Abstract Combining quantum sensing with quantum computing can lead to quantum computational sensing (QCS) protocols that are able to more efficiently extract task-specific information from physical signals than is possible otherwise. 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. Our approach to optimizing QCS protocols 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.
Abstract Combining quantum sensing with quantum computing can lead to quantum computational sensing (QCS) protocols that are able to more efficiently extract task-specific information from physical signals than is possible otherwise. 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. Our approach to optimizing QCS protocols 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.
Quantum computational sensing (QCS) combines quantum sensing with quantum computing to extract task-relevant information from the physical world. QCS can in principle achieve an accuracy advantage for specific tasks versus the alternative of raw-signal estimation using conventional quantum sensing followed by task-specific classical postprocessing. Here we report the experimental demonstration of quantum computational displacement sensing (QCDS) with a superconducting circuit comprising a qubit coupled to an oscillator. We consider binary classification sensing tasks, where the goal is to predict the class label of a single complex-valued displacement sensed once by the oscillator. Rather than estimating the displacement, our computational-sensing protocol -- using parameterized quantum circuits before and after sensing -- attempts to determine the binary class label using quantum processing and map it onto the ground or excited state of the qubit. A single measurement of the qubit directly outputs the prediction. We implemented circuits with up to 24 entangling gates and 38 free parameters, which were trained in silico. We show that increasing the circuit depth systematically improves expressivity and classification accuracy. We experimentally obtained an accuracy advantage over a suite of protocols that first use conventional quantum sensing to estimate the displacement before using classical postprocessing to perform prediction. For certain tasks, our protocol achieves a 15-percentage-points higher classification accuracy than most conventional approaches considered. Our results establish the feasibility of quantum computational sensing with noisy superconducting hardware and illustrate how integrating quantum computation with quantum sensing can enhance performance when the goal is to estimate a property or function of a signal rather than to estimate the signal.
A measurement of a single-qubit quantum sensor reveals at most 1 bit of information about the signal that was sensed. To perform a classification task on the signal, the conventional approach is to repeat a sensing protocol many times, averaging the measurement results to obtain a high-precision estimate of the sensed signal, and then to apply classical postprocessing. Quantum computational sensing (QCS) is an alternative approach that breaks with the paradigm of first obtaining a classical estimate of the signal and then computing a function of the estimated signal in postprocessing. QCS instead combines quantum sensing with quantum computing to concentrate information about the signal relevant to the task into the solitary bit revealed by each measurement. Here, we report on the experimental demonstration of QCS where sensing and computing were both performed by the same single superconducting transmon qubit. We consider various binary classification tasks based on static and oscillating magnetic fields induced by current through a flux line. The fields were sensed through a double-junction superconducting quantum interference device (SQUID) loop that was part of the qubit. We used a protocol based on quantum signal processing to preprocess the sensed signals in the quantum domain prior to measurement. For tasks on static magnetic fields, our protocol outperformed the conventional baseline of Ramsey-based phase estimation by as much as 15 percentage points. For tasks on oscillating magnetic fields, we classified signal amplitude and frequency with up to 20 and 15 percentage points higher accuracy, respectively, compared to the conventional baseline of optimized dynamical-decoupling protocols. Our results illustrate how quantum computing can enhance quantum sensing even with a minimally sized quantum system subject to the practical limitations of decoherence and error-prone operations.
Making sense of the world happens through receiving and processing signals, whether it be sound, light, or other waves that interact with us. The fields of nuclear magnetic resonance and digital signal processing each built a rigorous language for manipulating and extracting information from signals of particular types. Quantum signal processing (QSP) connects these two traditions, providing a unified algebraic framework for understanding how quantum systems are transformed by both classical and quantum signals. QSP provides a systematic framework for characterizing possible transformations. QSP was developed for qubit systems, but physical quantum systems are rarely two-level and the full richness of high-dimensional Hilbert spaces has remained largely unexplored. This thesis extends and applies QSP in two directions: from qubits to high-dimensional systems such as finite-level qudits and infinite-dimensional oscillators and from static signals to signals that include continuous-time noise processes. We will also show how QSP for qudits leads to novel experimental applications in trapped-ion systems. One type of high-dimensional system is a qubit coupled to an oscillator, and a qubit-oscillator qudit can be formed and universally controlled using only a limited set of interactions. In this qubit-oscillator space, a bosonic version of QSP allows novel incarnations of quantum algorithms and sensing. The quantum Fourier transform can be performed by clever conversion of information in a many-qubit system into a single oscillator, and an interferometric protocol uses binary decisions from a qubit to sense a signal affecting the oscillator. Another type of high-dimensional system is a qudit made from the electronic levels of an atom. This thesis presents a new construction of Grover’s algorithm using a qudit in an atomic hyperfine manifold, along with a calibration method that finds accurate QSP pulse parameters for the experiment. For decision algorithms, QSP in qudits enables theoretically perfect decision-making for quantum channel discrimination problems with certain symmetries. In the face of noise, temporal QSP is developed to extend the canonical framework to continuous-time stochastic noise. Combined with Kubo linear-response theory, a noise filter function description emerges which formalizes the optimization of atomic clock performance. These results from qudit, bosonic, and temporal QSP establish QSP as a natural language for high-dimensional quantum control and sensing.
Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.
Quantum neural networks (QNNs) represent a cutting-edge approach to machine learning and artificial intelligence, harnessing the principles of quantum mechanics to process and analyze data in fundamentally new ways. Unlike classical neural networks, which operate on classical bits and are limited by the laws of classical physics, QNNs use quantum bits (qubits) and exploit quantum phenomena such as superposition and entanglement to achieve unprecedented computational power and efficiency. This chapter explores the principles and applications of QNNs, including their potential for solving complex optimisation problems, pattern recognition tasks, and quantum simulation tasks. We discuss various QNN architectures, training algorithms, and applications, highlighting their advantages and challenges compared to classical neural networks. Additionally, we explore the potential impact of QNNs on fields such as quantum computing, quantum communication, and quantum sensing, as well as their implications for society and the economy. Overall, this chapter provides insights into the emerging field of quantum neural networks and sets the stage for further research and innovation in this exciting area.
Although linear quantum amplification has proven essential to the processing of weak quantum signals, extracting higher-order quantum features such as correlations in principle demands nonlinear operations. However, nonlinear processing of quantum signals is often associated with non-idealities and excess noise, and absent a general framework to harness nonlinearity, such regimes are typically avoided. Here we present a framework to uncover general quantum signal processing principles of a broad class of bosonic quantum nonlinear processors (QNPs), inspired by a remarkably analogous paradigm in nature: the processing of environmental stimuli by nonlinear, noisy neural ensembles, to enable perception. Using a quantum-coherent description of a QNP monitoring a quantum signal source, we show that quantum nonlinearity can be harnessed to calculate higher-order features of an incident quantum signal, concentrating them into linearly-measurable observables, a transduction not possible using linear amplifiers. Secondly, QNPs provide coherent nonlinear control over quantum fluctuations including their own added noise, enabling noise suppression in an observable without suppressing transduced information, a paradigm that bears striking similarities to optimal neural codings that allow perception even under highly stochastic neural dynamics. Unlike the neural case, we show that QNP-engineered noise distributions can exhibit non-classical correlations, providing a new means to harness resources such as entanglement. Finally, we show that even simple QNPs in realistic measurement chains can provide enhancements of signal-to-noise ratio for practical tasks such as quantum state discrimination. Our work provides pathways to utilize nonlinear quantum systems as general computation devices, and enables a new paradigm for nonlinear quantum information processing.