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Quantum Optimal Control for Pure-State Preparation Using One Initial State

Stefanie Günther, N. Anders Petersson, Jonathan L. DuBois

Abstract

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. We model open system quantum dynamics using the Markovian Lindblad master equation, driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process - independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.

Quantum Optimal Control for Pure-State Preparation Using One Initial State

Abstract

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. We model open system quantum dynamics using the Markovian Lindblad master equation, driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process - independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.

Paper Structure

This paper contains 10 sections, 43 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. One Initial Condition for Pure-State Optimization
  3. Modeling a coupled qudit-cavity system
  4. Numerical Approach
  5. Numerical results
  6. Conclusion
  7. Proof that $B^{kj}$ are linearly independent density matrices in $\mathds{C}^{N\times N}$.
  8. Parameterizing density matrices using $B^{kj}$.
  9. General pure-state preparation.
  10. Driving a qudit-cavity system to the $|10\rangle$ state.

Figures (12)

  • Figure 1: Optimization history for optimal reset of a qudit in a cavity.
  • Figure 2: Optimal qudit reset: Evolution of expected energy level of the qubit (solid lines) and the cavity (dashed lines) for initial qubit states $|0\rangle,|1\rangle,|2\rangle$, the cavity starts in the ground state. Average fidelity at $T=2.5$us: $99.50\%$ (qubit), $99.37\%$ (cavity).
  • Figure 3: Optimized rotating frame control pulses: B-spline envelopes for each carrier wave frequency driving the qubit and the cavity.
  • Figure 4: Fourier spectrum of the optimized control pulses for the qudit (left) and the cavity (right).
  • Figure 5: Optimization history for simultaneous reset of a qubit and a cavity.
  • ...and 7 more figures