arXiv subjects

Daniel Soh

Publications and source records attributed to Daniel Soh.

At least 19 recordsLinked to original sources

arXiv2026

A charge selection rule fixes what a squeezed-light reservoir computer can compute and afford

Reading an optical quantum reservoir costs repetitions growing super-exponentially with feature order: what it can afford is set by its detector, not its optics. For reservoirs encoding data in a parametric pump's phase, one conservation law fixes what is readable and what it costs. Pairwise photon exchange conserves an integer phase charge: across an ensemble of input masks, order-D readout reaches exactly the assemblies of at most D unit-charge kernels; degree-one homodyne readout is universal for fading-memory functionals along weak-squeezing families, at shot cost polynomial in accuracy; and at fixed squeezing no finite degree reaches every sector, at a computable distance. Nonlinearity sits in the optics, not the detector, whose per-shot variance is fixed at every order. In a hardware-faithful digital twin-no device was built-the rule is visible: on an open RF corpus a displacement-encoded control at identical photon number loses 17.7 accuracy points, as the charge algebra predicts.

quant-ph↗

arXiv2026

A Single Atom in Front of a Mirror is a Universal Reservoir Computer

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

quant-ph↗

arXiv2026

Computational Superiority of Non-Markovian Kerr Feedback in Continuous-Variable Quantum Reservoir Computing

A linear optical medium can delay, mix, and superpose light, but never make two pulses multiply: multiplication is nonlinear, and a linear system has no such operation. This roots a sharp limit on continuous-variable quantum reservoir computers (QRCs) built from Gaussian optics. Within the reservoir they cannot form genuine products of the input at different past times, the cross-time nonlinear correlations many temporal computations require; they can only fake them by storing each past input separately and multiplying in the readout, forcing an exponentially harder high-order measurement. We show that a single Kerr (intensity-dependent phase) element in a time-delayed feedback loop removes this limit. The Kerr effect makes phase depend on intensity, a true multiplication inside the medium; feedback makes the light revisit that element repeatedly, so one mode mixes its own history against itself once per round-trip. Feedback turns time into space: D passes through one nonlinear mode replace D parallel linear modes. We prove an unbounded resource separation (Theorem 3, Corollary 2): an N-mode Gaussian reservoir reaches cross-time nonlinear rank at most 2N, a hardware ceiling, while a single Kerr mode reaches rank equal to its feedback depth D, costing no extra modes. For every N, one Kerr mode performs a computation no N-mode linear reservoir can. Loss is the counterintuitive ingredient: each round-trip dims the light, so the nonlinear phase differs pass to pass, giving every echo its own fingerprint; without loss the passes would be redundant. We confirm activation on an exact open-system simulation and ground the separation in nonlinear channel equalization. Achievable D is 30 to 230 on integrated platforms, so one nonlinear mode replaces up to about 100 linear ones, at the price of measurement time.

quant-ph↗

arXiv2025

Quantum optical neural networks using atom-cavity interactions to provide all-optical nonlinearity

Optical neural networks (ONNs) have been developed to enhance processing speed and energy efficiency in machine learning by leveraging optical devices for nonlinear activation and establishing connections among neurons. In this work, we propose a quantum optical neural network (QONN) that utilizes atom-cavity neurons with controllable photon absorption and emission. These quantum neurons are designed to replace the electronic components in ONNs, which typically introduce delays and substantial energy consumption during nonlinear activation. To evaluate the performance of the QONN, we apply it to the MNIST digit classification task, considering the effects of photon absorption duration, random atom-cavity detuning, and stochastic photon loss. Additionally, we introduce a convolutional QONN to facilitate a real-world satellite image classification (SAT-6) task. Due to its compact hardware and low power consumption, the QONN offers a promising solution for real-time satellite sensing, reducing communication bandwidth with ground stations and thereby enhancing data security.

quant-ph↗

arXiv2025

Quantum-Limited Acoustoelectric Amplification in a Piezoelectric-2DEG Heterostructure

