Efficient fault-tolerant code switching via one-way transversal CNOT gates

Abstract

Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this work, we present a code switching scheme that respects the constraints of FT circuit design by only making use of transversal gates. These gates are intrinsically FT without additional qubit overhead. We analyze application of the scheme to low-distance color codes, which are suitable for operation in existing quantum processors, for instance based on trapped ions or neutral atoms. We briefly discuss connectivity constraints that arise for architectures based on superconducting qubits. Numerical simulations of circuit-level noise indicate that a logical $T$-gate, facilitated by our scheme, could outperform both flag-FT magic state injection protocols and a physical $T$-gate at low physical error rates. Transversal code switching naturally scales to code pairs of arbitrary code distance. We observe improved performance of a distance-5 protocol compared to both the distance-3 implementation and the physical gate for realistically attainable physical entangling gate error rates. We discuss how the scheme can be implemented with a large degree of parallelization, provided that logical auxiliary qubits can be prepared reliably enough. Our logical $T$-gate circumvents potentially costly magic state factories. The requirements to perform QEC and to achieve an FT universal gate set are then essentially the same: Prepare logical auxiliary qubits offline, execute transversal gates and perform fast-enough measurements. Transversal code switching thus serves to enable more practical hardware realizations of FT universal quantum computation. The scheme alleviates resource requirements for experimental demonstrations of quantum algorithms run on logical qubits.