Faster than Hermitian Quantum Mechanics

Abstract

Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum brachistochrone problem: Subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi_I> to |psi_F> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.

4 pages

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Cited by in corpus (180)

• Making Sense of Non-Hermitian Hamiltonians
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• Symmetry and Topology in Non-Hermitian Physics
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• Experimental Study of Active LRC Circuits with PT-Symmetries
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Shortcuts to adiabaticity
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum speed limits in open system dynamics
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
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• PT-Symmetric Electronics
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Variational quantum simulation of general processes
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Anomalous helical edge states in a non-Hermitian Chern insulator
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• Parity-time-symmetric topological superconductor
• Local PT symmetry violates the no-signaling principle
• Observation of Fast Evolution in Parity-Time-Symmetric System
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• Nonlocal bright spatial solitons in defocusing Kerr media supported by PT symmetric potentials
• Shortcuts to adiabaticity: fast-forward approach
• Shortcuts to adiabaticity for non-Hermitian systems
• Bypassing the bandwidth theorem with PT symmetry
• Observation of topological transport quantization by dissipation in fast Thouless pumps
• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Exceptional Point Dynamics in Photonic Honeycomb Lattices with PT Symmetry
• Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schrödinger Model
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Projective Hilbert space structures at exceptional points
• Non-Hermitian shortcut to adiabaticity
• Exceptional magnetic sensitivity of PT-symmetric cavity magnon polaritons
• Increase of entanglement by local PT -symmetric operations
• Quasi PT-symmetry in passive photonic lattices
• Conceptual Problems in Scattering from Localized non-Hermitian Potentials
• Observation of $\mathcal{P}\mathcal{T}$-symmetric quantum coherence in a single ion system
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• Topological Properties of a Coupled Spin-Photon System Induced by Damping
• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Non-Hermitian shortcut to stimulated Raman adiabatic passage
• Observation of quantum strong Mpemba effect
• Consistency of PT-symmetric quantum mechanics
• Zermelo Navigation and a Speed Limit to Quantum Information Processing
• Parity-time symmetry in optical microcavity systems
• Demonstration of quantum brachistochrones between distant states of an atom
• Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
• On complexified mechanics and coquaternions
• Time-dependent Hamiltonians with 100% evolution speed efficiency
• Relativistic Non-Hermitian Quantum Mechanics
• Time-dependent V-representability on lattice systems
• Magnon Accumulation in Chirally Coupled Magnets
• Experimental observation of information flow in the anti-$\mathcal{P}\mathcal{T}$-symmetric system
• Enhanced energy transfer in a Dicke quantum battery
• Interactions of Hermitian and non-Hermitian Hamiltonians
• Higher-order exceptional points in all-magnetic structures
• Multi-dimensional band structure spectroscopy in the synthetic frequency dimension
• Chiral coupling of magnons in waveguides
• The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes
• Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system
• Deformed quantum mechanics and q-Hermitian operators
• Simulating broken $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems by weak measurement
• Experimental simulation of the Parity-Time-symmetric dynamics using photonics qubits
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• Interpretation of quantum mechanics with indefinite norm
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• Quantum brachistochrone problem for spin-1 in a magnetic field
• Quantum battery with non-Hermitian charging
• Bragg gap solitons in $\mathcal{P}\mathcal{T}$ symmetric lattices with competing nonlinearity
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• Magnon Trap by Chiral Spin Pumping
• Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
• The quantum brachistochrone problem for non-Hermitian Hamiltonians
• Stable States with Non-Zero Entropy under Broken $\mathcal{P}\mathcal{T}$-Symmetry
• From PT-symmetric quantum mechanics to conformal field theory
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• The quantum brachistochrone problem for an arbitrary spin in a magnetic field
• Non-inertial quantum clock frames lead to non-Hermitian dynamics
• PT-Symmetric Representations of Fermionic Algebras
• Shortcuts to adiabaticity with general two-level non-Hermitian systems
• Lotka-Volterra population dynamics in coherent and tunable oscillators of trapped polariton condensates
• Non-hermitian exciton dynamics in a photosynthetic unit system
• Inverse engineering rigorous adiabatic Hamiltonian for non-Hermitian system
• An algorithm for solving unconstrained unitary quantum brachistochrone problems
• Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points
• Dependence of the Quantum Speed Limit on System Size and Control Complexity