We provide a quantum mechanical description of phonon amplification in a heterostructure consisting of a two-dimensional electron gas (2DEG) stacked on top of a piezoelectric material. An applied drift voltage effectively creates a population inversion in the momentum states of the 2DEG electrons, giving rise to spontaneous emission of phonons. Once an acoustic wave is launched, the pumped electrons release phonons via stimulated emission, returning to depleted ground states before being pumped back to the excited states. We show that whereas efficient amplification using a 1D electron gas requires the acoustic wavelength to roughly equal the average electron-electron spacing, a 2DEG enables efficient amplification for any wavelength greater than the average electron-electron spacing. We derive the imaginary and real parts of the 2DEG first-order acoustic susceptibility as functions of electronic drift velocity in specific limits and derive the gain per unit length for the signal and the quantum noise, with the gain matching the classical result in the short-electronic-lifetime (low-mobility) regime. Moreover, we analyze the gain clamping due to pump depletion and calculate the maximum achievable intensity. Our results provide a framework for designing novel acoustic devices including a quantum phononic laser and phase-insensitive quantum phononic amplifiers.

cond-mat.mes-hall↗

arXiv2025

Optical Echo State Network Reservoir Computing

We propose an innovative design for an optical Echo State Network (ESN), an advanced type of reservoir computer known for its universal computational capabilities. Our design enables an optical implementation of arbitrary ESNs, featuring flexibility in optical matrix multiplication and nonlinear activation. Leveraging the nonlinear characteristics of stimulated Brillouin scattering (SBS), the architecture efficiently realizes measurement-free nonlinear activation. The approach significantly reduces computational overhead and energy consumption compared to traditional software-based methods. Comprehensive simulations validate the system's memory capacity, nonlinear processing strength, and polynomial algebra capabilities, showcasing performance comparable to software ESNs across key benchmark tasks. Our design establishes a feasible, scalable, and universally applicable framework for optical reservoir computing, suitable for diverse machine learning applications.

physics.optics↗

arXiv2024

Minimalistic and Scalable Quantum Reservoir Computing Enhanced with Feedback

Quantum Reservoir Computing (QRC) leverages quantum systems to perform complex computational tasks with exceptional efficiency and reduced energy consumption. We introduce a minimalistic QRC framework utilizing as few as five atoms in a single-mode optical cavity, combined with continuous quantum measurement. The system is conveniently scalable, as newly added atoms naturally couple with existing ones via the shared cavity field. To achieve high computational expressivity with a minimal reservoir, we include two critical elements: reservoir feedback and polynomial regression. Reservoir feedback modifies the reservoir's dynamics without altering its internal quantum hardware, while polynomial regression nonlinearly enhances output resolution. We demonstrate significant QRC performance in memory retention and nonlinear data processing through two tasks: predicting chaotic time-series data via the Mackey-Glass task and classifying sine-square waveforms. This framework fulfills QRC's objectives to minimize hardware size and energy consumption, marking a significant advancement in integrating quantum physics with machine learning technology.

quant-ph↗

arXiv2024

Optical Gottesman-Kitaev-Preskill qubit generation via approximate squeezed coherent state superposition breeding

Gottesman-Kitaev-Preskill (GKP) qubits, known for their exceptional error-correction capabilities, are highly coveted in quantum computing. However, generating optical GKP qubits has been a significant challenge. Measurement-based methods, where a portion of entangled squeezed vacuum modes are measured with photon number resolving detectors heralding a desired state in the undetected modes, have emerged as leading candidates for optical GKP qubit generation due their minimal resource requirements. While the current measurement-based methods can produce high-quality GKP qubits, they suffer from low success probabilities limiting experimental realization. The heart of the problem lies in the duality of photon number resolving measurements, being both the source of nonlinearity needed to generate quality GKP qubits and the component driving down their probability of successful production. Our method, breeding approximate squeezed coherent state superpositions created by generalized photon subtraction, overcomes this problem by supplementing two photon number resolving measurements with a single high success probability homodyne measurement. This scheme achieves success probabilities $\geq 10^{-5}$, two orders of magnitude higher than strictly photon number resolving measurement-based methods, while still producing states with high fidelity, possessing error-correction capabilities equivalent to up to a 10 dB squeezed GKP qubit. This breakthrough significantly advances the practical use of the optical GKP qubit encoding.

