Reverse annealing for nonnegative/binary matrix factorization

Abstract

It was recently shown that quantum annealing can be used as an effective, fast subroutine in certain types of matrix factorization algorithms. The quantum annealing algorithm performed best for quick, approximate answers, but performance rapidly plateaued. In this paper, we utilize reverse annealing instead of forward annealing in the quantum annealing subroutine for nonnegative/binary matrix factorization problems. After an initial global search with forward annealing, reverse annealing performs a series of local searches that refine existing solutions. The combination of forward and reverse annealing significantly improves performance compared to forward annealing alone for all but the shortest run times.

Experimental test of search range in quantum annealing

“…Since the introduction of the reverse annealing feature, there have been many experimental results based on this protocol showing improvements over traditional forward annealing. These include: quantum simulation of the Kosterlitz-Thouless phase transition [17] which would not have been possible with traditional forward annealing; experiments showing that seeding the protocol with the result of a classical greedy search may improve portfolio optimisation [24]; evidence that repeated reverse anneals can improve performance in matrix factorization, [25,26]; and evidence that reverse annealing calls can improve genetic algorithms [27].…”

Single-Qubit Fidelity Assessment of Quantum Annealing Hardware

“…Although this section focused on a simple proof-ofconcept demonstration using the annealing time parameter, the other scheduling features of QA hardware such as pausing [39], [40], annealing offsets [41], [42], and custom annealing schedules [43]- [45] all suggest promising avenues for manipulating the effective qubit parameters recovered by the QASA protocol. To that end, we hope that the QASA protocol can provide a relatively fast QAVV assessment of how This work is licensed under a Creative Commons Attribution 4.0 License.…”

Quantum approximate optimization for hard problems in linear algebra

“…With respect to quantum annealing, O'Malley and Vesselinov's paper in 2016 [27] was one of the first that proposed to solve linear least squares. Other works in this domain were for solving specific NMF problems [17][18][19], polynomial system of equations [28], underdetermined binary linear systems [67] and polynomial least squares [30]. It's hard to speculate about speedups analytically with (i) D-wave's noisy implementation of quantum annealing [68] and (ii) the problem of exponential gap-closing between the problem Hamiltonian's ground state and its excited states [69].…”

“…The D-wave quantum annealer was able to beat those classical solvers for the benchmark, but the authors also mention that a combination of the two classical techniques would probably perform better than the D-wave by compensating for each other's shortcomings. The other important result in subsequent papers [18,19] was to show that combining reverse and forward annealing improved results over just using forward annealing for most cases. Golden and O'Malley saw an improvement of 12% over forward annealing [19], but that came at the price of having at least 7 reverse annealing runs per QUBO (which was reported to have the quantum runtime of 29 forward anneals).…”

“…In this paper, we explore and propose the use of QAOA for hard problems in linear algebra. In particular, we focus on the problem of binary linear least squares (BLLS) [14][15][16], a subroutine for solving certain types of non-negative matrix factorization (NMF) problems [17,18], for example, the problem of non-negative binary matrix factorization (NBMF) [17,19]. These are linear dimensionality reduction (LDR) tools useful in machine learning for learning a basis that would be used to model data [20], such as learning facial features in computer vision [21], topic modeling in documents [22] and properties of astronomical objects [23,24].…”