Multi-qubit correction for quantum annealers

Abstract

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.

EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

“…where N is the number of qubits, h i ∈ R specifies the linear coefficient of qubit i, J i, j ∈ R represents the coupler weight between qubits i and j, and z i is the variable that can take its value from {−1, +1} Figure 1(a) shows the energy histogram of a random benchmark problem (on the log scale) on a D-Wave 2000Q machine. We can think of QA as a machine that samples from a Boltzmann distribution such that samples with lower energy values, according to f (z), are exponentially more likely to be observed 27,42 . In theory, therefore, QA can find the optimal solution with a very high probability 41 .…”

“…For the benchmarks, we draw the Hamiltonian coefficients of the QMIs from the standard normal distribution (a mean of 0 and a standard deviation of 1). This approach is a common practice used in prior works related to benchmarking QAs 7,27,31,49,50 . To avoid the impact of embedding on our evaluations, we directly use the connectivity graph of the D-Wave QA.…”

“…Moreover, to the best of our knowledge, all proposals for generating random hard optimization problems for QAs generate Ising Hamiltonians with integer coefficients 52 . However, physical QAs have limited precision (i.e., about 7-8 bits precision on the D-Wave QAs), and benchmarks with integer coefficients cannot capture this limitation (i.e., the impact of truncating coefficients prior to the annealing) 27 .…”

“…4. We propose EQUAL+ that combines EQUAL with existing single-qubit correction (SQC) 27 error mitigation technique to improve the reliability further.…”

“…QAs available today with 5,000-plus qubits [9][10][11] are much larger, scale faster , and have the potential to power a wide range of real-world applications-including, but not limited to, planning 12 , scheduling 13,14 , constraint satisfaction problems 15 , Boolean satisfiability (SAT) 16,17 , matrix factorization 18 , cryptography 19,20 , compressive sensing 21,22 , control of automated vehicles 23 , finance 24 , material design 25 , and protein folding 26 . Although promising, QA hardware suffers from various drawbacks such as noise, device errors, limited programmability, and confined annealing schedule, which degrade their reliability 6,8,27 . Addressing these limitations requires device-level enhancements that may span generations of QAs.…”