State injection, lattice surgery and dense packing of the deformation-based surface code

TL;DR

This paper introduces a deformation-based surface code approach using superstabilizers to reduce resource costs and enable dense logical qubit placement, improving efficiency over traditional planar codes.

Contribution

It presents a novel deformation-based surface code with superstabilizers, enabling dense qubit packing and resource-efficient logical operations, including state injection and lattice surgery.

Findings

Resource cost per logical qubit reduced by about 55% compared to planar code.

Allows logical qubits to be placed closer together using superstabilizers.

Demonstrates a conversion process from defect-based to deformation-based surface code.

Abstract

Resource consumption of the conventional surface code is expensive, in part due to the need to separate the defects that create the logical qubit far apart on the physical qubit lattice. We propose that instantiating the deformation-based surface code using superstabilizers makes it possible to detect short error chains connecting the superstabilizers, allowing us to place logical qubits close together. Additionally, we demonstrate the process of conversion from the defect-based surface code, which works as arbitrary state injection, and a lattice surgery-like CNOT gate implementation that requires fewer physical qubits than the braiding CNOT gate. Finally we propose a placement design for the deformation-based surface code and analyze its resource consumption; large scale quantum computation requires $\frac{25}{4}d^2 +5d + 1$ physical qubits per logical qubit where $d$ is the code distance, whereas the planar code requires $16d^2 -16d + 4$ physical qubits per logical qubit, for a reduction of about 55%.