Quantum Memory and Autonomous Computation in Two Dimensions
quant-ph
Submitted: 2026-01-28
Updated: 2026-09-25
Comments: v1: 17 pages, preliminary version. v2: 26 pages, revised proofs and presentational improvements, results unchanged. v3: 35 pages, further presentational improvements
License: http://creativecommons.org/licenses/by/4.0/
The gist: Quantum error correction (QEC) normally requires active maintenance using measurements, classical processing and externally controlled correction schedules.
Terminology
Abstract
Quantum error correction (QEC) normally requires active maintenance using measurements, classical processing and externally controlled correction schedules. Passive QEC, by contrast, was previously 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 Gács (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. As an extension, we outline how this mechanism can also be implemented in continuous time by a time-independent, translation-invariant local Lindbladian. Quantum circuits can moreover be encoded in the automaton's initial state and executed fault-tolerantly with polylogarithmic overhead under the same circuit-independent rule. Our scheme thus realizes a self-correcting quantum computer capable of universal computation.
Sources
- Proposals for 3D self-correcting quantum memory
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- A local automaton for the 2D toric code
- Reversible quantum cellular automata
- Intrinsically universal one-dimensional quantum cellular automata in two flavours
- A new version of Toom's proof
- Fast Mixing of Quantum Spin Chains at All Temperatures
- Computational complexity of injective projected entangled pair states
- A Constant Rate Quantum Computer on a Line
- A passive self-correcting quantum memory in three dimensions
- Fault-Tolerant Postselected Quantum Computation: Schemes
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