Fault-tolerance thresholds for the surface code with fabrication errors

Abstract

The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a non-trivial topology such that the quantum information is encoded in the global degrees of freedom (i.e. the topology) of the manifold. However, the manufacturing of large-scale topological devices will undoubtedly suffer from fabrication errors---permanent faulty components such as missing physical qubits or failed entangling gates---introducing permanent defects into the topology of the lattice and hence significantly reducing the distance of the code and the quality of the encoded logical qubits. In this work we investigate how fabrication errors affect the performance of topological codes, using the surface code as the testbed. A known approach to mitigate defective lattices involves the use of primitive SWAP gates in a long sequence of syndrome extraction circuits. Instead, we show that in the presence of fabrication errors the syndrome can be determined using the supercheck operator approach and the outcome of the defective gauge stabilizer generators without any additional computational overhead or the use of SWAP gates. We report numerical fault-tolerance thresholds in the presence of both qubit fabrication and gate fabrication errors using a circuit-based noise model and the minimum-weight perfect matching decoder. Our numerical analysis is most applicable to 2D chip-based technologies, but the techniques presented here can be readily extended to other topological architectures. We find that in the presence of 8% qubit fabrication errors, the surface code can still tolerate a computational error rate of up to 0.1%.Comment: 10 pages, 15 figure

Fault-tolerant quantum computation with nondeterministic entangling gates

“…Our findings are particularly relevant to linear optics schemes, but our approach is sufficiently general that it can be applied to any system with non-deterministic entangling gates. The shared features of topological codes mean our results also give a qualitative insight for other topological codes, such as the surface code, with non-deterministic two-qubit gates, building on the recent work of [15]. Future work includes considering unheralded entanglement failure, where the locations of missing bonds are unknown, and combining this approach with [4] to attempt to reduce qubit and time overheads due to probabilistic GHZ state distillation for networks of trapped ions.…”

Leakage detection for a transmon-based surface code

“…In the latter case, a decoder could switch back and forth from standard surface-code decoding to e.g., the partial subsystem-code decoding in refs. [49][50][51] . Given control of the leakage conditional phases, the performance of this decoder can be optimized by setting ϕ L stat ¼ π and ϕ L flux ¼ 0, minimizing the spread of phase errors on the neighboring data qubits by a leaked ancilla qubit, as well as the noise on the weight-6 stabilizer extraction in the case of a leaked data qubit (see Supplementary Fig.…”

“…3d) to a back-action effect of the measurements of the neighboring stabilizers, whose outcomes are nearly randomized when the qubit is leaked (see sections "Leakage-induced anti-commutation" and "Projection of data-qubit leakage by stabilizer-measurement back-action" of Supplementary Methods). The weight-3 checks can also be interpreted as gauge operators, whose pairwise product results in weight-6 stabilizer checks, which can be used for decoding [49][50][51][52] , effectively reducing the code distance from 3 to 2.…”

Blueprint for fault-tolerant quantum computation with Rydberg atoms

“…Deterministic loading of traps remains a major hurdle for Rydberg atom quantum computation, but methods to overcome this have been suggested, including starting with a partially loaded lattice and rearranging the qubits [29] this approach has been successfully used to construct 2D lattice geometries of ∼ 50 qubits [30] with atomic separations of a few µm using optical tweezers, which would be sufficient for a prototype device. It is not necessary to construct a perfect lattice, as low rates of missing qubits can be handled with no additional quantum processing [31]. Z Z Z Z X X X X Figure 4: Arrangement of Rydberg atoms for a planar code.…”