Practicality of Fault-Tolerant Quantum Computation

Jangwoo Kim, Junpyo Kim, Junhyuk Choi +7 more

To run a practical size of quantum program, computer architects have been making tremendous efforts to realize fault-tolerant quantum computing (FTQC) which constructs a fault-tolerant logical qubit by correcting many erroneous physical qubits during runtime. However, it is extremely challenging to build a full-stack FTQC system consisting of heterogeneous stacks, where each stack incurs unique challenges regarding the fault tolerance and the interplay of the challenges incurs very complicated overall design choice problem. Therefore, computer architects must fully understand stack-specific optimizations and their system-level trade-offs, and resolve all the challenges together. In this article, we first introduce critical design challenges in architecting an FTQC system built on the superconducting technology, and then present our research outcomes to resolve the challenges to build an FTQC system realizing thousands of logical qubits. We also outline near-future directions to resolve the remaining challenges and provide insights toward realizing more scalable future FTQC systems.

David Peter Divincenzo

Mollie E. Schwartz, Danna Rosenberg, David K. Kim +6 more

Yanzhang Zhu, Siyuan Niu, Di Wu

Quantum computing has showcased potentials to address classically unsolvable problems and attracted research investigation all around the world. However, quantum devices are inherently noisy and create hurdles from true quantum supremacy. Despite researchers have strived to demonstrate quantum advantages at small scales in the noisy intermediate-scale quantum (NISQ) era, we are now at the turning point to craft fault tolerant quantum computers (FTQC) for large scale quantum computing. In this paper, we review the current status of available error control techniques, discuss the missing pieces of each technique for their practical adaptation, and envision the necessity to synergize them across vast design stacks, to enable fault tolerance in quantum computing.

Satoshi Yoshida, Ethan Lake, Hayata Yamasaki

Fast decoders that achieve strong error suppression are essential for fault-tolerant quantum computation (FTQC) from both practical and theoretical perspectives. The union-find (UF) decoder for the surface code is widely regarded as a promising candidate, offering almost-linear time complexity and favorable empirical error suppression supported by numerical evidence. However, the lack of a rigorous threshold theorem has left open whether the UF decoder can achieve fault tolerance beyond the error models and parameter regimes tested in numerical simulations. Here, we provide a rigorous proof of a finite threshold for the UF decoder on the surface code under the circuit-level local stochastic error model. To this end, we develop a refined error-clustering framework that extends techniques previously used to analyze cellular-automaton and renormalization-group decoders, by showing that error clusters can be separated by substantially larger buffers, thereby enabling analytical control over the behavior of the UF decoder. Using this guarantee, we further prove a quasi-polylogarithmic upper bound on the average runtime of a parallel UF decoder in terms of the code size. We also show that this framework yields a finite threshold for the greedy decoder, a simpler decoder with lower complexity but weaker empirical error suppression. These results provide a solid theoretical foundation for the practical use of UF-based decoders in the development of fault-tolerant quantum computers, while offering a unified framework for studying fault tolerance across these practical decoders.

Andrew M. Steane