Rigorous Bounds on the Performance of a Hybrid Dynamical Decoupling-Quantum Computing Scheme

TL;DR

This paper establishes rigorous bounds on the effectiveness of hybrid dynamical decoupling combined with quantum logic gates, revealing scalability limits for protecting quantum computation against environmental noise.

Contribution

It provides the first rigorous error bounds for a hybrid dynamical decoupling and quantum computation scheme in multi-qubit systems.

Findings

Error bounds depend on the operator norm of the effective Hamiltonian.

Maintaining fidelity requires the number of decoupling cycles to scale inversely with the square of the number of qubits.

Scalability of periodic dynamical decoupling is limited by these bounds.

Abstract

We study dynamical decoupling in a multi-qubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the computation. We derive a rigorous error bound on the trace distance or fidelity between the desired computational state and the actual time-evolved state, for a system subject to coupling to a bounded-strength bath. The bound is expressed in terms of the operator norm of the effective Hamiltonian generating the evolution in the presence of decoupling and logic operations. We apply the bound to the case of periodic pulse sequences and find that in order maintain a constant trace distance or fidelity, the number of cycles -- at fixed pulse interval and width -- scales in inverse proportion to the square of the number of qubits. This sets a scalability limit on the protection of quantum computation using periodic dynamical decoupling.