arXiv subjects

David S. Simon

Publications and source records attributed to David S. Simon.

At least 19 recordsLinked to original sources

arXiv2026

Deterministic linear-optical computing with symmetry-based qubits

A particular type of linear optical multiport, the Grover four-port, has previously been shown to couple the spatial symmetry of a photon to its direction of travel. It is shown here that use of a nonstandard choice of qubit, based on symmetry, allows Grover four ports to act as compact, low-resource deterministic linear optical controlledNOTgates, with no post-selection or ancilla measurements required. This approach allows programmable devices, made from Grover multiports in combination with other standard optical components, that can implement multiple different one-, two-, and three-qubit gates, including the Fredkin and Toffoli gates.

quant-ph↗

arXiv2025

Strain sensitivity enhancement in a Grover-Michelson interferometer

The Michelson interferometric phase detection resolution can be enhanced by replacing conventional beam splitters with novel directionally unbiased four-port scatterers, such as Grover coins. We present a quantitative analysis of the noise-to-signal ratio of sideband frequencies generated by gravitational wave-induced phase perturbations in a Grover-Michelson interferometer (GMI). We discuss the principles of GMI signal enhancement and demonstrate how combining this configuration with additional light-recycling arrangements further enhances the performance.

quant-ph↗

arXiv2025

Next-generation interferometry with gauge-invariant linear optical scatterers

Measurement technology employing optical interference phenomena such as a fringe pattern or frequency shift has been evolving for more than a century. The systems are being designed better, and their components are being built better. But the major components themselves hardly change. Most modern interferometers rely on the same conventional set of components to separate the electromagnetic field into multiple beams, such as plate optics and beam-splitters. This naturally limits the design scope and thus the potential applicability and performance. However, recent investigations suggest that incorporating novel, higher-dimensional linear-optical splitters in interferometer design can lead to several improvements. In this work, we review the underlying theory of these novel optical scatterers and some demonstrated configurations with enhanced resolution. The basic principles of optical interference and optical phase sensing are discussed in tandem. Emphasis is placed on both familiar and unfamiliar scatterers, such as the maximally-symmetric Grover multiport, whose actions are left unchanged by certain gauge transformations. These higher-dimensional, gauge-invariant multiports embody a new class of building blocks which can tailor optical interference for metrology in unconventional ways.

physics.optics↗

arXiv2025

Scalar computational primitives with perturbative phase interferometry

We describe how weak phase modulations applied to classical coherent light in specially modified linear interferometers can be used to perform primitive computational tasks. Instead of encoding operations within a fixed unitary state, the operations are enacted by moving from one state to another. This harnesses the particular phase parametrization of an interferometer, allowing entirely linear optics to produce nonlinear operations such as division and powers. This is due to the nonlinear structure of the underlying phase parametrizations. The realized operations are approximate but can be made more accurate by decreasing the size of the input perturbations. For each operation, the inputs and outputs are changes in phase relative to a fixed bias point. The output phase is ultimately read out as a change in optical power.

physics.optics↗

arXiv2025

Grover-Sagnac interferometer

We demonstrate a nontraditional design of the Sagnac interferometer by replacing the commonly used beam splitter with a linear-optical Grover multiport. This substitution creates a pole at the origin of the device parameter space with an associated resonance in the output intensity. The structure of this resonance is dictated only by the non-reciprocal portion of the phase acquired in the Sagnac loop. This property directly results from adopting the more symmetric and higher-dimensional central scattering coin, and allows for a different approach to registering and detecting the non-reciprocal Sagnac phase. This parameter may be extracted from the width of a peak or dip in the interferogram instead of tracing small changes in power as in traditional Sagnac interferometry. We discuss how losses affect the system and potential metrological applications.

physics.optics↗

arXiv2024

Experimental demonstration of a Grover-Michelson interferometer

We present a low-resource and robust optical implementation of the four-dimensional Grover coin, a four-port linear-optical scatterer that augments the low dimensionality of a regular beam-splitter. While prior realizations of the Grover coin required a potentially unstable ring-cavity to be formed, this version of the scatterer does not exhibit any internal interference. When this Grover coin is placed in another system, it can be used for interferometry with a higher-dimensional set of optical field modes. In this case, we formed a Grover-Michelson interferometer, which results when the traditional beam-splitter of a Michelson interferometer is replaced with a four-port Grover coin. This replacement has been shown to remove a phase parameter redundancy in the original Michelson system, now allowing continuous tuning of the shape and slope of the interference pattern. We observed an intensity interferogram with $97\%$ visibility and a phase sensitivity more than an order of magnitude larger than a regular Michelson interferometer. Because this device is readily formed with nearly the same number of optomechanical resources as a Michelson interferometer, but can outperform it drastically in phase delay evaluation, it has a great potential to improve many interferometric sensing and control systems.

