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arXiv:2609.36004

Digital Quantum Algorithms for Generating and Utilizing Spin Squeezed States

Mingru Yang, Ruby Wei, Chao Yin

quant-phcond-mat.str-elSubmitted Sep 28, 2026• Announced Sep 30, 2026• 0 citations
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Abstract

Spin squeezed states (SSSs) are conventionally viewed as analog resources for quantum metrology. Here we develop algorithms to efficiently generate and exploit SSSs on a digital quantum computer. We introduce an adaptive local-circuit protocol that prepares SSSs with squeezing parameter $ξ$ in depth $\mathrm{O}\left(\log{1/ξ}\right)$, yielding an exponential improvement over non-adaptive approaches. We prove that this depth is optimal for permutation symmetric SSSs by deriving a matching lower bound on entanglement entropy. We further leverage the squeezing paradigm to deterministically prepare the Dicke states using asymptotically fewer resources than prior methods. Remarkably, classical simulations of our preparation protocols under realistic noise models predicts a metrological gain of 4.2 dB beyond the standard quantum limit with 55 superconducting qubits in total including ancillae. Our work paves the way for performing quantum metrology on near-term digital quantum devices.

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Spin squeezed states (SSSs) are conventionally viewed as analog resources for quantum metrology. Here we develop algorithms to efficiently generate and exploit SSSs on a digital quantum computer. We introduce an adaptive local-circuit protocol that prepares SSSs with squeezing parameter ξξξ in depth O(log⁡1/ξ)\mathrm{O}\left(\log{1/ξ}\right)O(log1/ξ), yielding an exponential improvement over non-adaptive approaches. We prove that this depth is optimal for permutation symmetric SSSs by deriving a matching lower bound on entanglement entropy. We further leverage the squeezing paradigm to deterministically prepare the Dicke states using asymptotically fewer resources than prior methods. Remarkably, classical simulations of our preparation protocols under realistic noise models predicts a metrological gain of 4.2 dB beyond the standard quantum limit with 55 superconducting qubits in total including ancillae. Our work paves the way for performing quantum metrology on near-term digital quantum devices.
Abstract Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the performance. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology.
In this dissertation we focused on some quantum states with strong entanglement and robustness to noise. We constructed a spinor BEC Hamiltonian which has already been realized in experiment with several different kinds of atoms and proposed an adiabatic passage method to produce the maximal entangled Dicke state. We also analyzed the entanglement behavior of the Dicke state under various noises and demonstrate its use in high precision measurement experiment. We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing, which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as the Dicke squeezing parameter attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the Dicke squeezed states are more robust to decoherence and give better measurement precision under typical experimental noise. On the other hand, we explore other choices of precision measurement with spin squeezed states. Spin squeezed states have strong manybody entanglement and are good candidates to be used in quantum metrology. A robust squeezing parameter is proposed to characterize the experimental phase measurement precision for spin squeezed states. The behavior of this parameter under various experimental noises is compared with other parameters in the history and it is shown to have better performance. Finally we present a scalable implementation scheme for Boson sampling using local transverse phonon modes in trapped ion system, which is a promising model for quantum computers.
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Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.
The nnn-qubit kkk-weight Dicke states ∣Dkn⟩|D^n_k\rangle∣Dkn​⟩, defined as the uniform superposition of all computational basis states with exactly kkk qubits in state ∣1⟩|1\rangle∣1⟩, form a basis of the symmetric subspace and represent an important class of entangled quantum states with broad applications in quantum computing. We propose deterministic quantum circuits for Dicke state preparation under two commonly seen qubit connectivity constraints: 1. All-to-all qubit connectivity: our circuit has depth O(log⁡(k)log⁡(n/k)+k)O(\log(k)\log(n/k)+k)O(log(k)log(n/k)+k), which improves the previous best bound of O(klog⁡(n/k))O(k\log(n/k))O(klog(n/k)). 2. Grid qubit connectivity ((n1×n2)(n_1\times n_2)(n1​×n2​)-grid, n1≤n2n_1\le n_2n1​≤n2​): (a) For k≥n2/n1k\ge n_2/n_1k≥n2​/n1​, we design a circuit with depth O(klog⁡(n/k)+n2)O(k\log(n/k)+n_2)O(klog(n/k)+n2​), surpassing the prior O(nk)O(\sqrt{nk})O(nk​) bound. (b) For k<n2/n1k< n_2/n_1k<n2​/n1​, we design an optimal-depth circuit with depth O(n2)O(n_2)O(n2​). Furthermore, we establish the depth lower bounds of Ω(log⁡(n))Ω(\log(n))Ω(log(n)) for all-to-all qubit connectivity and Ω(n2)Ω(n_2)Ω(n2​) for (n1×n2)(n_1\times n_2)(n1​×n2​)-grid connectivity constraints, demonstrating the near-optimality of our constructions.