Harnessing subspace controllability: Dynamical generation of Dicke states in Heisenberg-coupled qubit arrays with a single local control

Abstract

We explore the feasibility of realizing Dicke states in qubit arrays with always-on isotropic Heisenberg coupling between adjacent qubits, assuming a single Zeeman-type control acting in the $z$ direction on an actuator qubit. The Lie-algebraic criteria of controllability imply that such an array is not completely controllable, but satisfies the conditions for subspace controllability on any subspace with a fixed number of excitations. Therefore, a qubit array described by the model under consideration is state-to-state controllable for an arbitrary choice of initial and final states that have the same Hamming weight. This limited controllability is exploited here for the time-efficient dynamical generation of an $a$-excitation Dicke state $|D_a^N⟩$ ($a=1,2,\dots ,N-1$) in a linear array with $N$ qubits starting from a generic Hamming-weight-$a$ product state. To dynamically generate the desired Dicke states -- including $W$ states $|W_N⟩$ as their special ($a=1$) case -- in the shortest possible time with a single local $Z$ control, we employ an optimal-control scheme based on the {\em dressed chopped random basis} (dCRAB) algorithm. We optimize the target-state fidelity over the expansion coefficients of smoothly-varying control fields in a truncated random Fourier basis; this is done by combining Nelder-Mead-type local optimizations with the multistart-based clustering algorithm that facilitates searches for global extrema. In this manner, we obtain the optimal control fields for Dicke-state preparation in arrays with up to $9$ qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as $\mathcal{O}(N^{2.08})$ for $W$ states and $\mathcal{O}(N^{1.78})$ for $a=2$ Dicke states.

final, published version

References in corpus (65)

• Quantum Computing in the NISQ era and beyond
• Universal Quantum Computation with the Exchange Interaction
• Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
• Electrically driven single electron spin resonance in a slanting Zeeman field
• Qubit architecture with high coherence and fast tunable coupling
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Multipartite entanglement and high precision metrology
• Optimal Control at the Quantum Speed Limit
• Universal quantum computation with spin-1/2 pairs and Heisenberg exchange
• Chopped random-basis quantum optimization
• Silicon CMOS architecture for a spin-based quantum computer
• Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
• Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
• Experimental entanglement of a six-photon symmetric Dicke state
• Quantum Computing with an 'Always On' Heisenberg Interaction
• Detection of multipartite entanglement in the vicinity of symmetric Dicke states
• Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape
• Krotov: A Python implementation of Krotov's method for quantum optimal control
• One decade of quantum optimal control in the chopped random basis
• Simulations of Information Transport in Spin Chains
• Permutation-invariant quantum codes
• Entanglement criteria for Dicke states
• Quantum-state transfer via resonant tunnelling through local field induced barriers
• Preparation of Dicke States in an Ion Chain
• A necessary and sufficient condition to play games in quantum mechanical settings
• Local quantum control of Heisenberg spin chains
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Quantum optimal control via gradient ascent in function space and the time-bandwidth quantum speed limit
• 12-spin-qubit arrays fabricated on a 300 mm semiconductor manufacturing line
• Quantum-control approach to realizing a Toffoli gate in circuit QED
• The SMART protocol -- Pulse engineering of a global field for robust and universal quantum computation
• Generation of long-lived $W$ states via reservoir engineering in dissipatively coupled systems
• Symmetries on Spin Chains: Limited Controllability and Minimal Controls for Full Controllability
• Global controllability with a single local actuator
• Quantum-entanglement aspects of polaron systems
• Entanglement robustness against particle loss in multiqubit systems
• Bare-Excitation Ground State of a Spinless-Fermion -- Boson Model and $W$-State Engineering in an Array of Superconducting Qubits and Resonators
• Scalable $W$-type entanglement resource in neutral-atom arrays with Rydberg-dressed resonant dipole-dipole interaction
• Conversion from $W$ to Greenberger-Horne-Zeilinger states in the Rydberg-blockade regime of neutral-atom systems: Dynamical-symmetry-based approach
• Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit
• Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles
• Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models
• Deterministic generation of arbitrary symmetric states and entanglement classes
• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Fast charging of an Ising spin pair quantum battery using optimal control
• Universal gates for transforming multipartite entangled Dicke states
• Dynamical generation of chiral $W$ and Greenberger-Horne-Zeilinger states in laser-controlled Rydberg-atom trimers
• Quantum dynamics of the small-polaron formation in a superconducting analog simulator
• Quantum-brachistochrone approach to the conversion from $W$ to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits
• Controlling qubit networks in polynomial time
• Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Unified generation and fast emission of arbitrary single-photon multimode $W$ states
• Strategy for implementing stabilizer-based codes on solid-state qubits
• Feasibility of single-shot realizations of conditional three-qubit gates in exchange-coupled qubit arrays with local control
• Preserving universal resources for one-way quantum computing
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Cavity polariton blockade for non-local entangling gates with trapped atoms
• Digital Quantum Simulation of Scalar Yukawa Coupling
• Entanglement-enhanced quantum sensing via optimal global control with neutral atoms in a cavity
• Efficient nonclassical state preparation via generalized parity measurement
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• Overcoming disorder in superconducting globally driven quantum computing
• Robust implicit quantum control of interacting spin chains
• Equally entangled multiqubit states