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

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Cited by in corpus (8)

• Efficient preparation of Dicke states
• Efficient preparation of entangled states in cavity QED with Grover's algorithm
• Deterministic carving of quantum states with Grover's algorithm
• Dicke subsystems are entangled
• Measurement-free code-switching for low overhead quantum computation using permutation invariant codes
• Simple ways of preparing qudit Dicke states
• Spin-$s$ $U(1)$-eigenstate preparation
• Quantum optimal control of the Dicke manifold in dipolar Rydberg atom arrays