NISQ+: Boosting quantum computing power by approximating quantum error correction

Quantum computers are growing in size, and design decisions are being made now that attempt to squeeze more computation out of these machines. In this spirit, we design a method to boost the computational power of nearterm quantum computers by adapting protocols used in quantum error correction to implement “Approximate Quantum Error Correction (AQEC):” By approximating fully-fledged error correction mechanisms, we can increase the compute volume (qubits $\times$ gates, or “Simple Quantum Volume (SQV)”) of near-term machines. The crux of our design is a fast hardware decoder that can approximately decode detected error syndromes rapidly. Specifically, we demonstrate a proof-of-concept that approximate error decoding can be accomplished online in near-term quantum systems by designing and implementing a novel algorithm in superconducting Single Flux Quantum (SFQ) logic technology. This avoids a critical decoding backlog, hidden in all offline decoding schemes, that leads to idle time exponential in the number of T gates in a program [58]. Our design utilizes one SFQ processing module per physical quantum bit. Employing state-of-the-art SFQ synthesis tools, we show that the circuit area, power, and latency are within the constraints of typical, contemporary quantum system designs. Under a pure dephasing error model, the proposed accelerator and AQEC solution is able to expand SQV by factors between 3,402 and 11,163 on expected near-term machines. The decoder achieves a 5% accuracy threshold as well as pseudo-thresholds of approximately 5%, 4.75%, 4.5%, and 3.5% physical error rates for code distances 3, 5, 7, and 9, respectively. Decoding solutions are achieved in a maximum of $\sim$20 nanoseconds on the largest code distances studied. By avoiding the exponential idle time in offline decoders, we achieve a 10x reduction in required code distances to achieve the same logical performance as alternative designs.