Measurement-free code-switching for low overhead quantum computation using permutation invariant codes

TL;DR

This paper introduces a measurement-free code-switching protocol for universal quantum computation that reduces gate overhead by combining stabilizer and permutation-invariant codes, enabling efficient non-Clifford gates.

Contribution

It presents a novel measurement-free code-switching method between stabilizer and permutation-invariant codes for fault-tolerant quantum computing.

Findings

Reduced gate count for universal quantum gates.

New class of permutation-invariant codes with tunable distance.

Demonstrated efficiency of controlled-NOTs using bosonic modes.

Abstract

Transversal gates on quantum error correction codes have been a promising approach for fault-tolerant quantum computing, but are limited by the Eastin-Knill no-go theorem. Existing solutions like gate teleportation and magic state distillation are resource-intensive. We present a measurement-free code-switching protocol for universal quantum computation, switching between a stabiliser code for transversal Cliffords and a permutation-invariant (PI) code for transversal non-Cliffords that are logical $Z$ rotations for any rational multiple of $\pi$. The novel non-Clifford gates enabled by this code-switching protocol provide for a lower gate count implementation of a universal gate set relative to the Clifford$+T$ gate set. To achieve this, we present a protocol for performing controlled-NOTs between the codes using near-term quantum control operations that employ a catalytic bosonic mode. We also present a new class of PI codes with tunable code distance, supporting transversal non-Clifford gates, and demonstrate their reduced gate count overhead relative to a comparable stabilizer code to stabilizer code switching scheme.