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arXiv:1405.6209 · Physical Review A

Chiral quantum walks

Dawei Lu, Jacob Biamonte, Jun Li, Hang Li, T. H. Johnson, Ville Bergholm, Mauro Faccin, Zoltán Zimborás, Raymond Laflamme, Jonathan Baugh, Seth Lloyd

Published Apr 1, 2016• 58 citations
arXivHTMLPDF

Abstract

Given its importance to many other areas of physics, from condensed-matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal theory, classifying Hamiltonians and quantum circuits as time symmetric or not in terms of the elements and geometries of their underlying networks. Many of the typical circuits of quantum information science are found to exhibit time asymmetry. Moreover, we show that time asymmetry in circuits can be controlled using local gates only and can simulate time asymmetry in Hamiltonian evolution. We experimentally implement a fundamental example in which controlled time-reversal asymmetry in a palindromic quantum circuit leads to near-perfect transport. Our results pave the way for using time-symmetry breaking to control coherent transport and imply that time asymmetry represents an omnipresent yet poorly understood effect in quantum information science.

DOI
10.1103/physreva.93.042302

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Abstract Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the Harper–Hofstadter, the Haldane models, demonstrating one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by time-symmetry breaking. In quantum walk algorithms, recent work has discovered implications time-reversal symmetry breaking has on the transport of quantum states which has enabled a host of new experimental implementations. We provide a full topological classification of Hamiltonian operators that do not exhibit symmetry under time-reversal with respect to the induced transition probabilities between elements in a preferred site-basis, i.e. the nodes of the graph on which the walk takes place. We prove that a quantum process is necessarily time-symmetric for any choice of time-independent Hamiltonian precisely when the underlying support graph is bipartite or no Aharonov–Bohm phases are present in the gauge field. We further prove that certain bipartite graphs exhibit transition probability suppression, but not broken time-reversal symmetry. Furthermore, our development of a general framework characterizes gauge potentials on combinatorial graphs. These results and techniques fill an important missing gap in understanding the role this omnipresent effect has in quantum information and computation.
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.
Particle transport in quantum systems, which can be modeled by quantum walks on graphs, demonstrates a faster propagation advantage over the corresponding transport in classical systems. As known from several graph examples, achieving further advantages is possible by adding directional control in quantum walks. One way to introduce directional bias is via time-reversal symmetry breaking that can be achieved with chiral quantum walks, where complex phases are added to the edge weights. However, it is not known for which complex phases values and on which graphs quantum transport can be enhanced. Therefore, the classification of graph properties remains an open problem. Here we tackle this graph classification problem with a graph convolutional neural network trained on a set of simulated examples. We find that chiral quantum-walk dynamics leads to almost always faster transport on hypercubes compared to nonchiral dynamics. We connect our paper to physical implementations of quantum walks in superconducting qubits and optical waveguides. Our results open the possibility and flexibility of experimental implementations in demonstrating quantum-walk advantage.
The chiral transfer of quantum information in a metal nanoring network is presented. A system of three metal nanorings coupled to a two-level quantum dot enables the chiral transport of quantum states by breaking the time-reversal symmetry, which provides a platform for chiral quantum information processing in nanorings. The direction of the chirality can be controlled by preparing the quantum dot in its ground or excited state. We show that the system dynamics can be controlled such that one can achieve a perfect or a partial chiral transfer of the excitation. The synthetic magnetic field that enables the chirality in the system makes the generation of specifically tailored entangled nanoring states possible. As particular examples, we show that in this platform the generation of a two-excitation NOON state and entangled coherent states among nanorings can be realized.
Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an ensemble of random quantum circuits that are representative of the dynamics of generic TR-invariant many-body quantum systems. We derive a general statistical mechanics model describing entanglement, many-body quantum chaos, and quantum information dynamics in such TR-invariant circuits. As an example of application of our formalism, we study the universal properties of measurement-induced phase transitions in monitored TR-invariant systems, with measurements performed in a TR-invariant basis. We find that TR invariance of the unitary part of the dynamics does not affect the universality class, unless measurement outcomes are postselected to satisfy the global TR invariance of each quantum trajectory. We confirm these predictions numerically and find, for both generic and Clifford-based evolutions, critical exponents in the case of “strong,” i.e., global TR invariance where each quantum trajectory is TR invariant.