We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel it is the first explicit code shown to have this universal property. Here we show that a variant of the surface code-the XZZX code-offers remarkable performance for fault-tolerant quantum computation.
The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation. We also show that a highly-squeezed GKP state of GKP squeezing ≳12dB can be experimentally realized by using a dissipative stabilization method, namely, the Big-small-Big method, with fairly conservative experimental parameters.
#Alexei kitaev quantum error correction full
Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface code decoder. More importantly, we show that a low logical failure rate p_L<10⁻⁷ can be achieved with moderate hardware requirements, e.g., 291 modes and 97 qubits at a GKP squeezing of 12dB as opposed to 1457 bare qubits for the standard rotated surface code at an equivalent noise level (i.e., p=0.36%). Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by 9.9dB under the the assumption that finite-squeezing of the GKP states is the dominant noise source. Our proposed decoding reduces the total CNOT failure rate of the GKP qubits, e.g., from 0.87% to 0.36% at a GKP squeezing of 12dB, compared to the case where the simple closest-integer decoding is used. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. In this work, we propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. We find a fault-tolerant squeezing threshold of 12.7 dB, with room for further improvement.įault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. To validate fault tolerance, the architecture is simulated using surface-GKP codes, including noise from GKP states as well as gate noise caused by finite squeezing in the cluster state. Because of its three-dimensional structure, the architecture supports topological qubit error correction, while GKP error correction is efficiently realized within the architecture by teleportation. To accommodate scalability, we propose architectures that allow both spatial and temporal multiplexing, with the temporally encoded version requiring as little as two squeezed light sources. In this work, we propose a simple architecture for the preparation of a cluster state in three dimensions in which gates can be efficiently implemented by gate teleportation. However, no complete fault-tolerant architecture exists that includes everything from cluster-state generation with finite squeezing to gate implementations with realistic noise and error correction. Continuous-variable measurement-based quantum computation on cluster states has in recent years shown great potential for scalable, universal, and fault-tolerant quantum computation when combined with the Gottesman-Kitaev-Preskill (GKP) code and quantum error correction.