arXiv subjects

Peter L. McMahon

Publications and source records attributed to Peter L. McMahon.

At least 37 records · Page 2Linked to original sources

arXiv2025

Exponential advantage in quantum sensing of correlated parameters

Conventionally in quantum sensing, the goal is to estimate one or more unknown parameters that are assumed to be deterministic - that is, they do not change between shots of the quantum-sensing protocol. We instead consider the setting where the parameters are stochastic: each shot of the quantum-sensing protocol senses parameter values that come from independent random draws. In this work, we explore three examples where the stochastic parameters are correlated and show how using entanglement provides a benefit in classification or estimation tasks: (1) a two-parameter classification task, for which there is an advantage in the low-shot regime; (2) an $N$-parameter estimation task and a classification variant of it, for which an entangled sensor requires just a constant number (independent of $N$) shots to achieve the same accuracy as an unentangled sensor using exponentially many (${\sim}2^N$) shots; (3) classifying the magnetization of a spin chain in thermal equilibrium, where the individual spins fluctuate but the total spin in one direction is conserved - this gives a practical setting in which stochastic parameters are correlated in a way that an entangled sensor can be designed to exploit. We also present a theoretical framework for assessing, for a given choice of entangled sensing protocol and distributions to discriminate between, how much advantage the entangled sensor would have over an unentangled sensor. Our work motivates the further study of sensing correlated stochastic parameters using entangled quantum sensors - and since classical sensors by definition cannot be entangled, our work shows the possibility for entangled quantum sensors to achieve an exponential advantage in sample complexity over classical sensors, in contrast to the typical quadratic advantage.

quant-ph↗

arXiv2025

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 spatiotemporal 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, 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. 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.

quant-ph↗

arXiv2025

Solving the compute crisis with physics-based ASICs

Escalating artificial intelligence (AI) demands expose a critical "compute crisis" characterized by unsustainable energy consumption, prohibitive training costs, and the approaching limits of conventional CMOS scaling. Physics-based Application-Specific Integrated Circuits (ASICs) present a transformative paradigm by directly harnessing intrinsic physical dynamics for computation rather than expending resources to enforce idealized digital abstractions. By relaxing the constraints needed for traditional ASICs, like enforced statelessness, unidirectionality, determinism, and synchronization, these devices aim to operate as exact realizations of physical processes, offering substantial gains in energy efficiency and computational throughput. This approach enables novel co-design strategies, aligning algorithmic requirements with the inherent computational primitives of physical systems. Physics-based ASICs could accelerate critical AI applications like diffusion models, sampling, optimization, and neural network inference as well as traditional computational workloads like scientific simulation of materials and molecules. Ultimately, this vision points towards a future of heterogeneous, highly-specialized computing platforms capable of overcoming current scaling bottlenecks and unlocking new frontiers in computational power and efficiency.

cs.ET↗

arXiv2025

Large-scale quantum reservoir computing using a Gaussian Boson Sampler

A Gaussian boson sampler (GBS) is a special-purpose quantum computer that can be practically realized at large scale in optics. Here we report on experiments in which we used a frequency-multiplexed GBS with $>400$ modes as the reservoir in the quantum-machine-learning approach of quantum reservoir computing. We evaluated the accuracy of our GBS-based reservoir computer on a variety of benchmark tasks, including spoken-vowels classification and MNIST handwritten-digit classification. We found that when the reservoir computer was given access to the correlations between measured modes of the GBS, the achieved accuracies were the same or higher than when it was only given access to the mean photon number in each mode -- and in several cases the advantage in accuracy from using the correlations was greater than 20 percentage points. This provides experimental evidence in support of theoretical predictions that access to correlations enhances the power of quantum reservoir computers. We also tested our reservoir computer when operating the reservoir with various sources of classical rather than squeezed (quantum) light and found that using squeezed light consistently resulted in the highest (or tied highest, for simple tasks) accuracies. Our work experimentally establishes that a GBS can be an effective reservoir for quantum reservoir computing and provides a practical platform for experimentally exploring the role of quantumness and correlations in quantum machine learning at very large system sizes.

