Speeding up critical system dynamics through optimized evolution

Abstract

The number of defects which are generated on crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is $T\sim \pi /\Delta$, where $\Delta$ is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is non-adiabatic, this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action $s=T\Delta$.

6 pages, 6 figures

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Control of quantum phenomena: Past, present, and future
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Optimal control technique for Many Body Quantum Systems dynamics
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Anderson localization casts clouds over adiabatic quantum optimization
• Geometric derivation of the quantum speed limit
• First order phase transition in the Quantum Adiabatic Algorithm
• Quantum Adiabatic Brachistochrone
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Robust optimal quantum gates for Josephson charge qubits
• Accuracy vs run time in adiabatic quantum search

Cited by in corpus (61)

• Training Schrödinger's cat: quantum optimal control
• Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
• Optimal control of complex atomic quantum systems
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Exploring the Quantum Speed Limit with Computer Games
• An information theoretical analysis of quantum optimal control
• One decade of quantum optimal control in the chopped random basis
• Speeding up and slowing down the relaxation of a qubit by optimal control
• Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
• Optimal control of a qubit in an optical cavity
• Counterdiabatic Optimised Local Driving
• Exploring the trade-off between fidelity- and time-optimal control of quantum unitary transformations
• Demonstration of quantum brachistochrones between distant states of an atom
• Different Strategies for Optimization Using the Quantum Adiabatic Algorithm
• Fast closed-loop optimal control of ultracold atoms in an optical lattice
• High-Speed Driving of a Two-Level System
• Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model
• Optimal Control of Majorana Zero Modes
• Controlling the transport of an ion: Classical and quantum mechanical solutions
• Quantum optimal control of multi-level dissipative quantum systems with Reinforcement Learning
• Optimizing for an arbitrary perfect entangler. II. Application
• Controlling quantum critical dynamics of isolated systems
• Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: preparing a maximally entangled state with singular bang-bang protocols
• How difficult is it to prepare a quantum state?
• Geometric quantum speed limits and short-time accessibility to unitary operations
• Cooling through optimal control of quantum evolution
• Exploring adiabatic quantum trajectories via optimal control
• On the complexity of controlling quantum many-body dynamics
• Optimal control of Rydberg lattice gases
• Noise-resistant optimal spin squeezing via quantum control
• Searching for quantum optimal controls under severe constraints
• Optimal suppression of defect generation during a passage across a quantum critical point
• Optimal preparation of quantum states on an atom chip device
• Suppressing defect production during passage through a quantum critical point
• Local shortcut to adiabaticity for quantum many-body systems
• A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator
• Measurement-based cooling of a nonlinear mechanical resonator
• Robust population inversion in three-level systems by composite pulses
• Approximate Dynamics Lead to More Optimal Control: Efficient Exact Derivatives
• Many-body excitations and de-excitations in trapped ultracold bosonic clouds
• Time limited optimal dynamics beyond the Quantum Speed Limit
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Macroscopic Hyperpolarization Enhanced with Quantum Optimal Control
• Optimal amplification of the dynamical Casimir effect in a parametrically driven system
• On the time optimal thermalization of single mode Gaussian states
• Ultrafast critical ground state preparation via bang-bang protocols
• Analysis of lower bounds for quantum control times and their relation to the quantum speed limit
• Non universality of entanglement convertibility
• Symmetry-Protected Quantum Adiabatic Evolution in Spontaneous Symmetry-Breaking Transitions
• Quantum dynamics with an ensemble of Hamiltonians
• Quantum mechanics and speed limit of ultrafast local control in spin chains
• Quantum circuit compilation with quantum computers
• Minimal action control method in quantum critical models
• Creating fractional quantum Hall states with atomic clusters using light-assisted insertion of angular momentum
• Optimal protocols for finite-duration quantum quenches in the Luttinger model
• Adiabatic preparation of a number-conserving atomic Majorana phase
• Time evolution of controlled many-body quantum systems with matrix product operators
• Many-body quantum dimerization in 2D atomic arrays
• Improving adiabatic quantum factorization via chopped random-basis optimization