Global Variational Quantum Circuits for Arbitrary Symmetric State Preparation

Abstract

Quantum states that are symmetric under particle exchange play a crucial role in fields such as quantum metrology and quantum error correction. We use a variational circuit composed of global one-axis twisting and global rotations to efficiently prepare arbitrary symmetric states, i.e. any superposition of Dicke states. The circuit does not require local addressability or ancilla qubits and thus can be readily implemented in a variety of experimental platforms including trapped-ion quantum simulators and cavity QED systems. We provide analytic and numerical evidence that any $N$-qubit symmetric state can be prepared in $2N/3$ steps. We demonstrate the utility of our protocol by preparing (i) metrologically useful $N$-qubit Dicke states of up to $N=300$ qubits in $\mathcal{O}(1)$ gate steps with theoretical infidelities $1-\mathcal{F}<10^{-3}$, (ii) the $N=9$ Ruskai codewords in $P=4$ gate steps with $1-\mathcal{F}<10^{-4}$, and (iii) the $N=13$ Gross codewords in $P=7$ gate steps with $1-\mathcal{F}<10^{-4}$. Focusing on trapped-ion platforms, for the $N=9$ Ruskai and $N=13$ Gross codewords we estimate that the protocol achieves fidelities $\gtrsim 95\%$ in the presence of typical experimental noise levels, thus providing a pathway to the preparation of a wide range of useful highly-entangled quantum states.

V2. 7+4 pages, 4+2 figures. New title. Added figure & supplemental material. Close to published version

References in corpus (44)

• A variational eigenvalue solver on a quantum processor
• The theory of variational hybrid quantum-classical algorithms
• Quantum metrology with nonclassical states of atomic ensembles
• Quantum Error Correction for Quantum Memories
• 14-qubit entanglement: creation and coherence
• Logical quantum processor based on reconfigurable atom arrays
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
• Multipartite entanglement and high precision metrology
• Real-time quantum error correction beyond break-even
• Observation of multi-component atomic Schrödinger cat states of up to 20 qubits
• Entanglement and Tunable Spin-Spin Couplings Between Trapped Ions Using Multiple Transverse Modes
• Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
• Permutationally invariant quantum tomography
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Optimal metrology with programmable quantum sensors
• Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
• Variational spin-squeezing algorithms on programmable quantum sensors
• Superabsorption of light via quantum engineering
• Deterministic entanglement of ions in thermal states of motion
• Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks
• Trapped Ion Quantum Information Processing with Squeezed Phonons
• Permutation-invariant quantum codes
• Preparation of Dicke States in an Ion Chain
• Encoding a qubit in a spin
• Pairwise entanglement in symmetric multi-qubit systems
• Theory of robust multi-qubit non-adiabatic gates for trapped-ions
• A Divide-and-Conquer Approach to Dicke State Preparation
• Efficient compression of quantum information
• Creation of 2000-atom Greenberger-Horne-Zeilinger states by entanglement amplification
• Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
• Detecting metrologically useful entanglement in the vicinity of Dicke states
• State preparation by shallow circuits using feed forward
• Entanglement robustness against particle loss in multiqubit systems
• Geometric pathway to scalable quantum sensing
• Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles
• Creation of arbitrary Dicke and NOON states of trapped-ion qubits by global addressing with composite pulses
• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Controllability of Symmetric Spin Networks
• Generation of any superposition of Dicke state of excitons in coupled quantum dots
• A high-fidelity method for a single-step $N$-bit Toffoli gate in trapped ions
• The Effect of Micromotion and Local Stress in Quantum simulation with Trapped Ions in Optical Tweezers
• Universal Control of Symmetric States Using Spin Squeezing

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