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Science

Quantum walkers caught in a loop

Ian S. Osborne

Published Mar 7, 2019• 0 citations
Publisher

Abstract

Quantum Optics A quantum walk is the quantum mechanical analog of a classical random walk, describing the propagation of quantum walkers (photons) through an optical circuit. Because quantum walks generate large-scale quantum superposed states, they can be used for simulating many-body quantum systems and the development of algorithms for quantum computation. Nejadsattari et al. describe the photonic simulation with cyclic quantum systems. Using a multiple-site optical system, they explored the wave function dynamics and the probability distribution of quantum walkers as they loop through the system from site to site. With the ability to simulate a variety of different quantum operations and gates, they claim that the versatility of the approach should allow the study of more complex many-body systems. Optica 6 , 174 (2019).

DOI
10.1126/science.363.6431.1053-b

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Quantum Optics
A quantum walk is the quantum mechanical analog of a classical random walk, describing the propagation of quantum walkers (photons) through an optical circuit. Because quantum walks generate large-scale quantum superposed states, they can be used for simulating many-body quantum systems and the development of algorithms for quantum computation. Nejadsattari et al. describe the photonic simulation with cyclic quantum systems. Using a multiple-site optical system, they explored the wave function dynamics and the probability distribution of quantum walkers as they loop through the system from site to site. With the ability to simulate a variety of different quantum operations and gates, they claim that the versatility of the approach should allow the study of more complex many-body systems.
Optica 6 , 174 (2019).
Quantum walks serve as novel tools for performing efficient quantum computation and simulation. In a recent experimental demonstration [1] we have realized photonic quantum walks for simulating cyclic quantum systems, such as hexagonal lattices or aromatic molecules like benzene. In that experiment we explored the wave function dynamics and the probability distribution of a quantum particle located on a six-site system (with periodic boundary conditions), alongside with simpler demonstration of three- and four-site systems, under various initial conditions. Localization and revival of the wave function were demonstrated. After revisiting that experiment we will theoretically analyze the case of noisy quantum walks by implementing the bit-phase flip channel. This will allow us to draw conclusions regarding the performance of our photonic quantum simulation in noisy environments. Finally, we will briefly outline some future directions.
Quantum Electronics Quantum walks generate large-scale quantum superposed states. This allows for classically unavailable applications, such as simulating many-body quantum systems, and also yields quantum algorithms exponentially faster than classical computation. Yan et al. demonstrate quantum walks of one and two strongly correlated microwave photons in a one-dimensional array of 12 superconducting qubits with short-range interactions. The scalability of the superconducting platform could lead to large-scale implementations and the quantum simulation of complex systems. Science , this issue p. [753][1] [1]: /lookup/doi/10.1126/science.aaw1611
We present an optical module to simulate one step of a quantum walk algorithm. The quantum state of a system with a 2N2N2N-dimensional Hilbert space is encoded in the spatial distribution of the amplitude of the electromagnetic field in a plane. In such spatial encoding, the probability amplitude of each state of a basis is associated with the complex electromagnetic amplitude in a given slice of the laser wave front. We discuss the design and operation of an optical module that is used to implement one step of a quantum walk algorithm. Using this module, composed by standard optical elements, the evolution of the quantum state corresponds to the application of a Hadamard gate on a single qubit (representing the two-dimensional quantum coin) followed by a displacement of the NNN-dimensional quantum walker conditioned on the state of the coin. We show the actual implementation of the method and discuss its characteristics and limitations.
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems ( approximately 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects.
Quantum walks present novel tools for redesigning quantum algorithms, universal quantum computations, and quantum simulators. Hitherto, one- and two-dimensional quantum systems (lattices) have been simulated and studied with photonic systems. Here, we report the photonic simulation of cyclic quantum systems, such as hexagonal structures. We experimentally explore the wavefunction dynamics and probability distribution of a quantum particle located on a six-site system, along with three- and four-site systems while under different initial conditions. Various quantum walk systems employing Hadamard, C-NOT, and Pauli-Z gates are experimentally simulated, where we find configurations capable of simulating particle transport and probability density localization. Our technique can potentially be integrated into small-scale structures using microfabrication, and thus would open a venue towards simulating more complicated quantum systems comprised of cyclic structures.
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.