quant-ph↗

arXiv2025

Programmable on-chip nonlinear photonics

Nonlinear photonics uses coherent interactions between optical waves to engineer functionality that is not possible with purely linear optics. Traditionally, the function of a nonlinear-optical device is determined during design and fixed during fabrication. In this paper, we present a photonic device with highly programmable nonlinear functionality: an optical slab waveguide with an arbitrarily reconfigurable two-dimensional distribution of $χ^{(2)}$ nonlinearity. The nonlinearity is realized using electric-field-induced $χ^{(2)}$ in a $χ^{(3)}$ material. The programmability is engineered by massively parallel control of the electric-field distribution within the device using a photoconductive layer and optical programming with a spatial light pattern. To showcase the versatility of our device, we demonstrated spectral, spatial, and spatio-spectral engineering of second-harmonic generation by tailoring arbitrary quasi-phase-matching (QPM) grating structures in two dimensions. Second-harmonic light was generated with programmable spectra, enabled by real-time in situ inverse design of QPM gratings. Flexible spatial control was also achieved, including the generation of complex waveforms such as Airy beams and the simultaneous engineering of spectral and spatial features. This allowed us to create distinct spatial light profiles across multiple wavelengths. The programmability also allowed us to demonstrate in situ, real-time compensation of fluctuations in pump laser wavelength. Our work shows that we can transcend the conventional one-device--one-function paradigm, expanding the potential applications of nonlinear optics in situations where fast device reconfigurability is not merely practically convenient but essential -- such as in programmable optical quantum gates and quantum light sources, all-optical signal processing, optical computation, and structured light for sensing.

physics.optics↗

arXiv2025

Quantum-limited stochastic optical neural networks operating at a few quanta per activation

Energy efficiency in computation is ultimately limited by noise, with quantum limits setting the fundamental noise floor. Analog physical neural networks hold promise for improved energy efficiency compared to digital electronic neural networks. However, they are typically operated in a relatively high-power regime so that the signal-to-noise ratio (SNR) is large, and the noise can be treated as a perturbation. We study optical neural networks where all layers except the last are operated in the limit that each neuron can be activated by just a single photon, and as a result the noise on neuron activations is no longer merely perturbative. We show that by using a physics-based probabilistic model of the neuron activations in training, it is possible to perform accurate machine-learning inference in spite of the extremely high shot noise (SNR ~ 1). We experimentally demonstrated MNIST handwritten-digit classification with a test accuracy of 98% using an optical neural network with a hidden layer operating in the single-photon regime; the optical energy used to perform the classification corresponds to just 0.038 photons per multiply-accumulate (MAC) operation. Our physics-aware stochastic training approach might also prove useful with non-optical ultra-low-power hardware.

physics.optics↗

arXiv2025

Synthetic high angular momentum spin dynamics in a microwave oscillator

Spins and oscillators are foundational to much of physics and applied sciences. For quantum information, a spin 1/2 exemplifies the most basic unit, a qubit. High angular momentum spins (HAMSs) and harmonic oscillators provide multi-level manifolds (e.g., qudits) which have the potential for hardware-efficient protected encodings of quantum information and simulation of many-body quantum systems. In this work, we demonstrate a new quantum control protocol that conceptually merges these disparate hardware platforms. Namely, we show how to modify a harmonic oscillator on-demand to implement a continuous range of generators associated to resonant driving of a harmonic qudit, which we can interpret as accomplishing linear and nonlinear control over a harmonic HAMS degree of freedom. The spin-like dynamics are verified by demonstration of linear spin coherent (SU(2)) rotations, nonlinear spin control, and comparison to other manifolds like simply-truncated oscillators. Our scheme allows the first universal control of such a harmonic qudit encoding: we use linear operations to accomplish four logical gates, and further show that nonlinear harmonicity-preserving operations complete the logical gate set. Our results show how motion on a closed Hilbert space can be useful for quantum information processing and opens the door to superconducting circuit simulations of higher angular momentum quantum magnetism.

