Constant Depth Code Deformations in the Parity Architecture

TL;DR

This paper introduces a constant-depth quantum encoding and decoding protocol in the parity architecture, enabling efficient logical gate implementation and optimization of quantum algorithms like QAOA and quantum Fourier transform.

Contribution

It presents a novel constant-depth protocol for quantum state encoding and decoding in the parity architecture using measurements and local operations, improving quantum gate efficiency.

Findings

Enables constant-depth implementation of logical multi-qubit gates.

Reduces depth of quantum Fourier transform by a factor of two.

Allows flexible code deformation for more efficient quantum algorithms.

Abstract

We present a protocol to encode and decode arbitrary quantum states in the parity architecture with constant circuit depth using measurements, local nearest-neighbor and single-qubit operations only. While this procedure typically requires a quadratic overhead of simultaneous qubit measurements, it allows for a simple and low-depth implementation of logical multi-qubit gates in the parity encoding via code deformation. We discuss how such encoding and decoding schemes can be used to flexibly change the size and shape of the underlying code to enable a more efficient implementation of quantum gates or algorithms. We apply the new findings to the QAOA which leads to a constant depth implementation using local gates at the same optimization performance as the standard, potentially non-local, QAOA approach without the parity encoding. Furthermore, we show that our method can reduce the depth of implementing the quantum Fourier transform by a factor of two when allowing measurements.