Generation of complete graph states in a spin-$1/2$ Heisenberg chain with a globally optimized magnetic field

Abstract

Graph states possess significant practical value in measurement-based quantum computation, with complete graph states that exhibit exceptional performance in quantum metrology. In this work, we introduce a method for generating multiparticle complete graph states using a spin-$1/2$ Heisenberg $XX$ chain subjected to a time-varying magnetic field, which applies to a wide range of systems. Our scheme relies exclusively on nearest-neighbor interactions between atoms, with real-time magnetic field formation facilitated by quantum optimal control theory. We focus specifically on neutral-atom systems, finding that multiparticle complete graph states with $N=3\sim 6$ can be achieved in less than $0.25\mu \mathrm{s}$, utilizing a hopping amplitude of $J/(2\pi )=-2.443\mathrm{MHz}$. This assumes an initial state provided by an equal-weight superposition of all spin states that are encoded by the dipolar interacting Rydberg states. Additionally, we thoroughly address various experimental imperfections and showcase the robustness of our approach against atomic vibrations, fluctuations in pulse amplitude, and spontaneous emission of Rydberg states. Considering the common occurrence of disturbances in experimental setups of neutral-atom systems, our one-step strategy for achieving such graph states emerges as a more empirically viable alternative to techniques based on controlled-Z gates.

accepted by Physical Review A

References in corpus (24)

• Multi-party entanglement in graph states
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Quantum metrology from a quantum information science perspective
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• High-fidelity parallel entangling gates on a neutral atom quantum computer
• Spectral signatures of many-body localization with interacting photons
• Deterministic Generation of a Cluster State of Entangled Photons
• Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
• Microwave-engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms
• Quantum secret sharing with qudit graph states
• Scalable spin squeezing in a dipolar Rydberg atom array
• Ultrafast energy exchange between two single Rydberg atoms on the nanosecond timescale
• High fidelity entanglement of neutral atoms via a Rydberg-mediated single-modulated-pulse controlled-PHASE gate
• Supercharged two-dimensional tweezer array with more than 1000 atomic qubits
• Sequential generation of multiphoton entanglement with a Rydberg superatom
• Observation of magnon bound states in the long-range, anisotropic Heisenberg model
• Creation and transfer of non-classical states of motion using Rydberg dressing of atoms in a lattice
• Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions
• Time-Optimal Generation of Cluster States
• Quantum Hall states for Rydberg atoms with laser-assisted dipole-dipole interactions
• Topological graph states and quantum error correction codes
• A scheme for tunable quantum phase gate and effective preparation of graph-state entanglement
• Simulating long-distance entanglement in quantum spin chains by superconducting flux qubits
• Quantum control of Rydberg atoms for mesoscopic-scale quantum state and circuit preparation

Cited by in corpus (4)

• Rydberg superatoms: An artificial quantum system for quantum information processing and quantum optics
• Quantum superpositions of current states in Rydberg-atom networks
• Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
• Many-body quantum resources of graph states