quant-ph↗

arXiv2024

Stochastic Reservoir Computers

Reservoir computing is a form of machine learning that utilizes nonlinear dynamical systems to perform complex tasks in a cost-effective manner when compared to typical neural networks. Many recent advancements in reservoir computing, in particular quantum reservoir computing, make use of reservoirs that are inherently stochastic. However, the theoretical justification for using these systems has not yet been well established. In this paper, we investigate the universality of stochastic reservoir computers, in which we use a stochastic system for reservoir computing using the probabilities of each reservoir state as the readout instead of the states themselves. In stochastic reservoir computing, the number of distinct states of the entire reservoir computer can potentially scale exponentially with the size of the reservoir hardware, offering the advantage of compact device size. We prove that classes of stochastic echo state networks, and therefore the class of all stochastic reservoir computers, are universal approximating classes. We also investigate the performance of two practical examples of stochastic reservoir computers in classification and chaotic time series prediction. While shot noise is a limiting factor in the performance of stochastic reservoir computing, we show significantly improved performance compared to a deterministic reservoir computer with similar hardware in cases where the effects of noise are small.

cs.LG↗

arXiv2024

Practical Few-Atom Quantum Reservoir Computing

Quantum Reservoir Computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum reservoir, consisting of only a few two-level atoms within an optical cavity. The system is inherently scalable, as newly added atoms automatically couple with the existing ones through the shared cavity field. We demonstrate that the quantum reservoir outperforms traditional classical reservoir computing in both memory retention and nonlinear data processing through two tasks, namely the prediction of time-series data using the Mackey-Glass task and the classification of sine-square waveforms. Our results show significant performance improvements with an increasing number of atoms, facilitated by non-destructive, continuous quantum measurements and polynomial regression techniques. These findings confirm the potential of QRC as a practical and efficient solution to addressing complex computational challenges in quantum machine learning.

quant-ph↗

arXiv2024

Error analysis in large area multi-Raman pulse atom interferometry due to undesired spontaneous decay

Despite the fact that atom interferometry has been a successful application of quantum sensing, a major topic of interest is the further improvement of the sensitivity of these devices. In particular, the area enclosed by the interferometer (which controls the sensitivity) can be increased by providing a larger momentum kick to the atom cloud, increasing the extent of the momentum axis. One such atom optics technique involves increasing the number of central $\pi-$Raman pulses. This technique, while providing the prerequisite additional momentum boost, also causes the atom to remain in the intermediate high energy state for longer periods of time. This additional length of time is often neglected in many treatments due to the adiabatic elimination of the higher energy state enabled by the large optical detuning. The increased time in the intermediate high energy state results in a higher probability of undesired spontaneous decay and a loss of quantum information, thereby adding error to the atom interferometer. In this work, we consider an open quantum system using the Lindblad master equation to devise a model for the atomic state dynamics that includes the undesired spontaneous decay from the intermediate high energy state. We formulate an error figure of merit to analyze limitations of an atom interferometer configured for acceleration measurements. Our theoretical results show the error figure of merit will be dominated by a $N_{R}^{-2}$ scaling factor for low numbers of $\pi-$Raman pulses, but will be dominated by a monotonic increase in error for high number of $\pi-$Raman pulses. We determined the number of $\pi$-Raman pulses that accomplishes maximal momentum transfer with a the minimal error, depending on major system parameters.

quant-ph↗

arXiv2024

Ab-Initio Calculations of Nonlinear Susceptibility and Multi-Phonon Mixing Processes in a 2DEG-Piezoelectric Heterostructure

