A Divide-and-Conquer Approach to Dicke State Preparation

Aktar, Shamminuj; Bärtschi, Andreas; Badawy, Abdel-Hameed A.; Eidenbenz, Stephan

doi:10.1109/tqe.2022.3174547

Cited by 18 publications

(14 citation statements)

References 46 publications

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“…While our primary goal in this paper has been to lay out our algorithm in a concise manner, we are aware that further modifications can be done to reduce the number of CNOTs and tailor the algorithm for specific quantum computing architectures. These efforts have recently been explored for the Dicke state, ,, and the authors of ref experimented with implementing the Dicke state on a quantum computer. While some of these efforts can be readily extended to our AGP state preparation algorithm, future work could explore further along this direction.…”

Section: Discussionmentioning

confidence: 99%

“…Having defined a general ESP state, we highlight a special case in which x p = 1 for all p . The resulting state is equivalent to the Dicke state, which we can write as follows | D n m ⟩ = 1 true( true.25ex m n true) ∑ 1 ≤ p 1 < ... < p n ≤ m | 0 ··· 1 p n ··· 1 p 2 ··· 1 p 1 ··· 0 ⟩ The recursion relation of the Dicke state, a special case of eq , has been applied to design some of its preparation algorithms. ,, …”

Section: Preliminariesmentioning

confidence: 99%

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State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

2023

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The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen–Cooper–Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree–Fock based electronic structure methods.

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Section: Discussionmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

2023

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“…For the XY-QAOA circuit, a significant part of the two-qubit gate depth comes from the circuit preparing the initial state, which is a uniform superposition of all in-constraint states (Dicke state). To obtain circuits that are shallow enough to be executable on hardware, we leverage recently developed techniques for the shortdepth Dicke-state preparation [41][42][43]. Specifically, we use the divide-and-conquer approach [43] to generate circuits targeting a device with an all-to-all connectivity.…”

Section: Methodsmentioning

confidence: 99%

“…To obtain circuits that are shallow enough to be executable on hardware, we leverage recently developed techniques for the shortdepth Dicke-state preparation [41][42][43]. Specifically, we use the divide-and-conquer approach [43] to generate circuits targeting a device with an all-to-all connectivity.…”

Section: Methodsmentioning

confidence: 99%

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Constrained Quantum Optimization for Extractive Summarization on a Trapped-ion Quantum Computer

Niroula¹,

Shaydulin²,

Yalovetzky³

et al. 2022

Preprint

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Realizing the potential of near-term quantum computers to solve industry-relevant constrainedoptimization problems is a promising path to quantum advantage. In this work, we consider the extractive summarization constrained-optimization problem and demonstrate the largest-to-date execution of a quantum optimization algorithm that natively preserves constraints on quantum hardware. We report results with the Quantum Alternating Operator Ansatz algorithm with a Hamming-weight-preserving XY mixer (XY-QAOA) on the Quantinuum H1-1 trapped-ion quantum computer. We successfully execute XY-QAOA circuits that restrict the quantum evolution to the in-constraint subspace, using up to 765 two-qubit gates with a two-qubit gate depth of up to 159, and all 20 qubits of the H1-1 device. We demonstrate the necessity of directly encoding the constraints into the quantum circuit by showing the trade-off between the in-constraint probability and the quality of the solution that is implicit if unconstrained quantum optimization methods are used. We show that this trade-off makes choosing good parameters difficult in general. We compare XY-QAOA to the Layer Variational Quantum Eigensolver algorithm, which has a highly expressive constant-depth circuit, and the Quantum Approximate Optimization Algorithm. Our experimental results demonstrate that the rapid hardware and algorithmic progress is enabling the solution of constrained-optimization problems on quantum hardware.

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Alignment between initial state and mixer improves QAOA performance for constrained optimization

He,

Shaydulin,

Chakrabarti

et al. 2023

npj Quantum Inf

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Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as executed in practice with small to moderate depth. In this paper, we demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state. Specifically, we observe that the best performance is obtained when the initial state of QAOA is set to be the ground state of the mixing Hamiltonian, as required by the adiabatic algorithm. We provide numerical evidence using the examples of constrained portfolio optimization problems with both low (p ≤ 3) and high (p = 100) QAOA depth. Additionally, we successfully apply QAOA with XY mixer to portfolio optimization on a trapped-ion quantum processor using 32 qubits and discuss our findings in near-term experiments.

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A Divide-and-Conquer Approach to Dicke State Preparation

Abstract: IEEE Transactions on Quantum EngineeringDate of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Cited by 18 publications

References 46 publications

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

Constrained Quantum Optimization for Extractive Summarization on a Trapped-ion Quantum Computer

Alignment between initial state and mixer improves QAOA performance for constrained optimization

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