Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries

Abstract

A finite length ferromagnetic chain with opposite spin polarization imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls, and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterizing the annealer. The noise measured in this fashion is smaller than what is seen during the single-qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.

Using copies can improve precision in continuous-time quantum computing

“…They are similar to the multi-qubit variable mappings used on D-Wave machines for minor embedding [62][63][64]. However, unlike the SK spin glasses, finding the ground state of spin chains can be solved efficiently classically, and they have been shown to exhibit counter-intuitive statistical effects [57], so they are not suitable for gaining insight into the behavior of more general types of problem Hamiltonians. Nonetheless, they are important for real hardware architectures (e.g.…”

“…We have numerically tested our innovations on small instances of three problems: Sherrington-Kirkpatrick (SK) spin glasses as studied in [56]; maximum independent set; and Ising spin chains with random couplings. However, spin chains have been found to exhibit counter-intuitive statistical effects [57], so will not necessarily provide a good guide for how other types of problems behave. Understanding the behavior for Ising spin chains is important in relation to minor embedding techniques used to instantiate highly connected problems into less connected hardware.…”

Benchmarking quantum annealing with maximum cardinality matching problems

“…Studies with this aim were conducted by comparing D-Wave data with (simulated) QA and classical models often including, among others, Simulated Annealing (SA). Such studies either showed that previously considered classical models cannot reproduce the D-Wave results, for instance for freeze-out time vs. temperature (Johnson et al, 2011), for success probability distributions over many random spin glass instances (Boixo et al, 2014), and for the non-uniform probability of degenerate ground states of specially crafted problem instances where the probability of one ground state is suppressed in the quantum case and enhanced for SA (Boixo et al, 2013;Albash et al, 2015) or introduced another classical model such as noisy Boltzmann distributions (Chancellor et al, 2022), classical spin dynamics (Smolin and Smith, 2013), and spin-vector Monte Carlo (SVMC, also called SSSV model-from Shin Smith Smolin Vazirani) (Shin et al, 2014), which shows agreement with the studied D-Wave data. (ii) A second aspect is the comparison between different generations of processors to judge possible improvements.…”