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.
Jones J. A., Mosca M., Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer, 10.1063/1.476739
Vandersypen Lieven M. K., Steffen Matthias, Breyta Gregory, Yannoni Costantino S., Sherwood Mark H., Chuang Isaac L., Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance, 10.1038/414883a
Lanyon B. P., Whitfield J. D., Gillett G. G., Goggin M. E., Almeida M. P., Kassal I., Biamonte J. D., Mohseni M., Powell B. J., Barbieri M., Aspuru-Guzik A., White A. G., Towards quantum chemistry on a quantum computer, 10.1038/nchem.483
Zhang Jingfu, Yung Man-Hong, Laflamme Raymond, Aspuru-Guzik Alán, Baugh Jonathan, Digital quantum simulation of the statistical mechanics of a frustrated magnet, 10.1038/ncomms1860
Faccin Mauro, Johnson Tomi, Biamonte Jacob, Kais Sabre, Migdał Piotr, Degree Distribution in Quantum Walks on Complex Networks, 10.1103/physrevx.3.041007
Mülken Oliver, Blumen Alexander, Continuous-time quantum walks: Models for coherent transport on complex networks, 10.1016/j.physrep.2011.01.002
Perseguers S., Lewenstein M., Acín A., Cirac J. I., Quantum random networks, 10.1038/nphys1665
Zimborás Zoltán, Faccin Mauro, Kádár Zoltán, Whitfield James D., Lanyon Ben P., Biamonte Jacob, Quantum Transport Enhancement by Time-Reversal Symmetry Breaking, 10.1038/srep02361
Xiang Ping, Litinskaya Marina, Shapiro Evgeny A, Krems Roman V, Non-adiabatic control of quantum energy transfer in ordered and disordered arrays, 10.1088/1367-2630/15/6/063015
Bedkihal Salil, Bandyopadhyay Malay, Segal Dvira, The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport, 10.1140/epjb/e2013-40971-7
Manzano Daniel, Hurtado Pablo I., Symmetry and the thermodynamics of currents in open quantum systems, 10.1103/physrevb.90.125138
Sinayskiy I., Marais A., Petruccione F., Ekert A., Decoherence-Assisted Transport in a Dimer System, 10.1103/physrevlett.108.020602
Bose Sougato, Quantum communication through spin chain dynamics: an introductory overview, 10.1080/00107510701342313
Asbóth János K., Obuse Hideaki, Bulk-boundary correspondence for chiral symmetric quantum walks, 10.1103/physrevb.88.121406
Vandersypen L. M. K., Chuang I. L., NMR techniques for quantum control and computation, 10.1103/revmodphys.76.1037
Cory D. G., Fahmy A. F., Havel T. F., Ensemble quantum computing by NMR spectroscopy, 10.1073/pnas.94.5.1634
Khaneja Navin, Reiss Timo, Kehlet Cindie, Schulte-Herbrüggen Thomas, Glaser Steffen J., Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms, 10.1016/j.jmr.2004.11.004
Ryan C. A., Negrevergne C., Laforest M., Knill E., Laflamme R., Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods, 10.1103/physreva.78.012328
E. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (1959)
Skotiniotis Michael, Toloui Borzu, Durham Ian T., Sanders Barry C., Quantum Frameness forCPTSymmetry, 10.1103/physrevlett.111.020504
Peierls R., Zur Theorie des Diamagnetismus von Leitungselektronen, 10.1007/bf01342591
Hofstadter Douglas R., Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, 10.1103/physrevb.14.2239
S. Das Sarma, Perspectives in Quantum Hall Effects (2008)
Rhim W-K., Pines A., Waugh J. S., Time-Reversal Experiments in Dipolar-Coupled Spin Systems, 10.1103/physrevb.3.684
Cho H., Ladd T. D., Baugh J., Cory D. G., Ramanathan C., Multispin dynamics of the solid-state NMR free induction decay, 10.1103/physrevb.72.054427
Bibliographic reference
Lu, Dawei ; Biamonte, Jacob D. ; Li, Jun ; Li, Hang ; Johnson, Tomi H. ; et. al. Chiral quantum walks. In: Physical review. A, Atomic, molecular, and optical physics, , no.93, p. 042302 (2016)