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Photonics for Quantum (PfQ)

A simulation methodology for quantum photonic integrated circuits in the presence of fabrication imperfections, loss, and partially distinguishable photons

Sebastian Gitt, Božidar Novaković, Dylan McGuire, Jeff F. Young

Published Jul 19, 2023• 1 citation
Publisher

Abstract

Discrete variable quantum photonic circuits rely on the interference between indistinguishable photons to produce non-classical results. However, indistinguishability between photons is often spoiled due to timing delays, different spectral profiles, or the presence of unwanted spectral correlations. Additionally, variability in circuit components can introduce further errors. Here we present a method for simulating the frequency domain response of quantum photonic integrated circuits (PICs), allowing the fidelity and probability of success of realistic quantum circuits to be characterized. As an example, we first model the biphoton wavefunction produced by spontaneous four-wave mixing in a silicon nitride microring resonator, then use our methodology to simulate the interference between heralded signal photons from two such sources in the presence of spectral correlations and circuit component variability due to manufacturing imperfections.

DOI
10.1117/12.2675954

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•Dec 7, 2016•0 citations
Discrete variable quantum photonic circuits rely on the interference between indistinguishable photons to produce non-classical results. However, indistinguishability between photons is often spoiled due to timing delays, different spectral profiles, or the presence of unwanted spectral correlations. Additionally, variability in circuit components can introduce further errors. Here we present a method for simulating the frequency domain response of quantum photonic integrated circuits (PICs), allowing the fidelity and probability of success of realistic quantum circuits to be characterized. As an example, we first model the biphoton wavefunction produced by spontaneous four-wave mixing in a silicon nitride microring resonator, then use our methodology to simulate the interference between heralded signal photons from two such sources in the presence of spectral correlations and circuit component variability due to manufacturing imperfections.
Quantum photonic devices are typically based on either discrete variable (DV) or continuous variable (CV) principles. In either case, their performance must meet strict “fidelity” requirements, especially when scaled using integrated photonic circuitry. DV devices must be robust to imperfections such as timing delays between photons, unwanted spectral correlations present in photons from nonideal single photon sources and variations in circuit components. Furthermore, it becomes increasingly important to have a methodology for characterizing the performance of devices in the presence of such errors. Here, we present a method for simulating quantum photonic integrated circuits (PICs) and use it to model the behavior of a circuit constructed to model the evolution of a quantum state subject to a Bose-Hubbard Hamiltonian, introducing variations to the coupling gaps in the directional couplers inside the circuit. Input states consisting of both indistinguishable and distinguishable photons are modelled. Compact models for the directional couplers and other photonic circuit elements that are parameterized for a specific fabrication process can be incorporated into the circuit using a foundry-associated compact model library, ensuring consistency between circuit design and manufactured component. In CV applications, the degree of squeezing provided by some nonlinear element is often a key metric. Here we describe how the degree of squeezing produced by spontaneous four-wave mixing (SFWM) in a microring resonator can be modelled in the low-power limit, accounting for the effects of self-phase modulation (SPM), cross-phase modulation (XPM), and component losses.
The rapidly growing field of integrated photonic quantum computing has recently seen enormous breakthroughs, with integrated photonic devices capable of generating highly entangled states of photons on-chip. To scale these devices, simulation tools that model realistic sources and manufacturing imperfections are required when designing quantum building blocks that meet fidelity requirements and fault tolerance thresholds. To address this, we introduce a quantum circuit solver capable of calculating the heralded source biphoton wavefunction and corresponding frequency domain response of photonic integrated circuits in the Fock basis, yielding the fidelity of the output state and probability of success for a given measurement outcome.
Photonic integrated circuits (PICs) based on silicon-on-insulator (SOI) substrates provide a lightweight, compact platform for applications in quantum optics. We show the evaluation and characterization of an SOI-bascd PIC design for an entangled photon pair source, generating photon pairs by means of the nonlinear process of spontaneous four-wave mixing in microring resonators. Experimental results following from the chip fabrication fed back into the simulated parameter tuning effects, culminating in photon pair generation with measured correlations exceeding classically predicted limits.
