Tight lower bounds on the time it takes to generate a geometric phase
- URL: http://arxiv.org/abs/2305.12156v3
- Date: Fri, 15 Dec 2023 15:33:19 GMT
- Title: Tight lower bounds on the time it takes to generate a geometric phase
- Authors: Niklas H\"ornedal and Ole S\"onnerborn
- Abstract summary: We show that the evolution time of a cyclically evolving quantum system is restricted by the system's energy resources and the geometric phase acquired by the state.
We derive and examine three tight lower bounds on the time required to generate any prescribed Aharonov-Anandan geometric phase.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Geometric phase is a concept of central importance in virtually every branch
of physics. In this paper, we show that the evolution time of a cyclically
evolving quantum system is restricted by the system's energy resources and the
geometric phase acquired by the state. Specifically, we derive and examine
three tight lower bounds on the time required to generate any prescribed
Aharonov-Anandan geometric phase. The derivations are based on recent results
on the geometric character of the Mandelstam-Tamm and Margolus-Levitin quantum
speed limits.
Related papers
- Action formalism for geometric phases from self-closing quantum
trajectories [55.2480439325792]
We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system.
We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
arXiv Detail & Related papers (2023-12-22T15:20:02Z) - Geometric Phases in Open Quantum Systems: Analysis and Applications [0.0]
This thesis explores the relation between decoherence and environmentally-induced dissipative effects.
The first mention of such an object in the context of quantum mechanics goes back to the seminal work by Berry.
arXiv Detail & Related papers (2023-07-07T20:39:24Z) - Curves in quantum state space, geometric phases, and the brachistophase [0.0]
Given a curve in quantum spin state space, we inquire what is the relation between its geometry and the geometric phase accumulated along it.
We find a general expression for the derivatives of the geometric phase in terms of the covariant derivatives of the curve.
For example, the optimal evolution of a spin coherent state consists of a single Majorana star separating from the rest and tracing out a circle on the Majorana sphere.
arXiv Detail & Related papers (2023-02-13T21:45:15Z) - Geometric phases along quantum trajectories [58.720142291102135]
We study the distribution function of geometric phases in monitored quantum systems.
For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle.
For the same parameters, the density matrix does not show any interference.
arXiv Detail & Related papers (2023-01-10T22:05:18Z) - Topological transitions of the generalized Pancharatnam-Berry phase [55.41644538483948]
We show that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit.
We demonstrate and study this transition experimentally employing an optical platform.
Our protocol can be interpreted in terms of environment-induced geometric phases.
arXiv Detail & Related papers (2022-11-15T21:31:29Z) - Geometric phase and its applications: topological phases, quantum walks
and non-inertial quantum systems [0.0]
We have proposed a fresh perspective of geodesics and null phase curves, which are key ingredients in understanding the geometric phase.
We have also looked at a number of applications of geometric phases in topological phases, quantum walks, and non-inertial quantum systems.
arXiv Detail & Related papers (2022-09-11T08:01:17Z) - Genuine Multipartite Correlations in a Boundary Time Crystal [56.967919268256786]
We study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC)
We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state.
arXiv Detail & Related papers (2021-12-21T20:25:02Z) - Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware.
We present an algorithm that compresses the Trotter steps into a single block of quantum gates.
This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z) - Observing a Topological Transition in Weak-Measurement-Induced Geometric
Phases [55.41644538483948]
Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control.
We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength.
Our results open new horizons for measurement-enabled quantum control of many-body topological states.
arXiv Detail & Related papers (2021-02-10T19:00:00Z) - Dynamical decoupling of a geometric qubit [0.0]
Quantum bits or qubits naturally decohere by becoming entangled with uncontrollable environments.
Dynamical decoupling is required to disentangle qubits from an environment by periodically reversing the qubit bases.
We show that simply by introducing detuning, the dynamical decoupling of a geometric qubit can be made to spontaneously suppress error accumulation.
arXiv Detail & Related papers (2020-02-24T23:59:29Z) - Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond [0.0]
Though traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized.
This Review introduces the Aharonov-Bohm effect as an important realization of the geometric phase.
We discuss in detail the broader meaning, consequences and realizations of the geometric phase.
arXiv Detail & Related papers (2019-12-29T07:02:50Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.