Fighting Exponentially Small Gaps by Counterdiabatic Driving
arXiv:2410.02520 · doi:10.1103/tgzt-dy3h
Abstract
We investigate the efficiency of approximate counterdiabatic driving (CD) in accelerating adiabatic passage through exponentially small gaps. First, we analyze a minimal spin-glass bottleneck model that is analytically tractable and exhibits both an exponentially small gap at the transition point and a change in the ground state that involves a macroscopic rearrangement of spins. Using the variational Floquet-Krylov expansion to construct CD terms, we find that while the formation of excitations is significantly suppressed, achieving a fully adiabatic evolution remains challenging. Extending our investigation to realistic NP-hard spin-glass problems -- specifically, the -regular \textsc{Max Cut} and -\textsc{XORSAT} -- we find again that local CD expansions lead to negligible improvements in the final ground state fidelity. These results highlight the limited impact of local CD methods in overcoming the bottlenecks associated with first-order quantum phase transitions. To address this limitation, we propose an alternative method, termed quantum brachistochrone counterdiabatic driving (QBCD), which employs the approximate full CD connecting the ground state and the first excited state at a single parameter value close to the critical point. In the minimal spin-glass model, QBCD enables exponentially faster adiabatic evolution than the local strategies. To alleviate the challenges of its experimental and classical implementation for realistic \textsc{NP}-hard problems, we exponentially reduce the non-locality of the QBCD Hamiltonian by sparsifying its matrix elements to the density of the local expansions. Despite this drastic simplification, sparsified QBCD maintains finite ground-state fidelity at driving times exponentially shorter than in local strategies and counterdiabatic optimized local driving (COLD).
References in corpus (24)
- Universal adiabatic dynamics across a quantum critical point
- Bounds for the adiabatic approximation with applications to quantum computation
- Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
- Barren Plateaus in Variational Quantum Computing
- Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
- Adiabatic tracking of quantum many-body dynamics
- Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
- Quantum annealing with antiferromagnetic fluctuations
- Simple Glass Models and their Quantum Annealing
- The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
- Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
- Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
- Quantum annealing: the fastest route to quantum computation?
- Counterdiabatic driving of the quantum Ising model
- Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions
- Two-parameter counter-diabatic driving in quantum annealing
- Effect of Local Minima on Adiabatic Quantum Optimization
- A solvable model of quantum random optimization problems
- Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization
- Local Perturbations Perturb -Exponentially- Locally
- Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems
- Bias-field digitized counterdiabatic quantum optimization
- Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions
- Toward a Theory of Phase Transitions in Quantum Control Landscapes