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SPIE Quantum Technologies

Quantum photonic integrated circuits simulation tool for linear optical quantum computing gates

Argiris Ntanos, Giannis Giannoulis, Aristeidis Stathis, Dimitris Zavitsanos, H. Avramopoulos

Published Apr 5, 2024• 1 citation
Publisher

Abstract

This work presents a developed Wolfram Mathematica software tool based on the Quantum extension package. This tool is able to simulate the output state for any linear optical circuit based on Beam Splitters (BSs) and Phase Sifters (PSs) by using as input, quantum states of light. The input of the software is described via the use of photon number states capable of emulating Fock states or coherent states, whereas the output provides the probability of detecting a photon at each output port. This photonic circuit may include any number of linear optical elements, including beam splitters with variable splitting ratios, as well as phase shifters. By using the unitary transformation of any photonic circuit (e.g., photonic chip), the output states can be computed, and detection probabilities of the chip can be obtained. The unitary transformation of the Controlled NOT (CNOT) quantum gate through a linear optical layout is presented, validating the functionality of the proposed software tool. In conclusion, the proposed software aims to enable testing of simple photonic circuits in the quantum regime.

DOI
10.1117/12.3022597

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This work presents a developed Wolfram Mathematica software tool based on the Quantum extension package. This tool is able to simulate the output state for any linear optical circuit based on Beam Splitters (BSs) and Phase Sifters (PSs) by using as input, quantum states of light. The input of the software is described via the use of photon number states capable of emulating Fock states or coherent states, whereas the output provides the probability of detecting a photon at each output port. This photonic circuit may include any number of linear optical elements, including beam splitters with variable splitting ratios, as well as phase shifters. By using the unitary transformation of any photonic circuit (e.g., photonic chip), the output states can be computed, and detection probabilities of the chip can be obtained. The unitary transformation of the Controlled NOT (CNOT) quantum gate through a linear optical layout is presented, validating the functionality of the proposed software tool. In conclusion, the proposed software aims to enable testing of simple photonic circuits in the quantum regime.
Linear Optics Quantum Computing can be achieved by implementing a complete Silicon Photonic Integrated Circuit. This involves optimizing the layout and fabrication of photonic circuits tailored for quantum computing applications using linear optics principles. A prototype of this kind of circuit is the universal two-qubit Controlled-NOT gate. This scheme makes use of linear, coincidence basis gate that performs all the operations of a controlled-NOT gate and requires only single photons at the input. The key components in the photonic quantum circuit using the CNOT gate scheme are designed and simulated. Subsequently, the layouts for the chips incorporating the optimal parameters identified in simulations of all the components are designed.
ABSTRACT Unitary operations lie at the heart of quantum computing, enabling the manipulation of quantum states in a reversible and coherent manner. In photonic integrated circuits, these operations are realized using photonic waveguide architectures composed of passive beam splitters and reconfigurable phase shifters. This review provides an overview of photonic circuit architectures designed to implement unitary transformations. We examine various design strategies, material platforms, and the current state‐of‐the‐art in realizing high‐fidelity photonic unitaries. In addition, we explore the theoretical underpinnings of photon transport in such circuits, shedding light on the quantum behavior of light in unitary photonic systems. Finally, we introduce a simulation framework for modeling and analyzing these photonic networks, offering a practical tool for research and development in this rapidly growing field.
The first section of the work investigates light modes as a means of implementing optical qubits and qudits. The modes considered are polarization mode, path mode, transverse spatial mode, frequency mode, temporal bin-mode and temporal mode. Subsequently, mathematical model of linear optical elements like beam splitters (BS) and phase shifters are deduced and their capability of representing any single qubit optical gate is exposed. Finally Knill, Laflamme and Milburn (KLM) method of using linear optical elements to promote nonlinear operations based on nonlinear (nondeterministic) sign-flip gate (NS) is explained, and designs of two qubits conditional sign flip gate (c-z1/16) and CNOT gate, both based on KLM method, are demonstrated. So, universal set of quantum gates based on linear optics is possible.
This note reviews the model of computation generated by photonic circuits, comprising edges that are traversed by photons in a single time-bin and vertices given by idealised lossless beam splitters and phase shifters. The circuit model is abstracted as a representation of the symmetric monoidal category of unitary matrices on the bosonic Fock space of multimode photons. A diagrammatic language, designed to aid with the understanding and development of photonic algorithms, is presented that encapsulates the category properties of this representation. As demonstrations of the formalism, the boson sampling scheme and the protocol of Knill, Laflamme and Milburn are developed on the single-rail photonic computer, and a parity-based model for the qudit is investigated.
Linear optics is a promising physical architecture for the implementation of the quantum computing devices. The key element of the linear optical quantum computer is an optical circuit realizing the sequence of transformations defined by the required quantum algorithm. The most prominent approach is the reconfigurable integrated photonics which allows to miniaturize standard optical setups on the chosen integrated photonic platform. In this paper, we propose a universal linear-optical circuit design comprised of the series of multiport beamsplitters followed by the phaseshifting elements. The proposed unitary composer device can be straightforwardly implemented using standard integrated photonic technologies. We provide guidelines for appropriate multiport beamsplitter fabrication using integrated waveguide lattices. To exemplify the performance of the composer we provide the six-mode CNOT linear optical gate circuit design fitted to described interferometric circuit.
Boson sampling arising from multiphoton interference in linear-optical networks is a prominent non-universal model for quantum computation. Here, by encoding the multi-qubit state to bosonic Fock state, we present a scalable quantum-circuit framework for simulating boson sampling on a universal quantum computing platform. Beginning with balanced beam-splitter transformations on the single- and two-photon sectors, we derive equivalent quantum-circuit implementations and unify them within a common Hilbert-space representation using an ancilla-assisted encoding. This construction is then generalized to arbitrary interferometers by replacing each optical beam splitter with a repeating quantum-circuit unit that selectively acts only within the relevant local interference subspace, requiring N+1N+1N+1 qubits for a two-photon NNN-mode interferometer and a linear-overhead subspace-identification procedure. Using this framework, gate-based quantum circuit for a four-mode boson-sampling circuit is developed and experimentally implemented on a four-qubit gate-based photonic qubit system. The qubit framework for emulating boson sampling of n−n-n−photons in m−m-m−mode will be useful to solve a broad class of sampling complexity problem on a gate-based quantum computers.