Quantum error correction in the NISQ regime for sequential quantum computing

Abstract

We use density matrix simulations to study the performance of three distance three quantum error correcting codes in the context of the rare-earth-ion-doped crystal (RE) platform for quantum computing. We analyze pseudothresholds for these codes when parallel operations are not available, and examine the behavior both with and without resting errors. In RE systems, resting errors can be mitigated by extending the system's ground state coherence time. For the codes we study, we find that if the ground state coherence time is roughly 100 times larger than the excited state coherence time, resting errors become small enough to be negligible compared to other error sources. This leads us to the conclusion that beneficial QEC could be achieved in the RE system with the expected gate fidelities available in the NISQ regime. However, for codes using more qubits and operations, a factor of more than 100 would be required. Furthermore, we investigate how often QEC should be performed in a circuit. We find that for early experiments in RE systems, the minimal $[[5,1,3]]$ would be most suitable as it has a high threshold error and uses few qubits. However, when more qubits are available the $[[9,1,3]]$ surface code might be a better option due to its higher circuit performance. Our findings are important for steering experiments to an efficient path for realizing beneficial quantum error correcting codes in early RE systems where resources are limited.

References in corpus (21)

• Quantum Computing in the NISQ era and beyond
• Surface codes: Towards practical large-scale quantum computation
• Quantum Computing with Very Noisy Devices
• Elucidating Reaction Mechanisms on Quantum Computers
• Quantum Error Correction for Beginners
• Quantum error correction in a solid-state hybrid spin register
• Active stabilisation, quantum computation and quantum state synthesis
• Low-distance Surface Codes under Realistic Quantum Noise
• Robust dynamical decoupling for quantum computing and quantum memory
• Quantum error correction with only two extra qubits
• Towards practical classical processing for the surface code
• Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation
• Flag fault-tolerant error correction with arbitrary distance codes
• Surface code with decoherence: An analysis of three superconducting architectures
• Density-matrix simulation of small surface codes under current and projected experimental noise
• Simulating the performance of a distance-3 surface code in a linear ion trap
• State Preparation by Optical Pumping in Erbium Doped Solids using Stimulated Emission and Spin Mixing
• Robust quantum gates and a bus architecture for quantum computing with rare-earth-ion doped crystals
• High fidelity readout scheme for rare-earth solid state quantum computing
• Quantum processing with ensembles of rare earth ions in a stoichiometric crystal
• High connectivity quantum processor nodes using single-ion-qubits in rare-earth-ion-doped crystals

Cited by in corpus (1)

• Quantum networks using rare-earth ions