• Embedding, simulation and consistency of $\mathcal{P}\mathcal{T}$ -symmetric quantum Theory
• Scattering cross section resonance originating from a spectral singularity
• Quantum and Classical Statistical Mechanics of a Class of non-Hermitian Hamiltonians
• Localized modes in dissipative lattice media: An overview
• Quantum simulation of a general anti-PT-symmetric Hamiltonian with a trapped ion qubit
• Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians
• Generalised quantum speed limit for arbitrary time-continuous evolution
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions
• Alternative descriptions and bipartite compound quantum systems
• Quantum state discrimination in a PT-symmetric system
• Quantum brachistochrone problem for two spins-1/2 with anisotropic Heisenberg interaction
• The brachistochrone problem in open quantum systems
• Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems
• Geometry of a two-spin quantum state in evolution
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Algebraic maximum violation of the Leggett-Garg inequality in a two-level system under PT symmetric dynamics
• Observables in non-Hermitian systems: A methodological comparison
• Observing a Changing Hilbert-Space Inner Product
• Gauging non-Hermitian Hamiltonians
• Quantum deleting and cloning in a pseudo-unitary system
• Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution
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• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model
• Modulational instability in $\mathcal{P}\mathcal{T}$-symmetric Bragg grating structures with saturable nonlinearity
• Universal quantum control by non-Hermitian Hamiltonian
• Temporal correlation beyond quantum bounds in non-hermitian dynamics
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
• No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models
• Hybridization of topological surface states with a flat band
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Origin of branch points in the spectrum of PT-symmetric periodic potentials
• Quantum Optics of Non-Hermitian Optical Systems: Propagation of Squeezed State of Light through Dispersive non-Hermitian Optical Bilayers
• Non-Hermitian Model for Asymmetrical Tunneling
• Lower bound of minimal time evolution in quantum mechanics
• Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field
• Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor
• Dynamical evolution of an effective two-level system with PT symmetry
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Analogue Hawking radiation as a tunneling in a two-level $\mathcal{P}\mathcal{T}$-symmetric system
• Exceptional points and quantum correlations in precise measurements
• Controlling mobility via rapidly oscillating time-periodic stimulus
• Unconventional steady states and topological phases in an open two-level non-Hermitian system
• Is PT-symmetric quantum mechanics just quantum mechanics in a non-orthogonal basis?
• Passive $\mathcal{P}\mathcal{T}$-symmetric couplers without complex optical potentials
• The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
• Protection of quantum evolutions under parity-time symmetric non-Hermitian Hamiltonians by dynamical decoupling
• Entanglement Efficiencies in PT-Symmetric Quantum Mechanics
• Observation of quantum temporal correlations well beyond Luders bound
• Artificial Hawking radiation, weak pseudo-Hermiticity and Weyl semimetal blackhole analogy
• Quantum eigenvalue processing
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• The stabilizer group of honeycomb lattices and its application to deformed monolayers
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Faster than Hermitian Time Evolution
• $\mathcal{P}\mathcal{T}$-Symmetric Quantum Discrimination of Three States
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation
• Physical Meaning of Hermiticity and Shortcomings of the Composite (Hermitian + non-Hermitian) Quantum Theory of Gunther and Samsonov
• Discrimination between evolution operators
• Protecting coherence in the non-Hermitian two-level system
• Some Remarks on Quantum Brachistochrone
• Does Cosmology require Hermiticity in Quantum Mechanics?
• Quantum linear system algorithm with optimal queries to initial state preparation
• The stability and energy exchange mechanism of divergent states with real energy
• Effect of measurements on quantum speed limit
• Unitarization of Pseudo-Unitary Quantum Circuits in the S-matrix Framework
• Does Gravity Render Probability Quasilocal?
• Constraints on a Generalization of Geometric Quantum Mechanics from Neutrino and $B^0$-$\overline{B^0}$ Oscillations
• Time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Nonlinear speed-ups in ultracold quantum gases
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
• Quantifying non-Hermiticity using single- and many-particle quantum properties
• $\mathcal{P}\mathcal{T}$-Symmetric Quantum State Discrimination for Attack on BB84 Quantum Key Distribution
• Implementation of multiparticle quantum speed limits on observables
• Energy Optimal Interpolation in Quantum Evolution
• Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Evolution operator for time-dependent non-Hermitian Hamiltonians
• A mathematical formalism of non-Hermitian quantum mechanics and observable-geometric phases
• Optimal-speed unitary quantum time evolutions and propagation of light with maximal degree of coherence
• A Geometric Quantum Speed Limit: Theoretical Insights and Photonic Implementation