Quantum computation via measurements on the low-temperature state of a many-body system

TL;DR

This paper investigates measurement-based quantum computation on a thermal spin-lattice system, demonstrating that optimal cooling and specific measurement protocols can achieve fault-tolerance despite environmental interactions.

Contribution

It introduces a simplified model for fidelity loss in measurement-based quantum computation on thermal states, identifying conditions for fault-tolerance at low temperatures.

Findings

Existence of an optimal cooling rate balancing system temperature and isolation.

Fidelity loss can be described by a single quantum operation independent of measurement history.

Fault-tolerant thresholds are achievable at sufficiently low temperatures.

Abstract

We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium and, with adaptive measurements performed at a finite rate, the resulting dynamics reduces the fidelity of the computation. We show that it is possible to describe the loss in fidelity by a single quantum operation on the encoded quantum state that is independent of the measurement history. To achieve this simple description, we choose a particular form of spin-boson coupling to describe the interaction with the environment, and perform measurements periodically at a natural rate determined by the energy gap of the system. We found that an optimal cooling exists, which is a trade-off between keeping the system cool enough that the resource state remains close to the ground state, but also isolated enough that the cooling does not strongly interfere with the dynamics of the computation. For a sufficiently low temperature we obtain a fault-tolerant threshold for the couplings to the environment.