Quantum Inflection Points - Part 4

Quantum Error Thresholds & Approaching Fault Tolerance

Back in 2012, Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland published a paper in APS titled “Surface codes: Towards practical large-scale quantum computation” in which they established thresholds for scaling quantum computers.

“We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-not. We then describe the single-qubit Hadamard, ˆS and ˆT operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code.”

Fowler et al determined that two-qubit-gate error rates below 1% (fidelities above 99%) are required to surpass quantum error-correcting thresholds^. They made this determination 11 years ago.

Image source: Brian Lenahan/Midjourney