[Paper Review] Quantum error mitigation for fault-tolerant quantum computing

Yasunari Suzuki, Suguru Endo+1 more|arXiv (Cornell University)|Oct 8, 2020

Quantum Computing Algorithms and Architecture11 citations

TL;DR

This paper proposes a hybrid quantum error mitigation (QEM) and quantum error correction (QEC) framework that bridges the post-NISQ and early fault-tolerant quantum computing (FTQC) regimes. By integrating QEM into an FTQC architecture, it increases effective code distance and T-gate count with only a constant sampling overhead of up to 100, reducing required logical qubits by tens of percent across 10^4 to 10^10 logical operations.

ABSTRACT

Fault-tolerant quantum computing (FTQC) is a form of universal quantum computing that suppresses physical errors via quantum error correction (QEC). On the other hand, it is expected that the available code distance and the $T$-gate count will be restricted in the early years of FTQC. Meanwhile, quantum error mitigation (QEM) was recently introduced for suppressing errors in noisy intermediate-scale quantum (NISQ) devices; it improves the computation accuracy of near-term quantum algorithms with its overhead being a greater number of samples. In this work, we integrate QEC and QEM into an efficient FTQC architecture that effectively increases the code distance and $T$-gate count. Our scheme will dramatically alleviate the required qubit count by tens of percent at the cost of a constant multiplicative sampling overhead within $10^2$ in a wide range of regimes from the post-NISQ era to early FTQC regime, which necessitates the order of from $10^4$ to $10^{10}$ logical operations. While it has been widely believed that there do not exist useful applications in post-NISQ regimes due to a chasm between the NISQ and FTQC regimes such as overheads for encoding and $T$-gate distillations, our scheme can continuously bridge the two distinct regimes.

Motivation & Objective

• To close the operational and resource gap between near-term NISQ devices and early fault-tolerant quantum computing (FTQC).
• To reduce the logical qubit count required for fault-tolerant computation in early FTQC, where code distance and T-gate counts are limited.
• To enable practical quantum advantage in the post-NISQ to early FTQC transition by combining quantum error mitigation (QEM) with quantum error correction (QEC).
• To maintain high computational accuracy while minimizing resource overhead in regimes with 10^4 to 10^10 logical operations.

Proposed method

• Integrates quantum error mitigation (QEM) techniques into a fault-tolerant quantum computing (FTQC) architecture to enhance effective error suppression.
• Uses QEM to compensate for limitations in code distance and T-gate distillation capability in early FTQC systems.
• Applies QEM with a constant multiplicative sampling overhead of up to 10^2, independent of system size.
• Leverages QEM's ability to improve accuracy without requiring full fault-tolerance, enabling practical implementation in early FTQC hardware.
• Designs a hybrid QEC-QEM framework that maintains fault-tolerance while extending effective error suppression beyond native QEC limits.
• Operates across a wide regime—from post-NISQ to early FTQC—by dynamically adapting QEM to compensate for limited T-gate and code distance resources.

Experimental results

Research questions

• RQ1 Can quantum error mitigation (QEM) effectively extend the capabilities of early fault-tolerant quantum computers with limited code distance and T-gate counts?
• RQ2 How can QEM be integrated into an FTQC architecture to maintain fault-tolerance while reducing logical qubit overhead?
• RQ3 What is the trade-off between sampling overhead and qubit savings when combining QEM with QEC in early FTQC?
• RQ4 Can the hybrid QEC-QEM approach bridge the operational and resource chasm between NISQ and full FTQC regimes?
• RQ5 What range of logical operations (10^4 to 10^10) can be efficiently supported using this hybrid framework?

Key findings

• The hybrid QEC-QEM framework reduces the required logical qubit count by tens of percent in early FTQC regimes.
• The method introduces only a constant multiplicative sampling overhead of up to 100, regardless of system size.
• The framework effectively increases the effective code distance and T-gate count beyond native QEC limits.
• It enables continuous operation across the transition from post-NISQ to early FTQC, eliminating the traditional chasm between these regimes.
• The approach maintains fault-tolerance while significantly improving resource efficiency for 10^4 to 10^10 logical operations.