Dynamics of simulated quantum annealing in random Ising chains

Abstract

Simulated Quantum Annealing (SQA), that is emulating a Quantum Annealing (QA) dynamics on a classical computer by a Quantum Monte Carlo whose parameters are changed during the simulation, is a well established computational strategy to cope with the exponentially large Hilbert space. It has enjoyed some early successes but has also raised more recent criticisms. Here we investigate, on the paradigmatic case of a one-dimensional transverse field Ising chain, two issues related to SQA in its Path-Integral implementation: the question of Monte Carlo vs physical (Schrödinger) dynamics and the issue of the imaginary-time continuum limit to eliminate the Trotter error. We show that, while a proper time-continuum limit is able to restitute the correct Kibble-Zurek scaling of the residual energy εres(τ ) ∼ τ −1/2 for the ordered case − − − τ being the total annealing time -, the presence of disorder leads to a characteristic sampling crisis for a large number of Trotter time-slices, in the low-temperature ordered phase. Such sampling problem, in turn, leads to SQA results which are apparently unrelated to the coherent Schrödinger QA even at intermediate τ .

Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets

“…PIMC was even shown to simulate QA dynamics for single-path incoherent tunneling through a barrier 23 , casting doubt on the ability of QA to offer a computational advantage over PIMC. Furthermore, no previous experiment to date has shown QA to systematically outperform PIMC-based simulations of QA in scaling 19 , 21 , although a scaling advantage has been shown to be possible in theory, for ideal QA 22 , 24 , 25 .…”

“…Although there are many types of QMC, the most appropriate choice in this setting is path-integral Monte Carlo (PIMC) 15 , 16 —we discuss the limitations of other approaches in the Supplementary Information . Ever since the appearance of QA processors, PIMC has been promoted as a classical analog, and even as a simulator of QA 17 – 22 . PIMC was even shown to simulate QA dynamics for single-path incoherent tunneling through a barrier 23 , casting doubt on the ability of QA to offer a computational advantage over PIMC.…”

Optimal working point in digitized quantum annealing

“…Another interesting issue has to do with the role of disorder [47,48]. We have verified, and will report elsewhere, that the perfect degeneracy of the optimal solutions found in the present translationally invariant case is broken in the presence of disorder: the variational energy landscape becomes rugged, and the search for the global optimal solution turns to be computationally harder.…”

Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics

“…This method is known to reproduce some features of the outputs from the quantum device, the D-Wave quantum annealer [22,23]. Simulated quantum annealing (SQA) is another powerful classical tool that uses path-integral Monte Carlo [2, 5,18,[23][24][25][26][27][28][29][30][31][32][33][34]. This latter method is in principle designed to simulate equilibrium properties of quantum systems without a sign problem [35].…”

“…However, in the context of quantum annealing, it is used to simulate dynamical behaviors of the transverse-field Ising model, recent examples of which include Ref. [34], where the dynamics of a random Ising chain with transverse field was studied by SQA, and Refs. [36,37], where the performance of various embedding schemes was compared using SQA.…”