Solid-state elastic-wave phonons are a promising platform for a wide range of quantum information applications. An outstanding challenge and enabling capability in harnessing phonons for quantum information processing is achieving strong nonlinear interactions between them. To this end, we propose a general architecture using piezoelectric-semiconductor heterostructures consisting of a piezoelectric acoustic material hosting phonon modes in direct proximity to a two-dimensional electron gas (2DEG). Each phonon in the piezoelectric material carries an electric field, which extends into the 2DEG. The fields induce polarization of 2DEG electrons, which in turn interact with other piezoelectric phononic electric fields. The net result is coupling between the various phonon modes. We derive, from first principles, the nonlinear phononic susceptibility of the system. We show that many nonlinear processes are strongly favored at high electron mobility, motivating the use of the 2DEG to mediate the nonlinearities. We derive in detail the first, second, and third-order susceptibilities and calculate them for the case of a lithium niobate surface acoustic wave interacting with a GaAs-AlGaAs heterostructure 2DEG. We show that, for this system, the strong third-order nonlinearity could enable single-phonon Kerr shift in an acoustic cavity that exceeds realistic cavity linewidths, potentially leading to a new class of acoustic qubit. We further show that the strong second-order nonlinearity could be used to produce a high-gain, traveling-wave parametric amplifier to amplify--and ultimately detect--the outputs of the acoustic cavity qubits. Assuming favorable losses in such a system, these capabilities, combined with the ability to efficiently transduce phonons from microwave electromagnetic fields in transmission lines, thus hold promise for creating all-acoustic quantum information processors.

physics.app-ph↗

arXiv2023

Improving the Performance of Echo State Networks Through State Feedback

Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks (ESNs), a type of reservoir computer, mirror neural networks but simplify training. They apply fixed, random linear transformations to the internal state, followed by nonlinear changes. This process, guided by input signals and linear regression, adapts the system to match target characteristics, reducing computational demands. A potential drawback of ESNs is that the fixed reservoir may not offer the complexity needed for specific problems. While directly altering (training) the internal ESN would reintroduce the computational burden, an indirect modification can be achieved by redirecting some output as input. This feedback can influence the internal reservoir state, yielding ESNs with enhanced complexity suitable for broader challenges. In this paper, we demonstrate that by feeding some component of the reservoir state back into the network through the input, we can drastically improve upon the performance of a given ESN. We rigorously prove that, for any given ESN, feedback will almost always improve the accuracy of the output. For a set of three tasks, each representing different problem classes, we find that with feedback the average error measures are reduced by $30\%-60\%$. Remarkably, feedback provides at least an equivalent performance boost to doubling the initial number of computational nodes, a computationally expensive and technologically challenging alternative. These results demonstrate the broad applicability and substantial usefulness of this feedback scheme.

cs.LG↗

arXiv2023

Fundamental limits to the generation of highly displaced bright squeezed light using linear optics and parametric amplifiers

High quality squeezed light is an important resource for a variety of applications. Multiple methods for generating squeezed light are known, having been demonstrated theoretically and experimentally. However, the effectiveness of these methods -- in particular, the inherent limitations to the signals that can be produced -- has received little consideration. Here we present a comparative theoretical analysis for generating a highly-displaced high-brightness squeezed light from a linear optical method -- a beam-splitter mixing a squeezed vacuum and a strong coherent state -- and parametric amplification methods including an optical parametric oscillator, an optical parametric amplifier, and a dissipative optomechanical squeezer seeded with coherent states. We show that the quality of highly-displaced high-brightness squeeze states that can be generated using these methods is limited on a fundamental level by the physical mechanism utilized; across all methods there are significant tradeoffs between brightness, squeezing, and overall uncertainty. We explore the nature and extent of these tradeoffs specific to each mechanism and identify the optimal operation modes for each, and provide an argument for why this type of tradeoff is unavoidable for parametric amplifier type squeezers.

