Fault-tolerant quantum computation

TL;DR

The paper addresses the challenge of decoherence and imperfect quantum gates by introducing fault-tolerant quantum computation based on quantum error-correcting codes, enabling computations on encoded data without decoding. It develops a universal gate set for encoded qubits using Clifford operations and Toffoli gates, employing ancilla states and cat-state syndrome measurements to perform fault-tolerant error correction. The approach yields polynomial-size circuits with per-gate error tolerances on the order of 1/(log t)^c for t gates, albeit with polylogarithmic overhead and sophisticated fault-tolerant procedures. The work lays foundational techniques for scalable quantum computation and highlights both the potential and the open challenges in designing more efficient error-correcting codes and fault-tolerance schemes.

Abstract

Recently, it was 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 of realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer, thus making long computations impossible. A futher difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering the output of long computations unreliable. It was previously known that a quantum circuit with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per gate. We show, for any quantum computation with t gates, how to build a polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of inaccuracy and decoherence per gate, for some constant c. We do this by showing how to compute using quantum error correcting codes. These codes were previously known to provide resistance to errors while storing and transmitting quantum data.