Fault-Tolerant Quantum Computation

Years and Authors of Summarized Original Work

• 1996; Shor, Aharonov, Ben-Or, Kitaev

Problem Definition

Fault tolerance is the study of reliable computation using unreliable components. With a given noise model, can one still reliably compute? For example, one can run many copies of a classical calculation in parallel, periodically using majority gates to catch and correct faults. Von Neumann showed in 1956 that if each gate fails independently with probability p, flipping its output bit $0 \leftrightarrow 1$, then such a fault tolerance scheme still allows for arbitrarily reliable computation provided that p is below some constant threshold (whose value depends on the model details) [10].

In a quantum computer, the basic gates are much more vulnerable to noise than classical transistors – after all, depending on the implementation, they are manipulating single electron spins, photon polarizations, and similarly fragile subatomic particles. It might not be possible to engineer systems...