Photonic integrated circuits offer a scalable and robust route toward quantum information technologies by consolidating photon sources and linear optical networks onto compact, wafer-manufacturable chips. Although silicon photonics has enabled diverse discrete-variable quantum breakthroughs -- spanning multiphoton entanglement, quantum networking, and photonic qubit fusion for quantum computing -- scaling these platforms beyond proof-of-principle demonstrations remains severely constrained by a critical system-level bottleneck. Optical loss compounds rapidly across photon generation, routing, and state analysis, causing multiphoton generation probabilities to plummet exponentially as circuit depth and complexity grow. Here we overcome this rate-loss barrier by demonstrating a monolithic, ultralow-loss silicon nitride (Si3_33​N4_44​) integrated photonic platform engineered for high-performance discrete-variable quantum information processing. Our architecture seamlessly integrates narrowband photon-pair sources with low-loss qubit-fusion circuits and reconfigurable state-analysis interferometers. The on-chip sources prepare Einstein-Podolsky-Rosen (EPR) states with a fidelity of 0.9875(3) and exhibit near-unity photon indistinguishability, yielding a heralded Hong-Ou-Mandel interference visibility of 0.990(6). By executing on-chip fusion of two EPR states, we synthesize and characterize four-photon Greenberger-Horne-Zeilinger states with a record fidelity of 0.943(8) and a fourfold count rate of 27 Hz -- more than two orders of magnitude higher than previous silicon-photonic implementations. Combined with standard CMOS-compatible fabrication on 150-mm-diameter wafers, these results establish ultralow-loss Si3_33​N4_44​ integrated photonics as a definitive, manufacturable platform for deployable, large-scale quantum information processors.
To understand quantum optics experiments, we must perform calculations that consider the principal sources of noise, such as losses, spectral impurity, and partial distinguishability. In both discrete and continuous variable systems, these can be modeled as mixed Gaussian states over multiple modes. The modes are not all resolved by photon-number measurements and so require calculations on coarse-grained photon-number distributions. Existing methods can lead to a combinatorial explosion in the time complexity, making this task unfeasible for even moderately sized experiments of interest. We prove that the computation of this type of distribution can be done in exponential time, providing a combinatorial speed-up. We develop numerical techniques that allow us to determine coarse-grained photon number distributions of Gaussian states, as well as density matrix elements of heralded non-Gaussian states prepared in the presence of spectral impurity and partial distinguishability. These results offer significant speed-up and accuracy improvements to validation tests of both Fock and Gaussian boson samplers that rely on binned probability distributions. Moreover, they pave the way to a more efficient simulation of realistic photonic circuits, unlocking the ability to perform exact calculations at scales that were previously out of reach. In addition, our results, including loop Hafnian master theorems, may be of interest to the fields of combinatorics and graph theory.
Quantum information processing relies on the fundamental property of quantum interference, where the quality of the interference directly correlates to the indistinguishability of the interacting particles. The creation of these indistinguishable particles, photons in this case, has conventionally been accomplished with nonlinear crystals and optical filters to remove spectral distinguishability, albeit sacrificing the number of photons. This research describes the use of an integrated aluminum nitride microring resonator circuit to selectively generate photon pairs at the narrow cavity transmissions, thereby producing spectrally indistinguishable photons. These spectrally indistinguishable photons can then be routed through optical waveguide circuitry, concatenated interferometers, to manipulate and entangle the photons into the desired quantum states. Photon sources and circuitry are only two of the three required pieces of the puzzle. The final piece which this research is aimed at interfacing with are trapped ion quantum memories, based on trapped Ytterbium ions. These ions serve as very long lived and stable quantum memories with storage times on the order of 10’s of minutes, compared with photonic quantum memories which are limited to 10-6 to 10-3 seconds. The caveat with trapped ions is the interaction wavelength of the photons is 369.5nm and therefore the goal of this research is to develop entangled photon sources and circuitry in that wavelength regime to interact directly with the trapped ions and bypass the need for frequency conversion.