Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications

Abstract

Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and generated on a quantum processor in a way that requires exponentially fewer resources than direct implementation of the uniformly random set. Efficient pseudo-random operators can overcome the exponential cost of random operators required for quantum communication tasks such as super-dense coding of quantum states and approximately secure quantum data-hiding, and enable efficient stochastic methods for noise estimation on prototype quantum processors. This paper summarizes some recently published work demonstrating a random circuit method for the implementation of pseudo-random unitary operators on a quantum processor [Emerson et al., Science 302:2098 (Dec.~19, 2003)], and further elaborates the theory and applications of pseudo-random states and operators.

This paper is a synopsis of Emerson et al., Science 302: 2098 (Dec 19, 2003) and some related unpublished work; it is based on a talk given at QCMC04; 4 pages, 1 figure, aipproc.sty

References in corpus (2)

• Quantum Process Tomography of the Quantum Fourier Transform
• Entangling power of the quantum baker's map

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