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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-conceptmore » 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.« less

Building a quantum computer that surpasses the computational power of its classical counterpart is a great engineering challenge. Quantum software optimizations can provide an accelerated pathway to the first generation of quantum computing (QC) applications that might save years of engineering effort. Current quantum software stacks follow a layered approach similar to the stack of classical computers, which was designed to manage the complexity. In this review, we point out that greater efficiency of QC systems can be achieved by breaking the abstractions between these layers. Further, we review several works along this line, including two hardware-aware compilation optimizations thatmore » break the quantum instruction set architecture (ISA) abstraction and two error-correction/information-processing schemes that break the qubit abstraction. Last, we discuss several possible future directions.« less