A Divide-and-Conquer Approach to Dicke State Preparation

Abstract

We present a divide-and-conquer approach to deterministically prepare Dicke states $|D_k^n⟩$ (i.e., equal-weight superpositions of all $n$-qubit states with Hamming Weight $k$) on quantum computers. In an experimental evaluation for up to $n=6$ qubits on IBM Quantum Sydney and Montreal devices, we achieve significantly higher state fidelity compared to previous results [Mukherjee and others, TQE'2020], [Cruz and others, QuTe'2019]. The fidelity gains are achieved through several techniques: Our circuits first "divide" the Hamming weight between blocks of $n/2$ qubits, and then "conquer" those blocks with improved versions of Dicke state unitaries [Bärtschi and others, FCT'2019]. Due to the sparse connectivity on IBM's heavy-hex-architectures, these circuits are implemented for linear nearest neighbor topologies. Further gains in (estimating) the state fidelity are due to our use of measurement error mitigation and hardware progress.

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• Constrained Quantum Optimization for Extractive Summarization on a Trapped-ion Quantum Computer
• Alignment between Initial State and Mixer Improves QAOA Performance for Constrained Optimization
• Short-Depth Circuits for Dicke State Preparation
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Numerical Evidence for Exponential Speed-up of QAOA over Unstructured Search for Approximate Constrained Optimization
• Variational Quantum Algorithms for the Allocation of Resources in a Cloud/Edge Architecture
• $q$-analog qudit Dicke states
• Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers
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• Global Variational Quantum Circuits for Arbitrary Symmetric State Preparation
• State preparation of AGP on a quantum computer without number projection
• Efficient preparation of Dicke states
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• Quantum State Preparation Using an Exact CNOT Synthesis Formulation
• Deformations of the symmetric subspace of qubit chains
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• Deterministic carving of quantum states with Grover's algorithm
• Scalable Experimental Bounds for Entangled Quantum State Fidelities
• Electric Power Demand Portfolio Optimization by Fermionic QAOA with Self-Consistent Local Field Modulation