We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels-i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value-and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.
We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels-i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value-and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.
We study the effect of the anneal path control per qubit, a new user control feature offered on the D-Wave 2000Q quantum annealer, on the performance of quantum annealing for solving optimization problems by numerically solving the time-dependent Schrödinger equation for the time-dependent Hamiltonian modeling the annealing problems. The anneal path control is thereby modeled as a modified linear annealing scheme, resulting in an advanced and retarded scheme. The considered optimization problems are 2-SAT problems with 12 Boolean variables, a known unique ground state and a highly degenerate first excited state. We show that adjustment of the anneal path control can result in a widening of the minimal spectral gap by one or two orders of magnitude and an enhancement of the success probability of finding the solution of the optimization problem. We scrutinize various iterative methods based on the spin floppiness, the average spin value, and on the average energy and describe their performance in boosting the quantum annealing process.
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing.
To solve an optimization problem using a commercial quantum annealer, one has to represent the problem of interest as an Ising or a quadratic unconstrained binary optimization (QUBO) problem and submit its coefficients to the annealer, which then returns a user-specified number of low-energy solutions. It would be useful to know what happens in the quantum processor during the anneal process so that one could design better algorithms or suggest improvements to the hardware. However, existing quantum annealers are not able to directly extract such information from the processor. Hence, in this article we propose to use advanced features of D-Wave 2000Q to indirectly infer information about the dynamics of the state evolution during the anneal process. Specifically, D-Wave 2000Q allows the user to customize the anneal schedule, that is, the schedule with which the anneal fraction is changed from the start to the end of the anneal. Using this feature, we design a set of modified anneal schedules whose outputs can be used to generate information about the states of the system at user-defined time points during a standard anneal. With this process, called slicing , we obtain approximate distributions of lowest-energy anneal solutions as the anneal time evolves. We use our technique to obtain a variety of insights into the annealer, such as the state evolution during annealing, when individual bits in an evolving solution flip during the anneal process and when they stabilize, and we introduce a technique to estimate the freeze-out point of both the system as well as of individual qubits.
Quantum annealing is a computational paradigm in which optimisation problems are encoded in the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming an initial Hamiltonian into one whose ground state represents the solution, the system navigates complex energy landscapes through a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Quantum annealing is primarily designed for discrete optimisation and sampling tasks and provides a physically motivated heuristic for exploring rugged landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, making them among the largest controllable quantum devices currently available. Beyond optimisation, they also serve as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are challenging to access classically. In this review we introduce the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse the roles of tunnelling, spectral gaps, and open-system effects in determining performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges of benchmarking, scaling, and control. These developments position quantum annealing at the interface of optimisation, stochastic sampling, and programmable quantum dynamics.
Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.