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 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 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.
We theoretically analyze the case of noisy Quantum walks (QWs) by introducing four qubit decoherence models into the coin degree of freedom of linear and cyclic QWs. These models include flipping channels (bit flip, phase flip and bit-phase flip), depolarizing channel, phase damping channel and generalized amplitude damping channel. Explicit expressions for the probability distribution of QWs on a line and on a cyclic path are derived under localized and delocalized initial states. We show that QWs which begin from a delocalized state generate mixture probability distributions, which could give rise to useful algorithmic applications related to data encoding schemes. Specifically, we show how the combination of delocalzed initial states and decoherence can be used for computing the binomial transform of a given set of numbers. However, the sensitivity of QWs to noisy environments may negatively affect various other applications based on QWs.
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 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 (QWs) represent pillars of quantum dynamics and information processing. They provide a powerful framework for simulating quantum transport, designing search algorithms, and enabling universal quantum computation. Several physical platforms have been employed for their implementation, such as trapped atoms and ions, nuclear magnetic resonance systems, and photonic quantum architectures either in bulk optics or waveguide structures and fiber-loop networks. Here we focus on the most promising and versatile approach, that is photonic integrated circuits. In this work, we review how the employment of this versatile experimental platform has allowed to explore several phenomena related to QW-based protocols as, for instance, the evolution in presence of different kinds of noise. In this landscape, to the best of our knowledge, few examples report on the introduction of absorbing centers and their effects on the coherence of the dynamics. Here we present and discuss the results related to absorbing boundaries in QWs obtained through theoretical simulations and experiments conducted with the universal photonic quantum processors realized by Quix Quantum. We analyze how localized absorption along one lattice edge affects the walker dynamics depending on both the leakage probability and the initial injection site. Our results show that the presence of controlled losses modifies interference patterns and coherence, without fully destroying quantum features and providing an effective resource for engineering on-chip QWs and simulating open quantum systems.
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.