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Note on Non-Unitary Quantum Gates in Quantum Computing

Aleksander Zujev

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We study possible advantage of using non-unitary quantum gates in quantum computing. Our particular goal is to investigate the application of non-unitary quantum gates for solving NP-complete problems. In this note, we specifically study an example of non-unitary quantum computing, advanced by Nordin Zakaria.
DOI
10.13140/rg.2.2.30712.85767

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We elucidate the profound connection between physics and computation by proposing and examining the model of the non-Hermitian quantum computer (NQC). In addition to conventional quantum gates such as the Hadamard, phase, and CNOT gates, this model incorporates a non-unitary quantum gate GGG. We show that NQC is extraordinarily powerful, capable of solving not only all NP problems but also all problems within the complexity class P♯P\text{P}^{\sharp\text{P}}P♯P in polynomial time. We investigate two physical schemes for implementing the non-unitary gate GGG and find that the remarkable computational power of NQC originates from the exponentially large physical resources required.
The goal of finding a commutative group of gates from the set of unitary matrices is to simplify the process of quantum computing. If a set of gates is commutative, then we can apply the gates in any order without affecting the final outcome. This is important because quantum systems are very sensitive to errors and decoherence, and any disruption to the system can cause errors in the computation.By having a commutative group of gates, we can simplify the process of designing quantum algorithms and reduce the risk of errors. This is particularly important for solving complex computational problems that cannot be solved by classical computers.
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the basic steps is to implement the quantum circuit able to realize a given unitary operation. This task has been solved using decomposition of unitary matrices in simpler ones till reach quantum circuits having only single-qubits and CNOTs gates. Usually the goal is to find the minimal quantum circuit able to solve a given problem. In this paper we go in a different direction. We propose a general quantum circuit able to implement any specific quantum circuit by just setting correctly the parameters. In other words, we propose a programmable quantum circuit. This opens the possibility to construct a real quantum computer where several different quantum operations can be realized in the same hardware. The configuration is proposed and its optical implementation is discussed.
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