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Physics Today

Battling Decoherence: The Fault-Tolerant Quantum Computer

John P. Preskill

Published Jul 1, 2025• 2 citations
Publisher

Abstract

Quantum computers have the potential to do certain calculations faster than any foreseeable classical computers, but their success will depend on preserving complex coherent quantum states. Recent discoveries have shown us how to do that.
DOI
10.1063/pt.vbzv.arhx

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In a ground breaking discovery in 1994, Shor has shown that quantum computers, if built, can factor numbers efficiently. Since then quantum computing has become a burgeoning field of research, attracting theoreticians and experimentalists alike, and regrouping researchers from fields like computer science, physics, mathematics and engineering. Quantum information is very fragile and prone to decoherence. Yet by the middle of 1996 it has been shown that fault-tolerant quantum computation is possible. We give a simple description of the elements of quantum error-correction and quantum fault-tolerance. After characterizing quantum errors we present several error correction schemes and outline the elements of a full fledged fault-tolerant computation, which works error-free even though all of its components can be faulty. We also mention alternative approaches to error-correction, so called error-avoiding or decoherence-free schemes. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault–tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high–precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfil their destiny as the world's fastest computing devices. This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, December 1996.
It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer making long computations impossible. A further difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering long computations unreliable. However, these obstacles may not be as formidable as originally believed. For any quantum computation with t gates, we show how to build a polynomial size quantum circuit that tolerates O(1/log/sup c/t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O(1/t). We do this by showing that operations can be performed on quantum data encoded by quantum error-correcting codes without decoding this data.
Quantum computers are anticipated to provide computational advantages over classical devices for specific classes of problems.In quantum chemistry, such an advantage can be achieved on fault-tolerant quantum computers (FTQCs) using quantum phase estimation (QPE), which can, in principle, provide accurate electronic energies with polynomial scaling.However, the practical success of QPE and related algorithms critically depends on the availability of high-quality initial quantum states with sufficient overlap with the target eigenstates.Moreover, even FTQCs are expected to be limited in size and total computational resources for the foreseeable future, restricting quantum calculations to reduced subspaces and allowing only a partial treatment of electronic correlation.For chemically meaningful predictions, the remaining correlation effects must therefore be recovered through post-processing.