Sufficient condition on noise correlations for scalable quantum computing

TL;DR

This paper establishes a sufficient condition under which scalable quantum computing is feasible despite correlated noise, emphasizing the importance of decay properties of noise correlations with system size and qubit separation.

Contribution

It introduces a new criterion for fault-tolerance in quantum computing that accounts for correlated Hamiltonian noise and its decay properties.

Findings

Quantum computations remain reliable if noise correlations decay rapidly with system size.

The derived condition ensures scalability under specific decay rates of noise correlations.

Provides a theoretical foundation for designing noise-resilient quantum systems.

Abstract

I study the effectiveness of fault-tolerant quantum computation against correlated Hamiltonian noise, and derive a sufficient condition for scalability. Arbitrarily long quantum computations can be executed reliably provided that noise terms acting collectively on k system qubits are sufficiently weak, and decay sufficiently rapidly with increasing k and with increasing spatial separation of the qubits.