Geometric Speed Limit of Accessible Many-Body State Preparation
arXiv:1804.05399 · doi:10.1103/PhysRevX.9.011034
Abstract
We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model.
References in corpus (54)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- The maximum speed of dynamical evolution
- Observation of entanglement propagation in a quantum many-body system
- Training Schrödinger's cat: quantum optimal control
- Time Optimal Control in Spin Systems
- Shortcuts to adiabaticity
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Shortcuts to adiabaticity by counter-diabatic driving
- Enhancing the charging power of quantum batteries
- Quantum speed limit for physical processes
- Quantum speed limits in open system dynamics
- High-fidelity quantum driving
- Digitized adiabatic quantum computing with a superconducting circuit
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
- Onset of a Quantum Phase Transition with a Trapped Ion Quantum Simulator
- Chopped random-basis quantum optimization
- Geometry and non-adiabatic response in quantum and classical systems
- Quantum Brachistochrone
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Reinforcement Learning in Different Phases of Quantum Control
- Classical and quantum shortcuts to adiabaticity for scale-invariant driving
- Minimizing irreversible losses in quantum systems by local counter-diabatic driving
- Speeding up adiabatic quantum state transfer by using dressed states
- Generalized Geometric Quantum Speed Limits
- Fast population transfer engineering of three-level systems
- Driving at the quantum speed limit: Optimal control of a two-level system
- Reinforcement Learning with Neural Networks for Quantum Feedback
- Fast machine-learning online optimization of ultra-cold-atom experiments
- Geometric derivation of the quantum speed limit
- Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
- Classifying and measuring the geometry of the quantum ground state manifold
- Generating shortcuts to adiabaticity in quantum and classical dynamics
- Fidelity-based Probabilistic Q-learning for Control of Quantum Systems
- Tightening Quantum Speed Limits for Almost All States
- Optimal non-linear passage through a quantum critical point
- Optimal control of complex atomic quantum systems
- Sampling-based learning control of inhomogeneous quantum ensembles
- Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
- Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
- An information theoretical analysis of quantum optimal control
- Shortcut to adiabatic population transfer in quantum three-level systems: effective two-level problems and feasible counter-diabatic driving
- Three-level superadiabatic quantum driving
- Automatic spin-chain learning to explore the quantum speed limit
- Reinforcement learning for autonomous preparation of Floquet-engineered states: Inverting the quantum Kapitza oscillator
- Glassy Phase of Optimal Quantum Control
- Measurement-based adaptation protocol with quantum reinforcement learning
- Fast forward to the classical adiabatic invariant
- Neural-network-designed pulse sequences for robust control of singlet-triplet qubits
- Fast preparation of critical ground states using superluminal fronts
- Microscopic theory of non-adiabatic response in real and imaginary time
- Maximizing entanglement in bosonic Josephson junctions using shortcuts to adiabaticity and optimal control
- Broken symmetry in a two-qubit quantum control landscape
- Thermodynamic Cost for Classical Counterdiabatic Driving
- Superadiabatic driving of a three-level quantum system
Cited by in corpus (74)
- Shortcuts to adiabaticity: concepts, methods, and applications
- Quantum Natural Gradient
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
- Floquet-engineering counterdiabatic protocols in quantum many-body systems
- Excited-state quantum phase transitions
- An efficient quantum algorithm for the time evolution of parameterized circuits
- Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
- Unifying Quantum and Classical Speed Limits on Observables
- Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving
- Demonstration of quantum brachistochrones between distant states of an atom
- Quantum Speed Limit for States with a Bounded Energy Spectrum
- Probing Quantum Speed Limits with Ultracold Gases
- Energetic cost of quantum control protocols
- Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
- Swift heat transfer by fast-forward driving in open quantum systems
- Speed Limits for Macroscopic Transitions
- Rapid counter-diabatic sweeps in lattice gauge adiabatic quantum computing
- Quantum speed limits on operator flows and correlation functions
- Operational definition of a quantum speed limit
- Shortcuts to Adiabatic Pumping in Classical Stochastic Systems
- Topological Speed Limit
- Performance Evaluation of Adiabatic Quantum Computation via Quantum Speed Limits and Possible Applications to Many-Body Systems
- Floquet-engineered quantum state manipulation in a noisy qubit
- Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
- Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
- Effective calculation of the Green's function in the time domain on near-term quantum processors
- Extensions of the Mandelstam-Tamm quantum speed limit to systems in mixed states
- Effects of coherence on quantum speed limits and shortcuts to adiabaticity in many-particle systems
- Accelerating adiabatic protocols for entangling two qubits in circuit QED
- Time-optimal control of a dissipative qubit
- Shortcuts to Dynamic Polarization
- Quantum speed limit for thermal states
- Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics
- Persistent dark states in anisotropic central spin models
- Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
- Counterdiabatic control of transport in a synthetic tight-binding lattice
- Exact universal bounds on quantum dynamics and fast scrambling
- Tight and attainable quantum speed limit for open systems
- Bhatia-Davis formula in the quantum speed limit
- Universal shot-noise limit for quantum metrology with local Hamiltonians
- Integrability as an attractor of adiabatic flows
- Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
- Unified entropies and quantum speed limits for nonunitary dynamics
- Quantum Speed Limit under Brachistochrone Evolution
- Quantum lower and upper speed limits
- Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
- Toward a Theory of Phase Transitions in Quantum Control Landscapes
- Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
- Analyticity constraints bound the decay of the spectral form factor
- The Loschmidt Index
- Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
- Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
- Universal Counterdiabatic Driving
- Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
- High fidelity control of a many-body Tonks--Girardeau gas with an effective mean-field approach
- A new route toward orthogonality
- Initial-state-dependent quantum speed limit for dissipative state preparation: Framework and optimization
- Relaxation Control of Open Quantum Systems
- Quantum speed limit for the maximum coherent state under squeezed environment
- Search for optimal driving in finite quantum systems with precursors of criticality
- Family of attainable geometric quantum speed limits
- Quantum geometry in many-body systems with precursors of criticality
- Decoherence-assisted quantum driving
- Generalized Entropic Quantum Speed Limits
- Topological Phase Transitions in a Constrained Two-Qubit Quantum Control Landscape
- Quantum Speed Limits Based on the Sharma-Mittal Entropy
- Machine-learning-inspired quantum control in many-body dynamics
- Analytic approach to the Landau-Zener problem in bounded parameter space
- Affinity-based geometric discord and quantum speed limits of its creation and decay
- Time-dependent Hamiltonians and Geometry of Operators Generated by Them
- Quantum speed limits for an open system in contact with a thermal bath
- Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace
- Geometric speed limit of state preparation and curved control spaces
- Thermodynamic speed limit for non-adiabatic work and its classical-quantum decomposition