  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.
