Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

数理解析研究所講究録

Time Optimal Quantum Evolution Within a Given Fidelity Range (Non-Commutative Analysis and Micro-Macro Duality)

A. Carlini, Akio Hosoya, Tatsuhiko Koike, Yosuke Okudaira

Published Jul 1, 2008• 0 citations
OpenAlex

Abstract

In a series of previous works we formulated a variational principle to find out the time-optimal evolution for a quantum system with a given set of initial and final states.Here we show how to obtain the shortest duration time T(f) to reach the target state via quantum operations within a given fidelity larger than a specified value f $\leq$ 1.

Related papers

Time-Optimal Quantum Evolution

A. Carlini, Akio Hosoya, Tatsuhiko Koike +1 more

We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to that for the brachistochrone in classical mechanics. We reduce the problem to a formal equation for the Hamiltonian which depends on certain constraint functions specifying the range of available Hamiltonians. For some simple examples of the constraints, we explicitly find the optimal solutions.

arXiv:quant-ph/0511039•Physical Review Letters•Feb 15, 2006•311 citations

Time Optimal Quantum Operartion for Mixed States(Micro-Macro Duality in Quantum Analysis)

A. Carlini, Akio Hosoya, Tatsuhiko Koike +1 more

We formulate a variational principle for finding the time.optimalquantum evolution of mixed states subject to a master equation, when the Hamiltonian $H$ and the Lindblad operators $L_{f}$ are subject to certain constraints.We show that the problem can be reduced to solving first a fun- damental equation (the "quanbum brachistochrone") for $H(t)$ , which can be written down once the $\infty nstraints$ are specified, and then solving the constraints and the master equation for the $L_{f}(t)s$ and the density operator $\rho(t)$ .As an application of our fomalism, we $an\Phi ticM$ solve a simple one $qu$ , bit model where the optimal Lindblad operators correspond either to a measurement or to a decoherence process by the environment.

•Jul 1, 2007•0 citations

Time-optimal unitary operations

A. Carlini, Akio Hosoya, Tatsuhiko Koike +1 more

Extending our previous work on time-optimal quantum state evolution [Carlini et al., Phys. Rev. Lett. 96, 060503 (2006)], we formulate a variational principle for finding the time-optimal realization of a target unitary operation, when the available Hamiltonians are subject to certain constraints dictated either by experimental or by theoretical conditions. Since the time-optimal unitary evolutions do not depend on the input quantum state this is of more direct relevance to quantum computation. We explicitly illustrate our method by considering the case of a two-qubit system self-interacting via an anisotropic Heisenberg Hamiltonian and by deriving the time-optimal unitary evolution for three examples of target quantum gates, namely, the swap of qubits, the quantum Fourier transform, and the entangler gate. We also briefly discuss the case in which certain unitary operations take negligible time.

arXiv:quant-ph/0608039•Physical Review A•Apr 10, 2007•126 citations

Mathematical Theory of Time Operators in Quantum Physics (Non-Commutative Analysis and Micro-Macro Duality)

Asao Arai

•Jul 1, 2008•0 citations

A Covariant Optimal Quantum Clock (Non-Commutative Analysis and Micro-Macro Duality)

暁夫 細谷

数理解析研究所講究録•Jul 1, 2009•0 citations

Time-optimal control based on path distance

Lin-Feng Du, Li‐Guo Qin, Qin Guo +2 more

The average energy and energy spread of a quantum system are two important factors that affect a system's evolution speed, which is usually defined as the changing rate of the distance between a quantum state and the state during its evolution. Alternatively, the evolution speed of a quantum system could also be studied based on its evolution path. It is found that if we define the evolution speed of a quantum unitary system as the changing rate of the path distance between a quantum state and the state during its evolution, the instantaneous evolution speed is determined by the Hamiltonian's eigenvalues, rather than its expectation value or variance imposed on any quantum state. More specifically, the range of the Hamiltonian's eigenvalues determines the evolution speed of a quantum system through the relation ${\ensuremath{\omega}}_{H}=\frac{1}{2}({\ensuremath{\lambda}}_{max}\ensuremath{-}{\ensuremath{\lambda}}_{min})$, which is independent of the quantum state. Given an initial state ${\ensuremath{\rho}}_{0}$ in a quantum unitary system, the minimum time required to evolve it to a target state ${\ensuremath{\rho}}_{\ensuremath{\tau}}$ is ${\ensuremath{\tau}}_{min}=\frac{{\mathcal{L}}_{min}({\ensuremath{\rho}}_{0},{\ensuremath{\rho}}_{\ensuremath{\tau}})}{{\ensuremath{\omega}}_{H}}$, where ${\mathcal{L}}_{min}({\ensuremath{\rho}}_{0},{\ensuremath{\rho}}_{\ensuremath{\tau}})$ is the path distance contained in the shortest evolution from ${\ensuremath{\rho}}_{0}$ to ${\ensuremath{\rho}}_{\ensuremath{\tau}}$. This lower bound of the evolution time is tight and achievable in a finite-energy system.

