Imagine a movie showing particles in a gas moving and colliding with each other. Then when you play the movie backwards the velocity of the particles will be opposite, but their motion is still governed by the same laws of physics – we could just as well call the backwards film “forward” – there is no fundamental way to distinguish the arrow of time. This is called time-reversal symmetry.

A recent international collaboration including six members from the Institute for Quantum Computing (IQC) have shown how breaking time-reversal symmetry can be used as a resource to control the transport of quantum information.

One of the challenges in developing quantum applications, such as a quantum computer, is controlling how the quantum state evolves. One example is the probability of a particle starting at one physical location and arriving at another at a later time. The standard approach to achieve this requires the application of a sequence of discrete operations call quantum gates. Researchers need to determine these operations ahead of time and actively manipulate the system. When applied, some of the ‘quantumness’ of the state is lost because errors arise.

To address this fundamental challenge, the researchers viewed quantum evolution as a 'quantum walk' on a graph. In a quantum walk, once you set up a network a 'single particle quantum walker' moves on a graph and the system evolves on its own.

“Originally proposed by Richard Feynman, quantum walks have become a standard model used to study quantum transport,” said professor Jonathan Baugh, associate professor in the Department of Chemistry at the University of Waterloo. “Quantum walks can even represent a universal model of quantum computation as shown by IQC member Andrew Childs.”

IQC Postdoctoral fellow Dawei Lu used a liquid-state NMR system to specify the necessary network topologies and simulate this chiral quantum walk. In the joint experimental and theoretical collaboration, breaking time-reversal symmetry was shown to significantly enhance state transport.

a) On the right: The theoretical state-transfer probability, with the lighter color indicating higher probability. On the left we present four constant-α slices of this function. Solid lines are theoretical predictions, and dots represent experimental data. Dot height represents the experimental error (the inset in the bottom plot highlights the error bars for a few data points). (b) Quantum circuit diagram corresponding to the experiment. (c) Graph corresponding to the continuous-time quantum walk (on the single-excitation subspace) simulated by the circuit.

The future applications of time reversal symmetry breaking in quantum information science are ultimately unknown at this time. The results, Chiral Quantum Walks, appeared in Physical Review A on April 1, 2016.

“Our results imply that the physical effect of time-symmetry breaking can play a role in coherent transport and offer an alternative means to control a quantum process,” said Jacob Biamonte, IQC affiliate and lead of the Quantum Complexity Science Initiative at the University of Malta. “We have found the effect to be omnipresent in a range of quantum information protocols and algorithms and hence provides what might turn out to be a useful yet untapped resource.”

These ideas are expected to be useful in constructing new quantum algorithms and as a practical tool for implementing quantum control in real systems.