Early Fault-Tolerant Quantum Computing

TL;DR

This paper develops a performance model for early fault-tolerant quantum computers, demonstrating how such architectures can extend computational reach and efficiency in the transition era between NISQ and fully fault-tolerant quantum computing.

Contribution

It introduces a model for early fault-tolerant quantum architectures and shows how algorithms can be optimized for these systems to enhance performance.

Findings

Using over one million physical qubits, the reach for phase estimation extends from 90 to 130 qubits.

Early fault-tolerant algorithms can reduce circuit operations by 100 times.

Such algorithms increase circuit repetitions by 10,000 times, improving efficiency.

Abstract

Over the past decade, research in quantum computing has tended to fall into one of two camps: near-term intermediate scale quantum (NISQ) and fault-tolerant quantum computing (FTQC). Yet, a growing body of work has been investigating how to use quantum computers in transition between these two eras. This envisions operating with tens of thousands to millions of physical qubits, able to support fault-tolerant protocols, though operating close to the fault-tolerant threshold. Two challenges emerge from this picture: how to model the performance of devices that are continually improving and how to design algorithms to make the most use of these devices? In this work we develop a model for the performance of early fault-tolerant quantum computing (EFTQC) architectures and use this model to elucidate the regimes in which algorithms suited to such architectures are advantageous. As a concrete example, we show that, for the canonical task of phase estimation, in a regime of moderate scalability and using just over one million physical qubits, the ``reach'' of the quantum computer can be extended (compared to the standard approach) from 90-qubit instances to over 130-qubit instances using a simple early fault-tolerant quantum algorithm, which reduces the number of operations per circuit by a factor of 100 and increases the number of circuit repetitions by a factor of 10,000. This clarifies the role that such algorithms might play in the era of limited-scalability quantum computing.