Enhanced Squeezing and Faster Metrology from Layered Quantum Neural Networks

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.

💡 Research Summary

This paper presents a comparative analysis of three quantum architectures—Quantum Reservoir Computers (QRCs), Quantum Perceptrons, and multi-layer Quantum Neural Networks (QNNs)—for their performance in spin-squeezing-based quantum metrology. The study employs a standard sensing sequence: preparation of a coherent spin state, entangling dynamics via one-axis-twisting (OAT), encoding of a weak external field as a small rotation, time-reversal of the dynamics, and final collective spin measurement.

The analysis begins with a single quantum perceptron, where a block of input qubits interacts with a single output qubit via ZZ couplings. When the output qubit is strongly driven, it mediates an effective OAT Hamiltonian among the inputs via second-order processes. This perceptron achieves the same Heisenberg-limited phase sensitivity (Δφ ~ 1/N_in) as a conventional QRC with N_in qubits. However, a key finding is that the presence of the output qubit “steers” the input block, accelerating the squeezing dynamics in the perturbative regime without altering the ultimate sensitivity.

Stacking multiple perceptrons into a multi-layer QNN amplifies this effect. In a 2-layer QNN with N_in input and N_out output qubits, each output qubit acts as an independent mediator. This results in the effective OAT strength for a layer being multiplied by the number of qubits in the neighboring layer that drives it. Consequently, the time required to reach the optimal squeezing point is reduced by a factor of N_out, while the achievable sensitivity remains Heisenberg-limited with respect to the total number of qubits, Δφ ~ 1/(N_in + N_out).

The most significant result emerges from a protocol utilizing sequential squeezing between layers. In a 2-layer QNN, the outputs first squeeze the inputs, and after signal encoding, the inputs squeeze the outputs during time-reversal. Crucially, the linear response (derivative of the collective spin) to the weak signal adds constructively from the two stages. This leads to a measurable prefactor enhancement in sensitivity: for equal-sized layers (N_in = N_out), the 2-layer QNN achieves a √2 improvement in phase sensitivity over a QRC with the same total number of qubits (2N_in), while also requiring less total squeezing time.

Generalizing to an L-layer QNN, the study shows that the metrological gain scales as √L compared to a monolithic QRC, and the required squeezing time per layer scales as 1/N_l, where N_l is the number of qubits per layer. This demonstrates that the layered, modular architecture of QNNs—originally conceived for quantum machine learning—can be repurposed as a resource for quantum sensing. It enables both faster generation of metrologically useful entanglement (reducing vulnerability to decoherence) and higher ultimate precision, offering a practical advantage for near-term quantum hardware platforms like trapped ions, neutral atoms, and superconducting qubits where control over connectivity and sequence is available.