Quantum Signal Classification Techniques

*How can you use quantum neural networks (QNNs) to gain a quantum advantage on classical data?* We propose to use QNNs (and other quantum algorithms, including quantum signal processing) to process data in quantum sensors. Attempts over the past 7+ years to find near-term practical applications of quantum neural networks on classical data have faced a variety of challenges, including: if the classical data is small enough to be able to load into a quantum computer, then it has (empirically) always been possible to address the same problem with a classical neural network - and without the downsides of quantum computing with current (noisy) hardware. Rather than trying to tackle problems in the setting where the classical data originates from a classical computer's memory, we switch the framing of the problem slightly, but in a way that makes a huge difference: what if we use QNNs to perform classification on classical but a priori _unknown_ data? What do we mean by _unknown_ data? A quantum sensor senses a classical signal that is unknown to us, but is ultimately classical. We can use a QNN to help reveal a _trained nonlinear function_ of the unknown classical signal. One of the examples we have explored shows how you can gain an advantage where both the quantum sensing and quantum computing are performed by a single qubit! If you already knew the classical signal, there would be no hope for a quantum advantage (simulating a single qubit is of course trivial), but in the sensing setting we don't know the signal a priori. We have been able to show it is possible to gain a quantum computational-sensing advantage using quantum signal processing (QSP) treated as a QNN, versus first using a conventional quantum sensor and then postprocessing to compute the nonlinear classification function classically. By performing an approximation of the nonlinear classification function in the quantum system before measurement, the quantum sampling noise is greatly reduced: measurements of the system yield 0 or 1 with high probability depending on which of two classes the signal was in. We have a preprint on the arXiv showing various schemes for quantum computational sensing with a small number of qubits and/or bosonic modes, tested on a variety of binary and multiclass classification problems: https://lnkd.in/enQxFDNt I am optimistic about the prospects for experimental proof-of-concept demonstrations given the modest quantum resources required (down to just a single qubit and a not-particularly-deep circuit). Congratulations to Saeed Khan and Sridhar Prabhu, as well as Logan Wright!

⚛️ Quantum computational sensing using quantum signal processing, quantum neural networks, and Hamiltonian engineering 📑 Combining quantum sensing with quantum computing can lead to quantum computational sensors that are able to more efficiently extract task-specific information from physical signals than is possible otherwise. Early examples of quantum computational sensing (QCS) have largely focused on protocols where only a single sensing operation appears before measurement—with an exception being the recent application of Grover’s algorithm to signal detection. In this paper we present, in theory and numerical simulations, the application of two quantum algorithms—quantum signal processing and quantum neural networks—to various binary and multiclass machine-learning classification tasks in sensing. Here sensing operations are interleaved with computing operations, giving rise to nonlinear functions of the sensed signals. We have evaluated tasks based on static and time-varying signals, including a classification task that requires distinguishing magnetic-field signals sensed by up to 7 spatially separated qubits, where the task dataset was obtained from experimentally recorded spatiotemporal magnetoencephalography signals. Our approach to optimizing the circuit parameters in a QCS protocol takes into account quantum sampling noise and allows us to engineer protocols that can yield accurate results with as few as just a single measurement shot. In all cases, we have been able to show a regime of operation where a quantum computational sensor can achieve higher accuracy than a conventional quantum sensor for a given budget of sensing time, with a simulated accuracy advantage of >20 percentage points for some tasks. We also present protocols for performing nonlinear tasks using Hamiltonian-engineered bosonic systems and quantum signal processing with hybrid qubit-bosonic systems, and empirically show an advantage when the received signal has a limited mean photon number. Overall, we have shown that substantial quantum computational-sensing advantages can be obtained even if the quantum system is small, including few-qubit systems, systems comprising a single qubit and a single bosonic mode, and even just a single qubit alone—raising the prospects for experimental proof-of-principle and practical realizations. Altogether, our methods and results advance our understanding of how we can achieve quantum computational-sensing advantages for nonlinear tasks and provide further motivation for finding ways to fruitfully adapt quantum algorithms to coherently process sensed signals prior to measurement. ℹ️ Khan et al - 2025

A Cornell University study proposes a new method—quantum computational sensing (QCS)—that uses quantum computers to process sensor signals directly, improving speed and accuracy over traditional approaches. Simulations showed that even a single qubit could outperform conventional sensors in classifying magnetic patterns and brainwave signals, with up to 26 percentage points better accuracy. https://lnkd.in/egM89Bn5