prepared a Bacon–Shor logical qubit with 13 trapped-ion qubits and demonstrated a logical single-qubit Clifford gate. Up till now, no logical qubit/operation with high fidelity was realized in experiments since current gate noise rates are still much larger than the requirements. Our work sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes. Furthermore, we found many new channel-adaptive codes for error models involving nearest-neighbor correlated errors.
QUANTUM ERROR CORRECTION VIA CONVEX OPTIMIZATION CODE
We also found new ( ( 6, 2, 3 ) ) 2 and ( ( 7, 2, 3 ) ) 2 codes that are not equivalent to any stabilizer code, and extensive numerical evidence with VarQEC suggests that a ( ( 7, 3, 3 ) ) 2 code does not exist. We have verified its effectiveness by (re)discovering some symmetric and asymmetric codes, e.g., ( ( n, 2 n − 6, 3 ) ) 2 for n from 7 to 14. In principle, VarQEC can find quantum codes for any error model, whether additive or non-additive, degenerate or non-degenerate, pure or impure. Given the target noise channel (or the target code parameters) and the hardware connectivity graph, we optimize a shallow variational quantum circuit to prepare the basis states of an eligible code. The cost functions are inspired by the most general and fundamental requirements of a QECC, the Knill-Laflamme conditions. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. However, the majority of these codes are not suitable for near-term quantum devices. In the past two decades, various methods of QECC constructions have been developed, leading to many good families of codes.
Quantum error-correcting codes (QECCs) are believed to be a necessity for large-scale fault-tolerant quantum computation.