Diabatic Quantum Annealing for the Frustrated Ring Model
arXiv:2212.02624 · doi:10.1088/2058-9565/acfbaa
Abstract
Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable quantum annealing to circumvent bottlenecks associated with the standard implementation of quantum annealing.
9 pages for the main text, 2 pages for the appendix
References in corpus (31)
- Barren plateaus in quantum neural network training landscapes
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Quantum Amplitude Amplification and Estimation
- Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
- Shortcuts to adiabaticity: concepts, methods, and applications
- Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
- Quantum Search by Local Adiabatic Evolution
- Defining and detecting quantum speedup
- Quantum Data Fitting
- Bounds for the adiabatic approximation with applications to quantum computation
- Quantum Approximate Optimization of the Long-Range Ising Model with a Trapped-Ion Quantum Simulator
- Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
- Quantum Speedup by Quantum Annealing
- How Powerful is Adiabatic Quantum Computation?
- Theory of overparametrization in quantum neural networks
- Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
- Prospects for Quantum Enhancement with Diabatic Quantum Annealing
- Optimal Protocols in Quantum Annealing and QAOA Problems
- First Order Quantum Phase Transition in Adiabatic Quantum Computation
- Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
- Applying quantum algorithms to constraint satisfaction problems
- Genetic optimization of quantum annealing
- Quantum algorithm for tree size estimation, with applications to backtracking and 2-player games
- Faster quantum and classical SDP approximations for quadratic binary optimization
- Schedule path optimization for quantum annealing and adiabatic quantum computing
- Variationally Scheduled Quantum Simulation
- Faster than Classical Quantum Algorithm for dense Formulas of Exact Satisfiability and Occupation Problems
- Robust Quantum Control for Adiabatic Quantum Computation
- Optimally Stopped Optimization
- Deep learning optimal quantum annealing schedules for random Ising models
- Noise amplification at spin-glass bottlenecks of quantum annealing: a solvable model
Cited by in corpus (11)
- Lie-algebraic classical simulations for quantum computing
- Deep learning optimal quantum annealing schedules for random Ising models
- Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions
- Post-processing variationally scheduled quantum algorithm for constrained combinatorial optimization problems
- Beyond Quantum Annealing: Optimal control solutions to MaxCut problems
- Improving the efficiency of quantum annealing with controlled diagonal catalysts
- Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
- Fighting Exponentially Small Gaps by Counterdiabatic Driving
- Validity condition for high-fidelity Digitized Quantum Annealing
- Digital controllability of transverse field Ising chains
- Frustration-enhanced quantum annealing correction models with additional inter-replica interactions