Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

Abstract

Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for 171 Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.

Quantum Error Correction with Quantum Autoencoders

“…These signal the occurrence of potential erasures while leaving the quantum state invariant if no erasures have happened. Such detection protocols have been proposed or even implemented for various architectures [78,82,85]. To be able to protect a logical qubit from single erasures, a code consisting of at least four physical qubits is necessary [77].…”

Quantum error correction in a time-dependent transverse field Ising model

“…In addition to engineering U to encode the qubit, we must also measure the check operators in order to implement the error correcting code. This may be achieved through the use of an ancilla qubit for each check operator [48,[66][67][68]. For each qubit in a given check operator, we must then apply a two-qubit entangling gate with the ancilla gate, along with any necessary one-qubit gates.…”