Guided quantum walk

Abstract

We utilize the theory of local amplitude transfers (LAT) to gain insights into quantum walks (QWs) and quantum annealing (QA) beyond the adiabatic theorem. By representing the eigenspace of the problem Hamiltonian as a hypercube graph, we demonstrate that probability amplitude traverses the search space through a series of local Rabi oscillations. We argue that the amplitude movement can be systematically guided towards the ground state using a time-dependent hopping rate based solely on the problem's energy spectrum. Building upon these insights, we extend the concept of multi-stage QW by introducing the guided quantum walk (GQW) as a bridge between QW-like and QA-like procedures. We assess the performance of the GQW on exact cover, traveling salesperson and garden optimization problems with 9 to 30 qubits. Our results provide evidence for the existence of optimal annealing schedules, beyond the requirement of adiabatic time evolutions. These schedules might be capable of solving large-scale combinatorial optimization problems within evolution times that scale linearly in the problem size.

References in corpus (3)

• Spatial search by quantum walk
• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems

Cited by in corpus (8)

• Quantum algorithms for scientific computing
• Transfer learning of optimal QAOA parameters in combinatorial optimization
• Zeno-effect Computation: Opportunities and Challenges
• Continuous-time quantum optimisation without the adiabatic principle
• Discovery of energy landscapes towards optimized quantum transport: Environmental effects and long-range tunneling
• Quantum annealing and condensed matter physics
• Resource-Efficient Quantum Optimization via Higher-Order Encoding
• Improving success probability in the LHZ parity embedding by computing with quantum walks