Reduced Space-Time and Time Costs Using Dislocation Codes and Arbitrary Ancillas

TL;DR

This paper introduces two methods to enhance quantum surface code protocols: using dislocations to reduce space-time costs and arbitrary ancilla injections to minimize rotation overhead, with analysis of their performance and fault-tolerance.

Contribution

It presents novel approaches for logical qubit encoding with dislocations and a probabilistic ancilla injection protocol for arbitrary rotations, improving efficiency and scalability.

Findings

Dislocation-based codes can reduce spacetime volume.

Hadamard gates can be implemented in zero time with dislocations.

Arbitrary ancilla injection offers a constant-factor speedup over traditional methods.

Abstract

We propose two distinct methods of improving quantum computing protocols based on surface codes. First, we analyze the use of dislocations instead of holes to produce logical qubits, potentially reducing spacetime volume required. Dislocations induce defects which, in many respects, behave like Majorana quasi-particles. We construct circuits to implement these codes and present fault-tolerant measurement methods for these and other defects which may reduce spatial overhead. One advantage of these codes is that Hadamard gates take exactly $0$ time to implement. We numerically study the performance of these codes using a minimum weight and a greedy decoder using finite-size scaling. Second, we consider state injection of arbitrary ancillas to produce arbitrary rotations. This avoids the logarithmic (in precision) overhead in online cost required if $T$ gates are used to synthesize arbitrary rotations. While this has been considered before, we consider also the parallel performance of this protocol. Arbitrary ancilla injection leads to a probabilistic protocol in which there is a constant chance of success on each round; we use an amortized analysis to show that even in a parallel setting this leads to only a constant factor slowdown as opposed to the logarithmic slowdown that might be expected naively.