Approaching the Quantum Speed Limit in Quantum Gates with Geometric Control

Abstract

We present a geometric optimization method for implementing quantum gates by optimally controlling the Hamiltonian parameters, with the goal of approaching the Mandelstam-Tamm Quantum Speed Limit (MT-QSL). Achieving this bound requires satisfying precise geometric conditions that govern the evolution of quantum states. We extend this geometric framework to quantum unitary operators in arbitrary dimensions and analyze the conditions necessary for saturation of the bound. Additionally, we show that the quantum brachistochrone, when generalized to operators, does not, in general, saturate the MT-QSL bound. Finally, we propose a systematic optimal control strategy based on geometric principles to approach the quantum speed limit for unitary driving. We illustrate this optimization method on a set of four well-known two-qubit quantum gates. Our procedure significantly reduces the deviation from the optimal quantum speed limit while preserving high quantum fidelity.

References in corpus (33)

• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Chopped random-basis quantum optimization
• Quantum limits to dynamical evolution
• Quantum Brachistochrone
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Generalized Geometric Quantum Speed Limits
• Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Quantum Speed Limit is Not Quantum
• Tightening Quantum Speed Limits for Almost All States
• Time-information uncertainty relations in thermodynamics
• Time Optimal Unitary Operations
• Superadiabatic Controlled Evolutions and Universal Quantum Computation
• Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
• Unifying Quantum and Classical Speed Limits on Observables
• Speed limits for quantum gates in multi-qubit systems
• Kind of entanglement that speeds up quantum evolution
• On the Connection Between Entanglement and the Speed of Quantum Evolution
• Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed
• Quantum Speed Limit for States with a Bounded Energy Spectrum
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Quantum state control of a Bose-Einstein condensate in an optical lattice
• Quantum speed limits on operator flows and correlation functions
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Bounding generalized relative entropies: Nonasymptotic quantum speed limits
• Quantum coherence and speed limit in the mean-field Dicke model of superradiance
• Experimental Investigation of Geometric Quantum Speed Limits in an Open Quantum System
• Shortcut to synchronization in classical and quantum systems
• Quantum Speed Limit in Terms of Coherence Variations
• Quantum Speed Limit under Brachistochrone Evolution
• Quantum Speed Limit for Change of Basis