum annealing has previously been explored for this problem, the application of gate-based quantum algorithms remains largely unexplored. In this work, we present a gate-based quantum computing framework for codon optimization by formulating the optimization objective as an Ising Hamiltonian and expressing it in terms of Pauli operators suitable for gate-based quantum processors. The proposed framework is investigated using the Variational Quantum Eigensolver (VQE), Sampling Variational Quantum Eigensolver (SVQE), and the Quantum Approximate Optimization Algorithm (QAOA), with benchmarking against exact diagonalization, classical optimization, and quantum annealing. Using a three-amino-acid benchmark, the proposed implementations successfully reproduce the exact ground-state solutions while identifying optimized ansatz selections, optimization strategies, initialization schemes, and hardware execution settings that provide reproducible performance on current noisy quantum hardware. Hardware demonstrations are performed on IBM Quantum processors to evaluate the practical implementation of the proposed workflow. As a work in progress, this study establishes a reproducible computational framework for gate-based quantum codon optimization and provides the foundation for future investigations of larger protein sequences as quantum hardware and algorithms continue to advance.
In the near future, one of the main processes is solving large combinatorial optimization problems. However, the performance growth of von Neumann architecture will slow due to the end of semiconductor scaling. To resolve this problem, we propose an Ising computer that maps the optimization problems to the ground state search of Ising models. We previously proposed a computer that finds the ground state of Ising models by simulated annealing (SA) approximately. Though the solution quality of the previous prototype is comparable to that of SA, enhancing the solution quality will be required to solve real-world applications. In this paper, we present our FPGA-based Ising computer that executes simulated quantum annealing by using a path integral quantum Monte Carlo method for Ising models on a 48-by-48 king graph with 8-bit couplings. We also propose a shared random number supply, which contributes to decrease the number of random number generators to two. Experimental results indicate that the proposed Ising computer is more than 15 times faster to obtain 99.9%-solution with a probability of 99% than SA running on a state-of-the-art CPU.