An ancillabased quantum simulation framework for

Authors: Ammar Daskin Sabre Kais

Publish Date: 2016/12/23

Volume: 16, Issue: 1, Pages: 33-

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Abstract

The success probability in an ancillabased circuit generally decreases exponentially in the number of qubits consisted in the ancilla Although the probability can be amplified through the amplitude amplification process the input dependence of the amplitude amplification makes difficult to sequentially combine two or more ancillabased circuits A new version of the amplitude amplification known as the oblivious amplitude amplification runs independently of the input to the system register This allows us to sequentially combine two or more ancillabased circuits However this type of the amplification only works when the considered system is unitary or nonunitary but somehow close to a unitary In this paper we present a general framework to simulate nonunitary processes on ancillabased quantum circuits in which the success probability is maximized by using the oblivious amplitude amplification In particular we show how to extend a nonunitary matrix to an almost unitary matrix We then employ the extended matrix by using an ancillabased circuit design along with the oblivious amplitude amplification Measuring the distance of the produced matrix to the closest unitary matrix a lower bound for the fidelity of the final state obtained from the oblivious amplitude amplification process is presented Numerical simulations for random matrices of different sizes show that independent of the system size the final amplified probabilities are generally around 075 and the fidelity of the final state is mostly high and around 095 Furthermore we discuss the complexity analysis and show that combining two such ancillabased circuits a matrix product can be implemented This may lead us to efficiently implement matrix functions represented as infinite matrix products on quantum computers

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