Broken symmetry in a two-qubit quantum control landscape

Abstract

We analyze the physics of optimal protocols to prepare a target state with high fidelity in a symmetrically coupled two-qubit system. By varying the protocol duration, we find a discontinuous phase transition, which is characterized by a spontaneous breaking of a ${\mathbb{Z}}_2$ symmetry in the functional form of the optimal protocol, and occurs below the quantum speed limit. We study in detail this phase and demonstrate that even though high-fidelity protocols come degenerate with respect to their fidelity, they lead to final states of different entanglement entropy shared between the qubits. Consequently, while globally both optimal protocols are equally far away from the target state, one is locally closer than the other. An approximate variational mean-field theory which captures the physics of the different phases is developed.

References in corpus (9)

• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Fast population transfer engineering of three-level systems
• Fidelity-based Probabilistic Q-learning for Control of Quantum Systems
• Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
• Shortcut to adiabatic population transfer in quantum three-level systems: effective two-level problems and feasible counter-diabatic driving
• Shortcuts to adiabaticity using flow fields
• Fast forward to the classical adiabatic invariant
• Superadiabatic driving of a three-level quantum system
• Theory of quantum control landscapes: Overlooked hidden cracks

Cited by in corpus (20)

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• Quantum Optimal Control in a Chopped Basis: Applications in Control of Bose-Einstein Condensates
• Reinforcement learning for autonomous preparation of Floquet-engineered states: Inverting the quantum Kapitza oscillator
• Glassy Phase of Optimal Quantum Control
• Policy Gradient based Quantum Approximate Optimization Algorithm
• Quantum imaginary time evolution steered by reinforcement learning
• Quantifying the efficiency of state preparation via quantum variational eigensolvers
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach
• Toward a Theory of Phase Transitions in Quantum Control Landscapes
• Phenomenon of a stronger trapping behaviour in $\Lambda$-type quantum systems with symmetry
• Time-Optimal Quantum Driving by Variational Circuit Learning
• Quantum circuit compilation with quantum computers
• Topological Phase Transitions in a Constrained Two-Qubit Quantum Control Landscape
• Swinging small quantum systems out of available values of control parameters
• Optimal Work Extraction from Finite-Time Closed Quantum Dynamics
• Diverse efficiency of observable optimization for four-level quantum systems with higher-order traps