Enhanced Squeezing and Faster Metrology from Layered Quantum Neural Networks

TL;DR

This paper addresses whether the architecture of interacting qubits for squeezing-based quantum metrology affects performance when the underlying one-axis-twisting interaction is fixed. By comparing QRCs, quantum perceptrons, and multilayer QNNs, it shows that architectural layering can reduce the required squeezing time and modify the sensitivity prefactor while preserving Heisenberg scaling; notably, a 2-layer QNN achieves a 1/N_out reduction in squeezing time and a sqrt(2) sensitivity gain over a QRC with the same total qubits. Extending to L layers, the metrological gain scales as sqrt(L) and the squeezing time decreases roughly as 1/N_l, making layered QNNs both faster and more precise. The results imply that architectural design—rather than new interactions—can materially enhance near-term quantum sensors, with broad applicability across common quantum hardware platforms.

Abstract

Spin squeezing is a powerful resource for quantum metrology, and recent hardware platforms based on interacting qubits provide multiple possible architectures to generate and reverse squeezing during a sensing protocol. In this work, we compare the sensing performance of three such architectures: quantum reservoir computers (QRCs), quantum perceptrons, and multi-layer quantum neural networks (QNNs), when used as squeezing-based field sensors. For all models, we consider a standard metrological sequence consisting of coherent-spin preparation, one-axis-twisting dynamics, field encoding via a weak rotation, time-reversal, and collective readout. We show that a single quantum perceptron generates the same optimal sensitivity as a QRC, but in the perturbative regime it benefits from accelerated squeezing due to steering by the output qubit. Stacking perceptrons into a QNN further amplifies this effect: in a 2-layer QNN with N_in input and N_out output qubits, the optimal squeezing time is reduced by a factor of N_out, while the achievable phase sensitivity remains Heisenberg-limited, Delta phi ~ 1/(N_in + N_out). Moreover, if the layers are used sequentially, first using the outputs to squeeze the inputs and then the inputs to squeeze the outputs, the two contributions to the response add constructively. This yields a sqrt(2) enhancement in sensitivity over a QRC when N_in = N_out and requires shorter total squeezing time. Generalizing to L layers, we show that the metrological gain scales as sqrt(L) while the required squeezing time decreases as 1/N_l, where N_l is the number of qubits per layer. Our results demonstrate that the structure of quantum neural networks can be exploited not only for computation, but also to engineer faster and more sensitive squeezing-based quantum sensors.

Figures (2)

• Figure 1: Using quantum perceptrons for quantum metrology. (a) A single quantum perceptron composed of $N$ input qubits interacting via $ZZ$ couplings with a single output qubit, which is prepared in the $\ket{+}$ state during time reversal. Only the output qubit is directly controlled. (b) Stacking perceptrons such that each qubit in the rightmost layer interacts via $ZZ$ couplings with every qubit in the leftmost layer, with global control applied to the rightmost layer. (c) Two metrological schemes using multiple perceptrons: the left configuration treats the entire network with all-to-all interactions as a single sensor, while the right configuration senses only with the leftmost layer while qubits in the second layer are driven out. (d) Sensing protocol for a QNN with $L$ layers. One senses with the first layer and sequentially propagates the sensing operation through each layer. Neighboring layers drive the one-axis-twisting and time-reversal dynamics. This protocol enables all qubits to participate as sensors, achieving both maximal precision and a reduced optimal squeezing time.
• Figure 2: Comparison of squeezing dynamics and sensitivity across the QRC, perceptron, and QNN architectures.