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Chinese Physics B

Experimental implementation of a continuous-time quantum random walk on a solid-state quantum information processor*

Maimaitiyiming Tusun, Yang Wu, Wenquan Liu, Xing Rong, Jiangfeng Du

Published Sep 18, 2019• 1 citation
Publisher

Abstract

There are some problems that quantum computers seem to be exponentially faster than classical computers, like factoring large numbers, machine learning, and simulation of quantum systems. Constructing an appropriate quantum algorithm becomes more important for solving these specific problems. In principle, any quantum algorithm can recast by a quantum random walk algorithm. Although quantum random walk with a few qubits has been implemented in a variety of systems, the experimental demonstration of solid-state quantum random walk remains elusive. Here we report the experimental implementation of the quantum continuous-time random walk algorithm by a two-qubit quantum processor in a nitrogen–vacancy center in diamond. We found that quantum random walk on a circle does not converge to any stationary distribution and exhibit a reversible property. Our results represent a further investigation of quantum walking dynamics in solid spin platforms, may also lead to other practical applications by the use of quantum continuous-time random walk for quantum algorithm design and quantum coherence transport.

DOI
10.1088/1674-1056/ab44ae

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There are some problems that quantum computers seem to be exponentially faster than classical computers, like factoring large numbers, machine learning, and simulation of quantum systems. Constructing an appropriate quantum algorithm becomes more important for solving these specific problems. In principle, any quantum algorithm can recast by a quantum random walk algorithm. Although quantum random walk with a few qubits has been implemented in a variety of systems, the experimental demonstration of solid-state quantum random walk remains elusive. Here we report the experimental implementation of the quantum continuous-time random walk algorithm by a two-qubit quantum processor in a nitrogen–vacancy center in diamond. We found that quantum random walk on a circle does not converge to any stationary distribution and exhibit a reversible property. Our results represent a further investigation of quantum walking dynamics in solid spin platforms, may also lead to other practical applications by the use of quantum continuous-time random walk for quantum algorithm design and quantum coherence transport.
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.
Abstract Quantum computers, which take advantage of the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized state of qubits, which coherently evolves into a final state containing the result of the computation. Although quantum processors with a few qubits have been demonstrated on multiple quantum computing platforms, realization of solid-state programmable quantum processor under ambient conditions remains elusive. Here we report a programable quantum processor that can be programmed with fifteen parameters to realize arbitrary unitary transformations on two spin qubits in a nitrogen-vacancy (NV) center in diamond. We implemented the Deutsch-Jozsa and Grover search algorithms with average success rates above 80%. The results pave the way to implement the programmable method in a large-scale quantum processor.
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains ``quantum,'' this algorithm could serve as an important benchmarking protocol for ion trap quantum computers.
Abstract A random walk is one of the widely adopted random processes for simulation and approximation in multiple areas of science and engineering. Quantum random walk is an analog version of the classical random walk. It was first introduced in 1993 by Y. Aharonov et al. They presented that, with the nature of quantum characteristic, the average length of the walking path on a line is possible to larger than a classical random walk can produce. Therefore, the quantum random walk can be used as a tool to construct many other quantum algorithms. Moreover, it can solve graph problems that many real-world problems can be formulated. However, quantum algorithms are only useful in practice if we can implement them efficiently on a quantum computer. In this study, we are then interested in designing and implementing a quantum circuit that can be run on a real quantum computing device. We firstly focus on the most straightforward, which is a one-dimension, quantum random walk algorithm. Then, the quantum circuits are developed and implemented on a real quantum computer and a quantum computing simulator using software development kits provided by IBM. Lastly, the performance and results of the quantum circuits tested on both computing platforms are presented.
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. Quantum walks represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves onto the multi-qubit states in a quantum processor, we present different configurations of quantum circuits for the implementation of discrete-time quantum walks in one-dimensional position space. With example circuits for a five qubit machine we address scalability to higher dimensions and larger quantum processors.