TY - JOUR

T1 - Topological classification of time-asymmetry in unitary quantum processes

AU - Turner, Jacob

AU - Biamonte, Jacob

N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd.

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

KW - quantum transport

KW - quantum walks

KW - time-reversal

UR - http://www.scopus.com/inward/record.url?scp=85106388902&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/abf9d0

DO - 10.1088/1751-8121/abf9d0

M3 - Article

AN - SCOPUS:85106388902

VL - 54

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 23

M1 - 235301

ER -