quant-ph↗

arXiv2025

Roadmap on Neuromorphic Photonics

This roadmap consolidates recent advances while exploring emerging applications, reflecting the remarkable diversity of hardware platforms, neuromorphic concepts, and implementation philosophies reported in the field. It emphasizes the critical role of cross-disciplinary collaboration in this rapidly evolving field.

cs.ET↗

arXiv2024

Microwave signal processing using an analog quantum reservoir computer

Quantum reservoir computing (QRC) has been proposed as a paradigm for performing machine learning with quantum processors where the training is efficient in the number of required runs of the quantum processor and takes place in the classical domain, avoiding the issue of barren plateaus in parameterized-circuit quantum neural networks. It is natural to consider using a quantum processor based on superconducting circuits to classify microwave signals that are analog -- continuous in time. However, while theoretical proposals of analog QRC exist, to date QRC has been implemented using circuit-model quantum systems -- imposing a discretization of the incoming signal in time, with each time point input by executing a gate operation. In this paper we show how a quantum superconducting circuit comprising an oscillator coupled to a qubit can be used as an analog quantum reservoir for a variety of classification tasks, achieving high accuracy on all of them. Our quantum system was operated without artificially discretizing the input data, directly taking in microwave signals. Our work does not attempt to address the question of whether QRCs could provide a quantum computational advantage in classifying pre-recorded classical signals. However, beyond illustrating that sophisticated tasks can be performed with a modest-size quantum system and inexpensive training, our work opens up the possibility of achieving a different kind of advantage than a purely computational advantage: superconducting circuits can act as extremely sensitive detectors of microwave photons; our work demonstrates processing of ultra-low-power microwave signals in our superconducting circuit, and by combining sensitive detection with QRC processing within the same system, one could achieve a quantum sensing-computational advantage, i.e., an advantage in the overall analysis of microwave signals comprising just a few photons.

quant-ph↗

arXiv2024

Quantum Variational Solving of Nonlinear and Multi-Dimensional Partial Differential Equations

A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class of nonlinear PDEs as well as multidimensional PDEs, and study the performance of the variational quantum algorithm on several example equations. Specifically, we show via numerical simulations that the algorithm can solve instances of the Single-Asset Black-Scholes equation with a nontrivial nonlinear volatility model, the Double-Asset Black-Scholes equation, the Buckmaster equation, and the deterministic Kardar-Parisi-Zhang equation. Our simulations used up to $n=12$ ansatz qubits, computing PDE solutions with $2^n$ grid points. We also performed proof-of-concept experiments with a trapped-ion quantum processor from IonQ, showing accurate computation of two representative expectation values needed for the calculation of a single timestep of the nonlinear Black--Scholes equation. Through our classical simulations and experiments on quantum hardware, we have identified -- and we discuss -- several open challenges for using quantum variational methods to solve PDEs in a regime with a large number ($\gg 2^{20}$) of grid points, but also a practical number of gates per circuit and circuit shots.

quant-ph↗

arXiv2024

Training of Physical Neural Networks

Physical neural networks (PNNs) are a class of neural-like networks that leverage the properties of physical systems to perform computation. While PNNs are so far a niche research area with small-scale laboratory demonstrations, they are arguably one of the most underappreciated important opportunities in modern AI. Could we train AI models 1000x larger than current ones? Could we do this and also have them perform inference locally and privately on edge devices, such as smartphones or sensors? Research over the past few years has shown that the answer to all these questions is likely "yes, with enough research": PNNs could one day radically change what is possible and practical for AI systems. To do this will however require rethinking both how AI models work, and how they are trained - primarily by considering the problems through the constraints of the underlying hardware physics. To train PNNs at large scale, many methods including backpropagation-based and backpropagation-free approaches are now being explored. These methods have various trade-offs, and so far no method has been shown to scale to the same scale and performance as the backpropagation algorithm widely used in deep learning today. However, this is rapidly changing, and a diverse ecosystem of training techniques provides clues for how PNNs may one day be utilized to create both more efficient realizations of current-scale AI models, and to enable unprecedented-scale models.

