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.

No abstract

NETWORKS IN QUANTUM PHYSICS VS COMPLEXITYNetwork and graph theory fundamentally arises in nearly all aspects of quantum information and computation. As is the case with traditional network science, not arXiv:1702.08459v4 [quant-ph] 16 Apr 2019Box 1 Cross-pollination between the fields of complex networks and quantum information science.In recent years, seminal work has been carried out at the intersection of quantum information and computation and complex network theory. We attempt to catalog the scope of this work in Fig. 1. complex networks and quantum physics (current status) quantum algorithms for network analysis algorithms and descriptors quantum transport on complex networks quantum communication networks graphity and emergent models of space-time related types of quantum networks quantum inspired network tools network analysis adapted to quantum physical resources tools for understanding network information theory quantum centrality measures random network models detecting community structure in quantum systems random quantum circuits random tensor networks and geometry quantum generalizations of random graph models entanglement percolation on complex networks quantum inspired network measures polynomial and superpolynomial reductions for certain network problems such as flow and effective resistance polynomial and superpolynomial reductions for certain machine learning and data analysis problems quantum walks solving graph recognition and search engine ranking problems walk models of exciton transport in photosynthetic complexes

In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time probability distribution for the location of a unitary quantum walker to that of a corresponding classical walker. The distribution of the classical walker is proportional to the distribution of degrees, which measures the connectivity of the network nodes and underlies many methods for analyzing classical networks including website ranking. The quantum distribution becomes exactly equal to the classical distribution when the walk has zero energy and at higher energies the difference, the so-called quantumness, is bounded by the energy of the initial state. We give an example for which the quantumness equals a Renyi entropy of the normalized weighted degrees, guiding us to regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate.Comment: 8 pages, 4 figures; improved description and new examples; accepted for publication in Phys. Rev.

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.