Minimum time for the evolution to a nonorthogonal quantum state and upper bound of the geometric efficiency of quantum evolutions

• URL: http://arxiv.org/abs/2106.09378v2
• Date: Mon, 16 Aug 2021 08:43:06 GMT
• Title: Minimum time for the evolution to a nonorthogonal quantum state and upper bound of the geometric efficiency of quantum evolutions
• Authors: Carlo Cafaro, Paul M. Alsing
• Abstract summary: We present a proof of the minimum time for the quantum evolution between two arbitrary states. We discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a simple proof of the minimum time for the quantum evolution between two arbitrary states. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the efficiency inequality even when the system passes only through nonorthogonal quantum states.

Related papers

• Non-adiabatic holonomies as photonic quantum gates [36.136619420474766]
  We present the quantum-optical realization of non-adiabatic holonomies that can be used as single-qubit quantum gates. The inherent non-adiabaticity of the structures paves the way for unprecedented miniaturization.
  arXiv  Detail & Related papers  (2024-01-08T16:44:45Z)
• Upper limit on the acceleration of a quantum evolution in projective Hilbert space [0.0]
  We derive an upper bound for the rate of change of the speed of transportation in an arbitrary finite-dimensional projective Hilbert space. We show that the acceleration squared of a quantum evolution in projective space is upper bounded by the variance of the temporal rate of change of the Hamiltonian operator.
  arXiv  Detail & Related papers  (2023-11-30T11:22:59Z)
• Uniqueness of quantum state over time function [0.0]
  A fundamental asymmetry exists within the conventional framework of quantum theory between space and time. A new framework has recently been proposed, such that description of a quantum system can be encapsulated by a static quantum state over time. We show that the previously proposed axioms cannot yield a unique state over time function.
  arXiv  Detail & Related papers  (2023-08-24T12:57:06Z)
• Quantum Speed Limit for Change of Basis [55.500409696028626]
  We extend the notion of quantum speed limits to collections of quantum states. For two-qubit systems, we show that the fastest transformation implements two Hadamards and a swap of the qubits simultaneously. For qutrit systems the evolution time depends on the particular type of the unbiased basis.
  arXiv  Detail & Related papers  (2022-12-23T14:10:13Z)
• Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions [0.0]
  We present an explicit geodesic analysis of the trajectories that emerge from the quantum evolution of a single-qubit quantum state. In addition to viewing geodesics in ray space as paths of minimal length, we also verify the geodesicity of paths in terms of unit geometric efficiency and vanishing geometric phase.
  arXiv  Detail & Related papers  (2022-10-17T14:44:03Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Symmetries of quantum evolutions [0.5735035463793007]
  Wigner's theorem establishes that every symmetry of quantum state space must be either a unitary transformation, or an antiunitary transformation. We show that it is impossible to extend the time reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time symmetric formulation of quantum theory must either restrict the set of the allowed evolutions, or modify the operational interpretation of quantum states and processes.
  arXiv  Detail & Related papers  (2021-01-13T09:47:32Z)
• Quantum speed limits for time evolution of a system subspace [77.34726150561087]
  In the present work, we are concerned not with a single state but with a whole (possibly infinite-dimensional) subspace of the system states that are subject to the Schroedinger evolution. We derive an optimal estimate on the speed of such a subspace evolution that may be viewed as a natural generalization of the Fleming bound.
  arXiv  Detail & Related papers  (2020-11-05T12:13:18Z)
• Geometric aspects of analog quantum search evolutions [0.0]
  We show that the Farhi-Gutmann time optimal analog quantum search evolution is characterized by unit efficiency dynamical trajectories traced on a projective Hilbert space. We briefly discuss possible extensions of our work to the geometric analysis of the efficiency of thermal trajectories of relevance in quantum computing tasks.
  arXiv  Detail & Related papers  (2020-08-18T00:10:38Z)
• Quantum time dilation: A new test of relativistic quantum theory [91.3755431537592]
  A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially offering a new test of relativistic quantum theory.
  arXiv  Detail & Related papers  (2020-04-22T19:26:53Z)

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.