physics.app-ph↗

arXiv2024

Hamiltonian-reconstruction distance as a success metric for the Variational Quantum Eigensolver

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE -- as well as any other heuristic algorithm for finding ground states of Hamiltonians -- is to know how close the algorithm's output solution is to the true ground state, when the true ground state and ground-state energy are unknown. This is especially important in iterative algorithms, such as VQE, where one wants to avoid erroneous early termination. Recent developments in Hamiltonian reconstruction -- the inference of a Hamiltonian given an eigenstate -- give a metric can be used to assess the quality of a variational solution to a Hamiltonian-eigensolving problem. This metric can assess the proximity of the variational solution to the ground state without any knowledge of the true ground state or ground-state energy. In numerical simulations and in demonstrations on a cloud-based trapped-ion quantum computer, we show that for examples of both one-dimensional transverse-field-Ising (11 qubits) and two-dimensional J1-J2 transverse-field-Ising (6 qubits) spin problems, the Hamiltonian-reconstruction distance gives a helpful indication of whether VQE has yet found the ground state or not. Our experiments included cases where the energy plateaus as a function of the VQE iteration, which could have resulted in erroneous early stopping of the VQE algorithm, but where the Hamiltonian-reconstruction distance correctly suggests to continue iterating. We find that the Hamiltonian-reconstruction distance has a useful correlation with the fidelity between the VQE solution and the true ground state. Our work suggests that the Hamiltonian-reconstruction distance may be a useful tool for assessing success in VQE, including on noisy quantum processors in practice.

quant-ph↗

arXiv2024

Roadmap for Unconventional Computing with Nanotechnology

In the "Beyond Moore's Law" era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore's Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries.

cs.ET↗

arXiv2023

Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions

The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms. We introduce the Fourier Series Loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. The FSL method prepares a ($Dn$)-qubit state encoding the $2^{Dn}$-point uniform discretization of a $D$-dimensional function specified by a $D$-dimensional Fourier series. A free parameter $m < n$ determines the number of Fourier coefficients, $2^{D(m+1)}$, used to represent the function. The FSL method uses a quantum circuit of depth at most $2(n-2)+\lceil \log_{2}(n-m) \rceil + 2^{D(m+1)+2} -2D(m+1)$, which is linear in the number of Fourier coefficients, and linear in the number of qubits ($Dn$) despite the fact that the loaded function's discretization is over exponentially many ($2^{Dn}$) points. We present a classical compilation algorithm with runtime $O(2^{3D(m+1)})$ to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than $10^{-6}$ and $10^{-3}$, respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H$1$-$1$ and H$1$-$2$ trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over $95\%$, as well as various 1D real-valued functions on up to 6 qubits with classical fidelities $\approx 99\%$, and a 2D function on 10 qubits with a classical fidelity $\approx 94\%$.

quant-ph↗

arXiv2023

The hardware is the software

Human brains and bodies are not hardware running software: the hardware is the software. We reason that because the microscopic physics of artificial-intelligence hardware and of human biological "hardware" is distinct, neuromorphic engineers need to be cautious (and yet also creative) in how we take inspiration from biological intelligence. We should focus primarily on principles and design ideas that respect -- and embrace -- the underlying hardware physics of non-biological intelligent systems, rather than abstracting it away. We see a major role for neuroscience in neuromorphic computing as identifying the physics-agnostic principles of biological intelligence -- that is the principles of biological intelligence that can be gainfully adapted and applied to any physical hardware.

