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 (93)
- Barren plateaus in quantum neural network training landscapes
- Adiabatic Quantum Computing
- Quantum annealing with more than one hundred qubits
- Dynamics of a Quantum Phase Transition
- Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
- Dynamics of quantum phase transition: exact solution in quantum Ising model
- Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
- Universal adiabatic dynamics across a quantum critical point
- Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
- Bounds for the adiabatic approximation with applications to quantum computation
- The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
- Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking
- Observation of topological phenomena in a programmable lattice of 1,800 qubits
- Geometry and non-adiabatic response in quantum and classical systems
- Quantum Brachistochrone
- Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
- Minimizing irreversible losses in quantum systems by local counter-diabatic driving
- Trade-off between speed and cost in shortcuts to adiabaticity
- Coherent quantum annealing in a programmable 2000-qubit Ising chain
- Barren Plateaus in Variational Quantum Computing
- Floquet-engineering counterdiabatic protocols in quantum many-body systems
- Inconsistency in the application of the adiabatic theorem
- First order phase transition in the Quantum Adiabatic Algorithm
- Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again
- Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
- Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
- Adiabatic tracking of quantum many-body dynamics
- Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
- Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
- Quantum annealing with antiferromagnetic fluctuations
- Optimal Protocols in Quantum Annealing and QAOA Problems
- Beyond-classical computation in quantum simulation
- Transitionless quantum driving for spin systems
- Digitized-counterdiabatic quantum approximate optimization algorithm
- First Order Quantum Phase Transition in Adiabatic Quantum Computation
- Counterdiabaticity and the quantum approximate optimization algorithm
- Simple Glass Models and their Quantum Annealing
- Reverse annealing for the fully connected -spin model
- The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
- Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
- First-order transitions and the performance of quantum algorithms in random optimization problems
- Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
- Quantization of Hall Conductance For Interacting Electrons on a Torus
- Digital-Analog Quantum Simulations with Superconducting Circuits
- The quantum Ising chain for beginners
- Fermionic Gaussian states: an introduction to numerical approaches
- Scaling and diabatic effects in quantum annealing with a D-Wave device
- Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving
- Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
- Dynamics of reverse annealing for the fully-connected -spin model
- Counterdiabatic Optimised Local Driving
- Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
- Adiabatic Theorem for Quantum Spin Systems
- Digitized-Counterdiabatic Quantum Algorithm for Protein Folding
- Towards adiabatic quantum computing using compressed quantum circuits
- Energy consumption for Shortcuts To Adiabaticity
- Glassy Phase of Optimal Quantum Control
- Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space
- Does Adiabatic Quantum Optimization Truly Fail for NP-complete problems?
- The adiabatic theorem and linear response theory for extended quantum systems
- Symmetry breaking bias and the dynamics of a quantum phase transition
- Counterdiabatic driving in the quantum annealing of the -spin model: a variational approach
- Experimentally testing quantum critical dynamics beyond the Kibble-Zurek mechanism
- Energetic cost of quantum control protocols
- Quantum annealing: the fastest route to quantum computation?
- Role of Non-stoquastic Catalysts in Quantum Adiabatic Optimization
- Shortcuts to Adiabaticity in Krylov Space
- Counterdiabatic driving of the quantum Ising model
- Digitized-Counterdiabatic Quantum Optimization
- Spectral Gap Amplification
- Observation of generalized Kibble-Zurek mechanism across a first-order quantum phase transition in a spinor condensate
- Two-parameter counter-diabatic driving in quantum annealing
- Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions
- Effect of Local Minima on Adiabatic Quantum Optimization
- How fast and robust is the quantum adiabatic passage?
- Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
- A solvable model of quantum random optimization problems
- Local shortcut to adiabaticity for quantum many-body systems
- Topological defect formation in a phase transition with tunable order
- Application of Pontryagin's Minimum Principle to Grover's Quantum Search Problem
- Elimination of Perturbative Crossings in Adiabatic Quantum Optimization
- Efficient Paths for Local Counterdiabatic Driving
- The Effects of the Problem Hamiltonian Parameters on the Minimum Spectral Gap in Adiabatic Quantum Optimization
- Local Perturbations Perturb -Exponentially- Locally
- Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems
- Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization
- Diabatic Quantum Annealing for the Frustrated Ring Model
- Speedup of the Quantum Adiabatic Algorithm using Delocalization Catalysis
- Noise amplification at spin-glass bottlenecks of quantum annealing: a solvable model
- 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
- Scaling of errors in digitized counterdiabatic driving