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

NISQ+: Boosting quantum computing power by approximating quantum error correction, by Adam Holmes, Mohammad Reza Jokar, Ghasem Pasandi, Yongshan Ding, Massoud Pedram, Frederic T. Chong

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 near-term 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 × 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 Single-Flux Quantum (SFQ) superconducting 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.
Our design utilizes one SFQ processing module per physical qubit. Employing state-of-the-art SFQ synthesis tools, we show that the circuit area, power, and latency are within the constraints of contemporary quantum system designs. Under pure dephasing error models, 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 and pseudo-thresholds of ∼ 5%,4.75%,4.5%, and 3.5% physical error-rates for code distances 3,5,7, and 9. Decoding solutions are achieved in a maximum of ∼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.

This work is funded in part by EPiQC, an NSF Expedition in Computing, under grants CCF-1730449; in part by STAQ under grant NSF Phy-1818914; in part by DOE grants DE-SC0020289 and DE-SC0020331; in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the U.S. Army Research Office grant W911NF-17-1-0120.