Optimal control of the silicon-based donor electron spin quantum computing

TL;DR

This paper demonstrates high-fidelity, fast CNOT gates for silicon donor electron spins using optimal control, relaxing fabrication constraints and achieving error rates suitable for fault-tolerant quantum computing.

Contribution

It introduces a gradient ascent pulse engineering method to optimize control sequences for silicon donor qubits, improving speed and fidelity over previous schemes.

Findings

Achieved CNOT gate error of about 10^-6

Operation time reduced to 100ns from 297ns

Relaxed donor spacing constraints to about 30nm

Abstract

We demonstrate how gradient ascent pulse engineering optimal control methods can be implemented on donor electron spin qubits in Si semiconductors with an architecture complementary to the original Kane's proposal. We focus on the high-fidelity controlled-NOT (CNOT) gate and explicitly find its digitized control sequences by optimizing its fidelity over the external controls of the hyperfine A and exchange J interactions. This high-fidelity CNOT gate has an error of about $10^{-6}$, below the error threshold required for fault-tolerant quantum computation, and its operation time of 100ns is about 3 times faster than 297ns of the proposed global control scheme. It also relaxes significantly the stringent distance constraint of two neighboring donor atoms of 10~20nm as reported in the original Kane's proposal to about 30nm in which surface A and J gates may be built with current fabrication technology. The effects of the control voltage fluctuations, the dipole-dipole interaction and the electron spin decoherence on the CNOT gate fidelity are also discussed.