Dissipative Quantum Dynamics and Optimal Control using Iterative Time Ordering: An Application to Superconducting Qubits

Abstract

We combine a quantum dynamical propagator that explicitly accounts for quantum mechanical time ordering with optimal control theory. After analyzing its performance with a simple model, we apply it to a superconducting circuit under so-called Pythagorean control. Breakdown of the rotating-wave approximation is the main source of the very strong time-dependence in this example. While the propagator that accounts for the time ordering in an iterative fashion proves its numerical efficiency for the dynamics of the superconducting circuit, its performance when combined with optimal control turns out to be rather sensitive to the strength of the time-dependence. We discuss the kind of quantum gate operations that the superconducting circuit can implement including their performance bounds in terms of fidelity and speed.

arXiv comment16 pages, 11 figures

References in corpus (27)

• Concentrating Partial Entanglement by Local Operations
• Ultimate physical limits to computation
• Training Schrödinger's cat: quantum optimal control
• Building logical qubits in a superconducting quantum computing system
• Optimal Creation of Entanglement Using a Two--Qubit Gate
• A geometric theory of non-local two-qubit operations
• Overhead and noise threshold of fault-tolerant quantum error correction
• Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Optimal control theory for unitary transformations
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Quantum Computation with Vibrationally Excited Molecules
• Controlling open quantum systems: Tools, achievements, and limitations
• Monotonically convergent optimization in quantum control using Krotov's method
• Loading a Bose-Einstein Condensate onto an Optical Lattice: an Application of Optimal Control Theory to The Non Linear Schrödinger Equation
• Exploiting Non-Markovianity of the Environment for Quantum Control
• Controlling the Dynamics of Many-Electron Systems from First Principles: A Marriage of Optimal Control and Time-Dependent Density-Functional Theory
• The Quantum Speed Limit of Optimal Controlled Phasegates for Trapped Neutral Atoms
• Optimizing for an arbitrary perfect entangler: I. Functionals
• Optimizing for an arbitrary perfect entangler. II. Application
• Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems
• Optimal control of strong-field ionization with time-dependent density-functional theory
• A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians
• A Chebychev propagator for inhomogeneous Schrödinger equations
• Quantum optimal control of photoelectron spectra and angular distributions
• New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation
• Laser pulses for coherent xuv Raman excitation

Cited by in corpus (5)

• Krotov Method for Optimal Control in Closed Quantum Systems
• Quantum control of frequency tunable transmon superconducting qubits
• Analyzing the Positivity Preservation of Numerical Methods for the Liouville-von Neumann Equation
• Mitigating controller noise in quantum gates using optimal control theory
• Robustness of controlled Hamiltonian approaches to unitary quantum gates