Dependence of the Quantum Speed Limit on System Size and Control Complexity

Abstract

We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields. This bound is explicitly analyzed for a specific N-level system similar to those used to represent simple models of an atom, or the first excitation sector of a Heisenberg spin chain, both of which are of interest in quantum control for quantum computation. Specifically, it is shown that the resultant bound depends on the dimension of the system, and on the number of controls used to implement a specific target unitary operation. The value of the bound determined numerically, and an estimate of the true minimum gate time are systematically compared for a range of system dimension and number of controls; special attention is drawn to the relationship between these two variables. It is seen that the bound captures the scaling of the minimum time well for the systems studied, and quantitatively is correct in the order of magnitude.

References in corpus (39)

• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Control of quantum phenomena: Past, present, and future
• The maximum speed of dynamical evolution
• Training Schrödinger's cat: quantum optimal control
• Time Optimal Control in Spin Systems
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum Computation as Geometry
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Faster than Hermitian Quantum Mechanics
• Quantum Brachistochrone
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
• Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
• Driving at the quantum speed limit: Optimal control of a two-level system
• General optimality of the Heisenberg limit for quantum metrology
• Energy-time uncertainty relation for driven quantum systems
• Geometric derivation of the quantum speed limit
• Quantum speed limit for arbitrary initial states
• Time Optimal Unitary Operations
• Scalable quantum computation via local control of only two qubits
• Speed limits for quantum gates in multi-qubit systems
• Robust quantum gates for systems subject to decoherence via optimal control: Markovian vs non-Markovian dynamics
• Geometric quantum speed limits: a case for Wigner phase space
• Comment on "Geometric derivation of the quantum speed limit"
• Zermelo Navigation and a Speed Limit to Quantum Information Processing
• Quantum Speed Limit and optimal evolution time in a two-level system
• Driven quantum dynamics: will it blend?
• Distance Bounds on Quantum Dynamics
• Quantum speed limits and optimal Hamiltonians for driven systems in mixed states
• Zermelo Navigation in the Quantum Brachistochrone
• Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control
• Quantum Speed Limits for Quantum Information Processing Tasks
• Control of open quantum systems: Case study of the central spin model
• Global controllability with a single local actuator
• The roles of drift and control field constraints upon quantum control speed limits
• Controlling qubit networks in polynomial time
• Efficiently Controllable Graphs
• Quantum Speed Limit With Forbidden Speed Intervals

Cited by in corpus (15)

• From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms
• Tight, robust, and feasible quantum speed limits for open dynamics
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• Controlling decoherence speed limit of a single impurity atom in a Bose-Einstein-condensate reservoir
• Optimal Control in Disordered Quantum Systems
• Conservation-law-based global bounds to quantum optimal control
• Quantum Distance to Uncontrollability and Quantum Speed Limits
• Purity Speed Limit of Open Quantum Systems from Magic Subspaces
• Parameterized Hamiltonian simulation using quantum optimal control
• Generation of photonic tensor network states with Circuit QED
• Minimal Time Robust Control for Two Superconducting Qubits
• Exact and lower bounds for the quantum speed limit in finite dimensional systems
• Tighter Lower Bounds on Quantum Annealing Times
• Quantum Speed Limits from Symmetries in Quantum Control
• Trajectory-independent speed limits for controlled open quantum systems