quant-ph↗

arXiv2022

Label-free quantum super-resolution imaging using entangled multi-mode squeezed light

In this study, we explore the theoretical application of entangled multi-mode squeezed light for label-free optical super-resolution imaging. By generating massively entangled multi-mode squeezed light through an array of balanced beam splitters, using a single-mode squeezed light input, we create a multi-mode quantum light state with exceptional entanglement and noise suppression below the shot noise level. This significantly reduces imaging measurement errors compared to classical coherent state light imaging when the same number of photons are used on the imaging sample. We demonstrate how to optimize the imaging system's parameters to achieve the Heisenberg imaging error limit, taking into account the number of entangled modes and photons used. We also examine the effects of optical losses in the imaging system, necessitating adjustments to the optimized parameters based on the degree of optical loss. In practical applications, this new quantum imaging approach reduces the number of photons needed to achieve the same image quality by two orders of magnitude compared to classical imaging methods that use non-entangled, non-squeezed coherent state light.

quant-ph↗

arXiv2022

Ultra-High-Precision Detection of Single Microwave Photons based on a Hybrid System between Majorana Zero Mode and a Quantum Dot

The ability to detect single photons has become increasingly essential due to the rise of photon-based quantum computing. In this theoretical work, we propose a system consisting of a quantum dot (QD) side-coupled to a superconducting nanowire. The coupling opens a gap in both the QD mode and the Majorana zero mode (MZM) at the nanowire edge, enabling photon absorption in the system. We show that the absorbed photoelectron decays via rapid (sub-nanosecond to nanosecond) nonradiative heat transfer to the nanowire phonon modes rather than by spontaneous emission. Furthermore, we calculate the temperature increase and associated resistance increase induced by the absorption of a photon for a given appropriate set of material and environmental parameters, yielding a temperature increase in the millikelvin range and a resistance increase in the kiloohm range, vastly exceeding the photon-absorption-induced temperature and resistance increases for competing 2D-3D hybrid systems by 5 and 9 orders of magnitude, respectively. Lastly, we determine the detector efficiency and discuss the system density required for deterministic photon number measurement, demonstrating that a photon absorption probability of over 99.9 percent can be achieved for an integrated system consisting of an array of nanowire-QD complexes on-chip inside a cavity. Our results thus provide a basis for a deterministic microwave photon number detector with an unprecedented photon-number-detection resolution.

cond-mat.mes-hall↗

arXiv2021

Reconfigurable quantum phononic circuits via piezo-acoustomechanical interactions

We show that piezoelectric strain actuation of acoustomechanical interactions can produce large phase velocity changes in an existing quantum phononic platform: aluminum nitride on suspended silicon. Using finite element analysis, we demonstrate a piezo-acoustomechanical phase shifter waveguide capable of producing +/- pi phase shifts for GHz frequency phonons in 10s of microns with 10s of volts applied. Then, using the phase shifter as a building block, we demonstrate several phononic integrated circuit elements useful for quantum information processing. In particular, we show how to construct programmable multi-mode interferometers for linear phononic processing and a dynamically reconfigurable phononic memory that can switch between an ultra-long-lifetime state and a state strongly coupled to its bus waveguide. From the master equation for the full open quantum system of the reconfigurable phononic memory, we show that it is possible to perform "read" and "write" operations with over 90% quantum state transfer fidelity for an exponentially decaying pulse.

quant-ph↗

arXiv2021

Microwave response in a topological superconducting quantum interference device

Photon detection at microwave frequency is of great interest due to its application in quantum computation information science and technology. Herein are results from studying microwave response in a topological superconducting quantum interference device (SQUID) realized in Dirac semimetal Cd3As2. The temperature dependence and microwave power dependence of the SQUID junction resistance are studied, from which we obtain an effective temperature at each microwave power level. It is observed the effective temperature increases with the microwave power. This observation of microwave response may pave the way for single photon detection at the microwave frequency in topological quantum materials.

cond-mat.mtrl-sci↗