Resource-efficient high-threshold fault-tolerant quantum computation with weak nonlinear optics

TL;DR

This paper introduces a resource-efficient method for fault-tolerant quantum computation using weak nonlinear optics and hybrid GKP and single-photon qubits, achieving high error thresholds with reduced resource costs.

Contribution

It proposes a novel hybrid approach combining GKP and single-photon qubits with weak nonlinearities to enable scalable, high-threshold optical FTQC with lower resource requirements.

Findings

Achieves fault-tolerance with GKP squeezing of 7.4 and 8.4 dB at low loss rates.

Reduces resource costs compared to previous optical FTQC methods.

Allows GKP squeezing as low as 3.8 dB with very low photon loss.

Abstract

Quantum computation with light, compared with other platforms, offers the unique benefit of natural high-speed operations at room temperature and large clock rate, but a big obstacle of photonics is the lack of strong nonlinearities which also makes loss-tolerant or generally fault-tolerant quantum computation (FTQC) complicated in an all-optical setup. Typical current approaches to optical FTQC that aim at building suitable large multi-qubit cluster states by linearly fusing small elementary resource states would still demand either fairly expensive initial resources or rather low loss and error rates. Here we propose reintroducing weakly nonlinear operations, such as a weak cross-Kerr interaction, to achieve small initial resource cost and high error thresholds at the same time. More specifically, we propose an approach to generate a large-scale cluster state by hybridizing Gottesman-Kitaev-Preskill (GKP) and single-photon qubits. Our approach enables us to implement FTQC based on GKP squeezing of 7.4 and 8.4 dB and a photon loss rate of 1.0 and 5.0 %, respectively. In addition, our scheme has a reduced resource cost, i.e., number of physical qubits/photons per logical qubit or initial entanglement, compared to high-threshold FTQC with optical GKP qubits or fusion-based quantum computation with encoded single-photon-qubit states, respectively. Furthermore, our approach, when assuming very low photon loss, allows to employ GKP squeezing as little as 3.8 dB, which cannot be achieved by using GKP qubits alone.