Suppressing precision errors by connecting copies of Ising models for continuous-time quantum computing

Abstract

Classical optimization problems can be mapped to Ising models in order to be solved by continuous-time quantum computing. It was recognised in [Young et al, PRA (2013)], [Pearson et al, njp QI, (2019)] and [Albash et al, QST, (2019)], that these problems are susceptible to a lack of precision in the fields and couplings of the Ising model.
In this thesis we introduce a scheme first described in [Bennett et al, arXiv:2206.02545, (2022)], which aims to suppress errors caused by lack of precision. This scheme was inspired by quantum annealing correction (QAC), first introduced in [Young et al, PRA (2013)], where physical qubits in multiple copies of a Ising model are linked together.
However, we introduce several innovations thereby making our scheme distinct.
First, when determining the ground state of the problem, we require only one copy to be correct, because the solution quality can be checked efficiently.
Second, using this "one correct copy" setting, we find the optimal strength of links connecting the copies to be anti-ferromagnetic and close to the minimum strength allowed by the precision. Here we find an improvement (on average) above separate copies and copies connected ferromagnetically.
Third, we find that configurations of copies that contain frustration (e.g. a loop of three or five copies), provide a further improvement in fraction correct.
Numerically testing our innovations on small instances of spin chains and spin glasses, we find improved tolerance to lack of precision equating to around 3 bits of precision improvement at p=7.
We develop a link selection protocol which aims to determine in a computationally non-intensive fashion, whether or not to connect corresponding qubits in different copies. Here, we obtain mixed results, with improvement in fraction correct over separate copies only for precisions p<4.
Finally, we apply our error suppression scheme when computing with quantum walks. In this setting we find that the improvement from using our technique is lost for all values of precision. We hypothesise this is due to the way our error suppression scheme functions by allowing 'access' to excited states, available innately in quantum walks.