Efficient simulation of logical magic state preparation protocols

TL;DR

This paper introduces a scalable simulation method for logical magic state preparation protocols in quantum computing, enabling efficient analysis of complex protocols under realistic noise models without heavy computational resources.

Contribution

A novel polynomial-time simulation approach for logical magic state preparation protocols based on code switching, cultivation, and distillation, leveraging a unique error propagation property.

Findings

Simulation complexity is polynomial in qubits and non-stabilizerness.

The method applies to protocols with certain Clifford measurement structures.

Proof-of-principle simulation demonstrates practical feasibility.

Abstract

Developing space- and time-efficient logical magic state preparation protocols will likely be an essential step towards building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical magic state preparation protocols under the standard circuit-level noise model. When applied to protocols based on code switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the non-stabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical magic state preparation protocols without resorting to approximations or resource-intensive state-vector simulations.