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IEEE Access

An Overlap-Integral Approach to Quantum Optical Simulation

R. A. Brewster, Gerald Baumgartner, Yanne K. Chembo

Published Jan 1, 2023• 1 citation
Publisher

Abstract

A technique for the simulation of multimode quantum optical interferometry and protocols in quantum communications is introduced. This technique is very efficient at simulating in the single-photon-counting regime. This works by treating the photons in the system as members of a multiphoton pulse and reducing the computation of measurable quantities to overlap integrals that may be precomputed and combined in a recursive algorithm. The simulation of a Mach-Zehnder interferometer and the Hong-Ou-Mandel effect are demonstrated using this technique. The results of these simulations perfectly agree with the theoretical results. Additionally, since the effects of the components in the system can be integrated into the quantum operators involved, the technique is agnostic to the components introduced into the system.

DOI
10.1109/access.2023.3255514

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A technique for the simulation of multimode quantum optical interferometry and protocols in quantum communications is introduced. This technique is very efficient at simulating in the single-photon-counting regime. This works by treating the photons in the system as members of a multiphoton pulse and reducing the computation of measurable quantities to overlap integrals that may be precomputed and combined in a recursive algorithm. The simulation of a Mach-Zehnder interferometer and the Hong-Ou-Mandel effect are demonstrated using this technique. The results of these simulations perfectly agree with the theoretical results. Additionally, since the effects of the components in the system can be integrated into the quantum operators involved, the technique is agnostic to the components introduced into the system.
We analyze the interference of individual photons in two overlapping Mach–Zehnder interferometers joined via a common beam splitter. We show how two kinds of interference effects—single-photon Mach–Zehnder interference and two-photon Hong–Ou–Mandel interference—interfere with one another, partially canceling each other out. This configuration illustrates how quantum effects can combine nontrivially and, moreover, emphasizes that quantum interference happens at measurement. This work can serve as a bridge to more advanced quantum mechanical concepts, such as testing the predictions of quantum mechanics vs local realism.
Abstract Quantum computers can efficiently simulate quantum systems evolving according to local interactions, making them valuable for exploring quantum many-body dynamics, despite current hardware and algorithmic challenges. In this work, we address the digital quantum simulations of linear optical elements which are inherently bosonic quantum systems. We adopt an encoding scheme based on Gray code to map bosonic states to qubits, which is efficient in terms of qubits and gate counts. Using a beam splitter as a representative example, we demonstrate the construction of quantum algorithms to simulate linear optical elements in quantum computers. To validate our algorithm, we performed a digital quantum simulation of the Hong-Ou-Mandel interference, a two-photon experiment. Our simulations, conducted both in quantum simulators and IBM quantum hardwares, successfully reproduced the characteristics of Hong-Ou-Mandel interference, validating our approach.
Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.
Mach–Zehnder interferometers are commonly introduced in quantum mechanics instruction because they can be represented as two-state systems. With the availability of quantum computers in the cloud, we show how one can also simulate these experiments as perfect single-photon experiments, via quantum computer circuits. This simulation provides a great opportunity to bring quantum computation and single-quantum experiments into the physics classroom and to teach quantum computing via simulation rather than computer science-based algorithms.
Avalanche diodes (ADs) are widely used to count photons in quantum interferometry. In reality they do not count photons, but click once when a bunch of photons arrives in a light pulse. We model this behavior in typical quantum optical interferometers like the Hong-Ou-Mandel beam splitter and the Mach-Zehnder interferometer, and compare it with the behavior of the photon-number-resolving (PNR) detector and the Hanbury-Brown-Twiss detector in these measuring devices. Our results show that quantum interferometric measurements with biphotons could be performed with single ADs, if the noise of the diodes could be reduced. Even a single PNR detector can be used in these interferometers, if the variance of the measurement is determined, since it reveals information about biphoton interference in contrast to the single detector counting rate.