quant-ph↗

arXiv2024

Single-photon description of the lossless optical Y coupler

Using symmetry considerations, we derive a unitary scattering matrix for a three-port optical Y-coupler or Y-branch. The result is shown to be unique up to external phase shifts. Unlike traditional passive linear-optical one-way splitters, coupling light into the conventional output ports of the Y-coupler results in strong coherent back-reflections, making the device a hybrid between feed-forward devices like the beam splitter, which do not reverse the direction of light, and a recently considered class of directionally unbiased multiport scatterers (with dimension greater than two) which do. While the device could immediately find use as a novel scattering vertex for the implementation of quantum walks, we also design a few simple but nonetheless useful optical systems that can be constructed by taking advantage of the symmetry of the scattering process. This includes an interference-free, resource-efficient implementation of the Grover four-port and a higher-dimensional Fabry-Perot interferometer with tunable finesse. Symmetry-breaking generalizations are also considered.

quant-ph↗

arXiv2024

Exceptional points in SSH-like models with hopping amplitude gradient

The Su-Schrieffer-Heeger (SSH) system is a popular model for exploring topological insulators and topological phases in one dimension. Recent interest in exceptional points has led to re-examination of non-Hermitian generalizations of many physical models, including the SSH model. In such non-Hermitian systems, singular points called exceptional points (EPs) appear that are of interest for applications in super-resolution sensing systems and topological lasers. Here, a non-Hermitian and non-PT-symmetric variation of the SSH model is introduced, in which the hopping amplitudes are non-reciprocal and vary monotonically along the chain. It is found that, while the existence of the EPs is due to the nonreciprocal couplings, the number, position, and order of the EPs can all be altered by the addition of the hopping amplitude gradient, adding a new tool for tailoring the spectrum of a non-Hermitian system.

quant-ph↗

arXiv2024

Finite-element assembly approach of optical quantum walk networks

We present a finite-element approach for computing the aggregate scattering matrix of a network of linear coherent scatterers. These might be optical scatterers or more general scattering coins studied in quantum walk theory. While techniques exist for two-dimensional lattices of feed-forward scatterers, the present approach is applicable to any network configuration of any collection of scatterers. Unlike traditional finite-element methods in optics, this method does not directly solve Maxwell's equations; instead it is used to assemble and solve a linear, coupled scattering problem that emerges after Maxwell's equations are abstracted within the scattering matrix method. With this approach, a global unitary is assembled corresponding to one time step of the quantum walk on the network. After applying the relevant boundary conditions to this global matrix, the problem becomes non-unitary, and possesses a steady-state solution which is the output scattering state. We provide an algorithm to obtain this steady-state solution exactly using a matrix inversion, yielding the scattering state without requiring a direct calculation of the eigenspectrum. The approach is then numerically validated on a coupled-cavity interferometer example that possesses a known, closed-form solution. Finally, the method is shown to be a generalization of the Redheffer star product, which describes scatterers on one-dimensional lattices (2-regular graphs) and is often applied to the design of thin-film optics, making the current approach an invaluable tool for the design and validation of high-dimensional phase-reprogrammable optical devices and study of quantum walks on arbitrary graphs.

quant-ph↗

arXiv2024

Tunable linear-optical phase amplification

We combine lossless, phase-only transformations with fully-transmitting linear-optical scatterers to define the principle of linear-optical phase amplification. This enables a physical phase shift $ϕ$ to be nonlinearly mapped to a new space $γ(ϕ)$ using linear optics, resulting in a completely general and enhanced phase shifter that can replace any standard one. A particular phase amplifier is experimentally realized, allowing the phase enhancement parameter $dγ/dϕ$ to be continuously tuned. Placing this enhanced phase shifter in one arm of a Mach-Zehnder interferometer led to an intensity-phase slope more than twenty times steeper than what can be obtained with its unamplified counterpart.

physics.optics↗

arXiv2023

Enhanced-sensitivity interferometry with phase-sensitive unbiased multiports

Here we introduce interferometric devices by combining optical feedback (cavities) with unbiased multiports, which unlike traditional beam dividers, allow light to reflect back out of the port from which it originated. By replacing the traditional, directionally-biased beam-splitter in a Michelson interferometer with an unbiased multiport, the functional dependence of the scattering amplitudes changes. As a result, the derivative of transmittance with respect to an external phase perturbation can be made substantially large. This significantly enhances the resolution of phase measurement, and allows the phase response curves to be altered in real time by tuning an externally-controllable phase shift.

quant-ph↗

arXiv2022

Interferometry and higher-dimensional phase measurements using directionally unbiased linear optics

