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arXiv:2201.10973 · Optics Express

High-dimensional discrete Fourier transform gates with a quantum frequency processor

Hsuan‐Hao Lu, Navin B. Lingaraju, Daniel E. Leaird, Andrew M. Weiner, Joseph M. Lukens

Published Mar 4, 2022• 33 citations
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Abstract

The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms such as frequency bins. In this article, we show that d-point frequency-bin DFTs can be realized with a fixed three-component quantum frequency processor (QFP), simply by adding to the electro-optic modulation signals one radio-frequency harmonic per each incremental increase in d. We verify gate fidelity F W > 0.9997 and success probability P W > 0.965 up to d = 10 in numerical simulations, and experimentally implement the solution for d = 3, utilizing measurements with parallel DFTs to quantify entanglement and perform tomography of multiple two-photon frequency-bin states. Our results furnish new opportunities for high-dimensional frequency-bin protocols in quantum communications and networking.

DOI
10.1364/oe.454677

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The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms such as frequency bins. In this article, we show that d-point frequency-bin DFTs can be realized with a fixed three-component quantum frequency processor (QFP), simply by adding to the electro-optic modulation signals one radio-frequency harmonic per each incremental increase in d. We verify gate fidelity F W > 0.9997 and success probability P W > 0.965 up to d = 10 in numerical simulations, and experimentally implement the solution for d = 3, utilizing measurements with parallel DFTs to quantify entanglement and perform tomography of multiple two-photon frequency-bin states. Our results furnish new opportunities for high-dimensional frequency-bin protocols in quantum communications and networking.
Classical optical frequency combs have revolutionized a myriad of fields, from optical spectroscopy and optical clocks to arbitrary microwave synthesis and lightwave communication. Capitalizing on the inherent robustness and high dimensionality of this mature optical platform, their nonclassical counterparts, so-called “quantum frequency combs,” have recently begun to display significant promise for fiber-compatible quantum information processing (QIP) and quantum networks. In this review, the basic theory and experiments of frequency-bin QIP, as well as perspectives on opportunities for continued advances, will be covered. Particular emphasis is placed on the recent demonstration of the quantum frequency processor (QFP), a photonic device based on electro-optic modulation and Fourier-transform pulse shaping that is capable of realizing high-fidelity quantum frequency gates in a parallel, low-noise fashion.
Frequency-encoded quantum information offers intriguing opportunities for quantum communications and networking, with the quantum frequency processor paradigm—based on electro-optic phase modulators and Fourier-transform pulse shapers—providing a path for scalable construction of quantum gates. Yet all experimental demonstrations to date have relied on discrete fiber-optic components that occupy significant physical space and impart appreciable loss. In this article, we introduce a model for the design of quantum frequency processors comprising microring resonator-based pulse shapers and integrated phase modulators. We estimate the performance of single and parallel frequency-bin Hadamard gates, finding high fidelity values that extend to frequency bins with relatively wide bandwidths. By incorporating multi-order filter designs as well, we explore the limits of tight frequency spacings, a regime extremely difficult to obtain in bulk optics. Overall, our model is general, simple to use, and extendable to other material platforms, providing a much-needed design tool for future frequency processors in integrated photonics.
Frequency-bin qubits possess unique synergies with wavelength-multiplexed lightwave communications, suggesting valuable opportunities for quantum networking with the existing fiber-optic infrastructure. Although the coherent manipulation of frequency-bin states requires highly controllable multi-spectral-mode interference, the quantum frequency processor (QFP) provides a scalable path for gate synthesis leveraging standard telecom components. Here we summarize the state of the art in experimental QFP characterization. Distinguishing between physically motivated “open box” approaches that treat the QFP as a multiport interferometer, and “black box” approaches that view the QFP as a general quantum operation, we highlight the assumptions and results of multiple techniques, including quantum process tomography of a tunable beamsplitter—to our knowledge the first full process tomography of any frequency-bin operation. Our findings should inform future characterization efforts as the QFP increasingly moves beyond proof-of-principle tabletop demonstrations toward integrated devices and deployed quantum networking experiments.
Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.
Frequency-bin encoding has recently emerged as a powerful approach for photonic quantum information processing, offering high dimensionality, gate-parallelization, and compatibility with existing telecommunication infrastructure. However, its scalable deployment has so far been hindered by the lack of an integrated platform capable of unifying quantum state generation, coherent frequency mixing, and programmable spectral control.\\ Here, we report the first fully integrated quantum frequency processor, monolithically integrating on the same silicon photonic chip a microresonator-based biphoton quantum frequency comb source, a pump-rejection filter, high-speed phase modulators, and a four-channel, line-by-line pulse shaper. We demonstrate key functionalities, such as tunable frequency beamsplitters with success probabilities exceeding 94%94\%94% and fidelities above 99.9%99.9\%99.9%, as well as the ability to synthesize more general single-qubit gates. Finally, we generate and coherently manipulate high-dimensional frequency-bin entangled states entirely on chip, showcasing control over two-photon quantum walks and performing the first on-chip frequency-bin quantum state tomography of a Bell-state with a fidelity of 95.7(3)%95.7(3)\%95.7(3)%. By integrating all key functional elements on the same 4×7 mm24\times7\,\textrm{mm}^24×7mm2 chip, with the possibility of scaling to a larger number of modes, our work marks an important step toward large-scale frequency-domain photonic processors for both classical and quantum applications.