Constant depth code deformations in the parity architecture
22/03/2023
Quantum computing has come a long way in recent decades, both theoretically and experimentally, paving the way for demonstrating quantum advantage. But, as with any groundbreaking technology, there are challenges to overcome. Current quantum devices struggle with error-prone gates and quantum decoherence, which limit their potential. These issues will eventually be resolved with error correction techniques, but for now, quantum errors have to be mitigated or avoided by minimizing the number of gates and the circuit run time.
Recently, a universal gate set for the ParityQC architecture was proposed, allowing for an efficient implementation of corner-stone quantum algorithms like the quantum Fourier transform. In the parity encoding, a certain class of global multi-qubit gates can be implemented with physical single-qubit operations only, while other operators require CNOT sequences of depth scaling linear with the system size. Similarly, the encoding and decoding processes presented in previous works require sequences of CNOT gates of linear depth.
The paper “Constant Depth Code Deformations in the Parity Architecture”, written by Anette Messinger, Michael Fellner and Wolfgang Lechner, takes the research mentioned above one step forward.
In this work, the authors introduce a new protocol to encode and decode arbitrary quantum states in the ParityQC Architecture with the help of measurements, enabling a more efficient implementation of quantum gates or algorithms. This scheme can be implemented with a constant circuit depth, and using nearest-neighbor and single-qubit operations only. The methods introduced are similar to code deformation techniques known from error correction codes, and allow one to replace sequential CNOT gates by parallel measurements and classically-controlled single-qubit gates.
The authors show that such encoding and decoding schemes can be used to flexibly change the size and shape of the underlying parity code, in order to efficiently implement quantum gates or algorithms. These findings are then applied to a selection of quantum algorithms. The approach results in a constant-depth implementation of the Quantum Approximate Optimization Algorithm (QAOA) using local gates only, and an overall optimization performance which is at the same level as the standard, potentially non-local, QAOA approach without the parity encoding. The method is also shown to reduce the depth of implementing the quantum Fourier transform by a factor of two when allowing measurements.
Read the pre-print on arXiv here.