cs.ET↗

arXiv2023

The physics of optical computing

There has been a resurgence of interest in optical computing over the past decade, both in academia and in industry, with much of the excitement centered around special-purpose optical computers for neural-network processing. Optical computing has been a topic of periodic study for over 50 years, including for neural networks three decades ago, and a wide variety of optical-computing schemes and architectures have been proposed. In this paper we provide a systematic explanation of why and how optics might be able to give speed or energy-efficiency benefits over electronics for computing, enumerating 11 features of optics that can be harnessed when designing an optical computer. One often-mentioned motivation for optical computing -- that the speed of light $c$ is fast -- is not a key differentiating physical property of optics for computing; understanding where an advantage could come from is more subtle. We discuss how gaining an advantage over state-of-the-art electronic processors will likely only be achievable by careful design that harnesses more than one of the 11 features, while avoiding a number of pitfalls that we describe.

physics.optics↗

arXiv2023

Optical Transformers

The rapidly increasing size of deep-learning models has caused renewed and growing interest in alternatives to digital computers to dramatically reduce the energy cost of running state-of-the-art neural networks. Optical matrix-vector multipliers are best suited to performing computations with very large operands, which suggests that large Transformer models could be a good target for optical computing. To test this idea, we performed small-scale optical experiments with a prototype accelerator to demonstrate that Transformer operations can run on optical hardware despite noise and errors. Using simulations, validated by our experiments, we then explored the energy efficiency of optical implementations of Transformers and identified scaling laws for model performance with respect to optical energy usage. We found that the optical energy per multiply-accumulate (MAC) scales as $\frac{1}{d}$ where $d$ is the Transformer width, an asymptotic advantage over digital systems. We conclude that with well-engineered, large-scale optical hardware, it may be possible to achieve a $100 \times$ energy-efficiency advantage for running some of the largest current Transformer models, and that if both the models and the optical hardware are scaled to the quadrillion-parameter regime, optical computers could have a $>8,000\times$ energy-efficiency advantage over state-of-the-art digital-electronic processors that achieve 300 fJ/MAC. We analyzed how these results motivate and inform the construction of future optical accelerators along with optics-amenable deep-learning approaches. With assumptions about future improvements to electronics and Transformer quantization techniques (5$\times$ cheaper memory access, double the digital--analog conversion efficiency, and 4-bit precision), we estimated that optical computers' advantage against current 300-fJ/MAC digital processors could grow to $>100,000\times$.

cs.ET↗

arXiv2022

Simulation Intelligence: Towards a New Generation of Scientific Methods

The original "Seven Motifs" set forth a roadmap of essential methods for the field of scientific computing, where a motif is an algorithmic method that captures a pattern of computation and data movement. We present the "Nine Motifs of Simulation Intelligence", a roadmap for the development and integration of the essential algorithms necessary for a merger of scientific computing, scientific simulation, and artificial intelligence. We call this merger simulation intelligence (SI), for short. We argue the motifs of simulation intelligence are interconnected and interdependent, much like the components within the layers of an operating system. Using this metaphor, we explore the nature of each layer of the simulation intelligence operating system stack (SI-stack) and the motifs therein: (1) Multi-physics and multi-scale modeling; (2) Surrogate modeling and emulation; (3) Simulation-based inference; (4) Causal modeling and inference; (5) Agent-based modeling; (6) Probabilistic programming; (7) Differentiable programming; (8) Open-ended optimization; (9) Machine programming. We believe coordinated efforts between motifs offers immense opportunity to accelerate scientific discovery, from solving inverse problems in synthetic biology and climate science, to directing nuclear energy experiments and predicting emergent behavior in socioeconomic settings. We elaborate on each layer of the SI-stack, detailing the state-of-art methods, presenting examples to highlight challenges and opportunities, and advocating for specific ways to advance the motifs and the synergies from their combinations. Advancing and integrating these technologies can enable a robust and efficient hypothesis-simulation-analysis type of scientific method, which we introduce with several use-cases for human-machine teaming and automated science.

cs.AI↗