Criteria for universality of quantum gates

Abstract

We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{U_1,\dots ,U_n\}$ is universal. We provide the compact form criteria leading to a simple algorithm that allows deciding universality of any given set of gates in a finite number of steps. Moreover, for a non-universal $\mathcal{S}$ our criteria indicate what type of gates can be added to $\mathcal{S}$ to turn it into a universal set.

Significantly improved universality criteria and the much simpler algorithm that allows deciding universality of an arbitrary set of gates

References in corpus (2)

• Silica-on-Silicon Waveguide Quantum Circuits
• Classical simulation of fermionic linear optics augmented with noisy ancillas

Cited by in corpus (14)

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• Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry
• Calculable lower bounds on the efficiency of universal sets of quantum gates
• Matrix concentration inequalities and efficiency of random universal sets of quantum gates
• Quantum permutation puzzles with indistinguishable particles
• Products of finite order rotations and quantum gates universality