Grover multiports are higher-dimensional generalizations of beam splitters, in which input to any one of the four ports has equal probability of exiting at any of the same four ports, including the input port. In this paper, we demonstrate that interferometers built from such multiports have novel features. For example, when combined with two-photon input and coincidence measurements, it is shown that such interferometers have capabilities beyond those of standard beam-splitter-based interferometers, such as easily controlled interpolation between Hong-Ou-Mandel (HOM) and anti-HOM behavior. Further, it is shown that the Grover-based analog of the Mach-Zehnder interferometer can make three separate phase measurements simultaneously. By arranging the transmission lines between the two multiports to lie in different planes, the same interferometer acts as a higher-dimensional Sagnac interferometer, allowing rotation rates about three different axes to be measured with a single device.

quant-ph↗

arXiv2021

Controllable entangled state distribution in a dual-rail reconfigurable optical network

Reconfigurable distribution of entangled states is essential for operation of quantum networks connecting multiple devices such as quantum memories and quantum computers. We introduce new quantum distribution network architecture enabling control of the entangled state propagation direction using linear-optical devices and phase shifters and offering reconfigurable connections between multiple quantum nodes. The basic two-photon entanglement distribution scheme is first introduced to illustrate the principle of operation. The scheme is then extended to a network structure with increased number of spatial modes connecting potential end-users. We present several examples of controllable network configuration modifications using time-dependent phase shifters.

quant-ph↗

arXiv2020

Higher-dimensional Hong-Ou-Mandel effect and state redistribution with linear-optical multiports

We expand the two-photon Hong-Ou-Mandel (HOM) effect onto a higher-dimensional set of spatial modes and introduce an effect that allows controllable redistribution of quantum states over these modes using directionally unbiased linear-optical four-ports without post-selection. The original HOM effect only allows photon pairs to exit in two directions in space. But when accompanied by beam splitters and phase shifters, the result is a directionally controllable two-photon HOM effect in four spatial modes, with direction controlled by changing the phases in the system. This controllable quantum amplitude manipulation also allows demonstration of a "delayed" HOM effect by exploiting phase shifters in a system of two connected multiport devices. By this means, both spatial and temporal control of the propagation of the two-photon superposition state through a network can be achieved.

quant-ph↗

arXiv2020

Quantum-Clustered Two-Photon Walks

We demonstrate a previously unknown two-photon effect in a discrete-time quantum walk. Two identical bosons with no mutual interactions nonetheless can remain clustered together as they walk on a lattice of directionally-reversible optical four-ports acting as Grover coins; both photons move in the same direction at each step due to a two-photon quantum interference phenomenon reminiscent of the Hong-Ou-Mandel effect. The clustered two-photon amplitude splits into two localized parts, one oscillating near the initial point, and the other moving ballistically without spatial spread, in soliton-like fashion. But the two photons are always clustered in the same part of the superposition, leading to potential applications for transport of entanglement and opportunities for novel two-photon interferometry experiments.

quant-ph↗

arXiv2019

Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks

The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call "directionally-biased". Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated.

quant-ph↗

arXiv2018

Joint Entanglement of Topology and Polarization Enables Error-Protected Quantum Registers

Linear-optical systems can implement photonic quantum walks that simulate systems with nontrivial topological properties. Here, such photonic walks are used to jointly entangle polarization and winding number. This joint entanglement allows information processing tasks to be performed with interactive access to a wide variety of topological features. Topological considerations are used to suppress errors, with polarization allowing easy measurement and manipulation of qubits. We provide three examples of this approach: production of two-photon systems with entangled winding number (including topological analogs of Bell states), a topologically error-protected optical memory register, and production of entangled topologicallyprotected boundary states. In particular it is shown that a pair of quantum memory registers, entangled in polarization and winding number, with topologically-assisted error suppression can be made with qubits stored in superpositions of winding numbers; as a result, information processing with winding number-based qubits is a viable possibility.

quant-ph↗

arXiv2018

Experimental demonstration of a directionally-unbiased linear-optical multiport

All existing optical quantum walk approaches are based on the use of beamsplitters and multiple paths to explore the multitude of unitary transformations of quantum amplitudes in a Hilbert space. The beamsplitter is naturally a directionally biased device: the photon cannot travel in reverse direction. This causes rapid increases in optical hardware resources required for complex quantum walk applications, since the number of options for the walking particle grows with each step. Here we present the experimental demonstration of a directionally-unbiased linear-optical multiport, which allows reversibility of photon direction. An amplitude-controllable probability distribution matrix for a unitary three-edge vertex is reconstructed with only linear-optical devices. Such directionally-unbiased multiports allow direct execution of quantum walks over a multitude of complex graphs and in tensor networks. This approach would enable simulation of complex Hamiltonians of physical systems and quantum walk applications in a more efficient and compact setup, substantially reducing the required hardware resources.

quant-ph↗