Quantum Memory and Autonomous Computation in Two Dimensions

TL;DR

This paper presents a two-dimensional autonomous quantum error correction scheme using a dissipative cellular automaton, enabling self-correcting quantum memory and universal computation with a nonzero noise threshold.

Contribution

It introduces a novel 2D autonomous quantum error correction method with hierarchical control, achieving fault-tolerance and universal computation without active measurements.

Findings

Existence of a nonzero noise threshold for the scheme.

Logical errors are exponentially suppressed below the threshold.

Memory lifetime diverges with system size in the thermodynamic limit.

Abstract

Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an explicit scheme for autonomous quantum error correction and computation in two dimensions, formulated as a dissipative quantum cellular automaton with a fixed, local and translation-invariant update rule. The construction uses hierarchical, self-simulating control elements based on ideas from the seminal classical results of G\'acs (1986, 1989) together with a measurement-free concatenated quantum code. We prove the existence of a nonzero noise threshold under a local noise model. Below this threshold, logical errors on encoded initial states are suppressed exponentially with increasing system size and the memory lifetime diverges in the thermodynamic limit. We also describe an implementation in continuous time as a time-independent, translation-invariant local Lindbladian using engineered dissipative jump operators. The recursive nature of our protocol allows for the fault-tolerant execution of quantum circuits specified by the initial state, and thus constitutes a self-correcting quantum computer capable of universal computation.