Quantum Walk Search with Time-Reversal Symmetry Breaking

Abstract

We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry is too small to significantly affect the evolution: the system still approximately evolves in its ground and first excited states, rotating to the marked vertex in time $\pi \sqrt{N}/2$. Increasing the phase does not change the runtime, but rather changes the support for the 2D subspace, so the system evolves in its first and second excited states, or its second and third excited states, and so forth. Apart from the critical phases corresponding to these transitions in the support, which become more frequent as the phase grows, this reveals that our model of quantum search is robust against time-reversal symmetry breaking.

14 pages, 8 figures

References in corpus (5)

• Universal computation by quantum walk
• Spatial search by quantum walk
• Grover Search with Lackadaisical Quantum Walks
• Hamiltonian Oracles
• Faster transport with a directed quantum walk

Cited by in corpus (12)

• Faster Quantum Walk Search on a Weighted Graph
• Quantum-classical distance as a tool to design optimal chiral quantum walk
• Chiral quantum router with Rydberg atoms
• Irreconcilable Difference Between Quantum Walks and Adiabatic Quantum Computing
• Engineering the Success of Quantum Walk Search Using Weighted Graphs
• Topological classification of time-asymmetry in unitary quantum processes
• Entanglement transfer via Chiral Quantum Walk on a Triangular Chain
• Discrete-Time Quantum Walks on Oriented Graphs
• Short time behavior of continuous time quantum walks on graphs
• Scalable Structure For Chiral Quantum Routing
• Transport in extended Kitaev chain with time reversal symmetry breaking and long-range interaction
• Perturbed graphs achieve unit transport efficiency without environmental noise