A Fault Tolerant, Area Efficient Architecture for Shor's Factoring Algorithm

TL;DR

This paper presents an optimized, fault-tolerant quantum architecture for Shor's factoring algorithm, reducing area and latency through advanced error correction, circuit tuning, and a novel ADCR metric.

Contribution

It introduces a new architecture with improved fault tolerance and efficiency, including a custom CAD flow, ADCR metric, and insights into adder performance for quantum circuits.

Findings

Error correction optimization reduces ADCR by over an order of magnitude.

Quantum carry-lookahead adders outperform ripple-carry adders in ADCR.

Estimated area and latency for 1024-bit Shor's factoring are provided.

Abstract

We optimize the area and latency of Shor's factoring while simultaneously improving fault tolerance through: (1) balancing the use of ancilla generators, (2) aggressive optimization of error correction, and (3) tuning the core adder circuits. Our custom CAD flow produces detailed layouts of the physical components and utilizes simulation to analyze circuits in terms of area, latency, and success probability. We introduce a metric, called ADCR, which is the probabilistic equivalent of the classic Area-Delay product. Our error correction optimization can reduce ADCR by an order of magnitude or more. Contrary to conventional wisdom, we show that the area of an optimized quantum circuit is not dominated exclusively by error correction. Further, our adder evaluation shows that quantum carry-lookahead adders (QCLA) beat ripple-carry adders in ADCR, despite being larger and more complex. We conclude with what we believe is one of most accurate estimates of the area and latency required for 1024-bit Shor's factorization: 7659 mm$^{2}$ for the smallest circuit and $6 * 10^8$ seconds for the fastest circuit.