Qubit-efficient exponential suppression of errors*

Achieving a practical advantage with near-term quantum computers hinges on having effective methods to suppress errors. Recent breakthroughs have introduced methods capable of exponentially suppressing errors by preparing multiple noisy copies of a state and virtually distilling a more purified version. Here we present an alternative method, the Resource-Efficient Quantum Error Suppression Technique (REQUEST), that adapts this breakthrough to much fewer qubits by making use of active qubit resets, a feature now available on commercial platforms. Our approach exploits a space/time trade-off to achieve a similar error reduction using only 2N+1 qubits as opposed to MN+1 qubits, for M copies of an N qubit state. Additionally, we propose a method using near-Clifford circuits to find the optimal number of these copies in the presence of realistic noise, which limits this error suppression. We perform a numerical comparison between the original method and our qubit-efficient version with a realistic trapped-ion noise model. We  find that REQUEST can reproduce the exponential suppression of errors of the virtual distillation approach, while out-performing virtual distillation when fewer than 3N+1 qubits are available. Finally, we examine the scaling of the number of shots N_S required for REQUEST to achieve useful corrections. We find that N_S remains reasonable well into the quantum advantage regime where N is hundreds of qubits.