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Implementing Arbitrary Quantum Operations via Quantum Walks on a Cycle Graph by Lin, Jia-Yi; Li, Xin-Yu; Shao, Yu-Hao; Wang, Wei; Wu, Shengjun is a scholarly article available to read on EtoBox.

What is Implementing Arbitrary Quantum Operations via Quantum Walks on a Cycle Graph about?

The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. Here we propose an alternative approach; we use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation $U(N)$ without the need to decompose it into a sequence of gates of smaller sizes. Our model is essentially a quantum neural network based on DTQW. Firstly, it is universal as we show that any unitary operation $U(N)$ can be realized via an appropriate choice of coin operators. Secondly, our DTQW-based neural network can be updated efficiently via a learning algorithm, i.e., a modified stochastic gradient descent algorithm adapted to our network. By training this network, one can promisingly find approximations to arbitrary desired unitary operations. With an additional measurement on the output, the DTQW-based neural network can also implement general measurements described by positive-operator-valued measures (POVMs). We show its capacity in implementing arbitrary 2-outcome POVM measurements via numeric simulation. We further demonstrate that the netwo

Author

Lin, Jia-Yi; Li, Xin-Yu; Shao, Yu-Hao; Wang, Wei; Wu, Shengjun

Published

2022

Language

EN