Physical Review A•Aug 13, 2025•0 citations
In a series of previous works we formulated a variational principle to find out the time-optimal evolution for a quantum system with a given set of initial and final states.Here we show how to obtain the shortest duration time T(f) to reach the target state via quantum operations within a given fidelity larger than a specified value f ≤\leq≤ 1.
We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to that for the brachistochrone in classical mechanics. We reduce the problem to a formal equation for the Hamiltonian which depends on certain constraint functions specifying the range of available Hamiltonians. For some simple examples of the constraints, we explicitly find the optimal solutions.
We formulate a variational principle for finding the time.optimalquantum evolution of mixed states subject to a master equation, when the Hamiltonian HHH and the Lindblad operators LfL_{f}Lf​ are subject to certain constraints.We show that the problem can be reduced to solving first a fun- damental equation (the "quanbum brachistochrone") for H(t)H(t)H(t) , which can be written down once the ∞nstraints\infty nstraints∞nstraints are specified, and then solving the constraints and the master equation for the Lf(t)sL_{f}(t)sLf​(t)s and the density operator ρ(t)\rho(t)ρ(t) .As an application of our fomalism, we anΦticMan\Phi ticManΦticM solve a simple one quququ , bit model where the optimal Lindblad operators correspond either to a measurement or to a decoherence process by the environment.
Extending our previous work on time-optimal quantum state evolution [Carlini et al., Phys. Rev. Lett. 96, 060503 (2006)], we formulate a variational principle for finding the time-optimal realization of a target unitary operation, when the available Hamiltonians are subject to certain constraints dictated either by experimental or by theoretical conditions. Since the time-optimal unitary evolutions do not depend on the input quantum state this is of more direct relevance to quantum computation. We explicitly illustrate our method by considering the case of a two-qubit system self-interacting via an anisotropic Heisenberg Hamiltonian and by deriving the time-optimal unitary evolution for three examples of target quantum gates, namely, the swap of qubits, the quantum Fourier transform, and the entangler gate. We also briefly discuss the case in which certain unitary operations take negligible time.
The average energy and energy spread of a quantum system are two important factors that affect a system's evolution speed, which is usually defined as the changing rate of the distance between a quantum state and the state during its evolution. Alternatively, the evolution speed of a quantum system could also be studied based on its evolution path. It is found that if we define the evolution speed of a quantum unitary system as the changing rate of the path distance between a quantum state and the state during its evolution, the instantaneous evolution speed is determined by the Hamiltonian's eigenvalues, rather than its expectation value or variance imposed on any quantum state. More specifically, the range of the Hamiltonian's eigenvalues determines the evolution speed of a quantum system through the relation ${\ensuremath{\omega}}_{H}=\frac{1}{2}({\ensuremath{\lambda}}_{max}\ensuremath{-}{\ensuremath{\lambda}}_{min})$, which is independent of the quantum state. Given an initial state ${\ensuremath{\rho}}_{0}$ in a quantum unitary system, the minimum time required to evolve it to a target state ${\ensuremath{\rho}}_{\ensuremath{\tau}}$ is ${\ensuremath{\tau}}_{min}=\frac{{\mathcal{L}}_{min}({\ensuremath{\rho}}_{0},{\ensuremath{\rho}}_{\ensuremath{\tau}})}{{\ensuremath{\omega}}_{H}}$, where ${\mathcal{L}}_{min}({\ensuremath{\rho}}_{0},{\ensuremath{\rho}}_{\ensuremath{\tau}})$ is the path distance contained in the shortest evolution from ${\ensuremath{\rho}}_{0}$ to ${\ensuremath{\rho}}_{\ensuremath{\tau}}$. This lower bound of the evolution time is tight and achievable in a finite-energy system.