We report experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity (0.99998 ± 0.00003), requires only a single microwave drive tone for near-ideal performance, functions across the entire C-band (1530-1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits we implement a 3 × 3 extension of the Hadamard gate: the balanced tritter. This tritter-the first ever demonstrated for frequency modes-attains fidelity 0.9989 ± 0.0004. These gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding.Introduction.-The coherent translation of quantum states from one frequency to another via optical nonlinearites has been the focus of considerable research since the early 1990s [1]; yet only fairly recently have such processes been explored in the more elaborate context of time-frequency quantum information processing (QIP), where optical frequency is not just the carrier of quantum information but the information itself. Important examples include the quantum pulse gate [2,3], which uses nonlinear mixing with shaped classical pulses for selective conversion of the time-frequency modes of single photons [4][5][6], and demonstrations of frequency beamsplitters based on both χ (2) [7,8] and χ (3) [9][10][11] nonlinearities, which interfere two wavelength modes analogously to a spatial beamsplitter. These seminal experiments have shown key primitives in frequency-based QIP, but many challenges remain. For example, optical filters and/or low temperatures are required to remove background noise due to powerful optical pumps, either from the sources themselves or Raman scattering in the nonlinear medium. And achieving the necessary nonlinear mixing for arbitrary combinations of modes will require additional pump fields, as well as properly engineered phase-matching conditions.Recently we proposed a fundamentally distinct platform for frequency-bin manipulations, relying on electrooptic phase modulation and Fourier-transform pulse shaping for universal QIP [12]. Our approach requires no optical pump fields, is readily parallelized, and scales well with the number of modes. In this Letter, we apply this paradigm to experimentally demonstrate the first electro-optic-based frequency beamsplitter. Our frequency beamsplitter attains high fidelity, operates in * lougovskip@ornl.gov parallel on multiple two-mode subsets across the entire optical C-band, and retains excellent performance at the single-photon level. Moreover, by incorporating an additional harmonic in the microwave drive signal, we also realize a balanced frequency tritter, the threemode extension of the beamsplitter. This is the first frequency tritter demonstrated on any platform, and establishes our electro...

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has been co-authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

The realization of strong photon-photon interactions has presented an enduring challenge across photonics, particularly in quantum computing, where two-photon gates form essential components for scalable quantum information processing (QIP) [1]. While linear-optic schemes have enabled probabilistic entangling gates in spatio-polarization encoding [2,3], solutions for many other useful degrees of freedom remain missing. In particular, no two-photon gate for the important platform of frequency encoding [4][5][6][7] has been experimentally demonstrated, due in large part to the additional challenges imparted by the mismatched wavelengths of the interacting photons. In this article, we design and implement the first entangling gate for frequency-bin qubits, a coincidence-basis controlled-NOT (CNOT), using line-by-line pulse shaping and electro-optic modulation. We extract a quantum gate fidelity of 0.91 ± 0.01 via a novel parameter inference approach based on Bayesian machine learning, which enables accurate gate reconstruction from measurements in the two-photon computational basis alone. Our CNOT imparts a single-photon frequency shift controlled by the frequency of another photon-an important capability in itself-and should enable new directions in fiber-compatible QIP.arXiv:1809.05072v1 [quant-ph]

The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms. Currently most implementations of the PEA are based on qubits, where the computational units in the quantum circuits are 2D states. Performing quantum computing tasks with higher dimensional states—qudits —has been proposed, yet a qudit‐based PEA has not been realized. Using qudits can reduce the resources needed for achieving a given precision or success probability. Compared to other quantum computing hardware, photonic systems have the advantage of being resilient to noise, but the probabilistic nature of photon–photon interaction makes it difficult to realize two‐photon controlled gates that are necessary components in many quantum algorithms. In this work, an experimental realization of a qudit‐based PEA on a photonic platform is reported, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. The controlled‐unitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. This first implementation of a qudit PEA, on any platform, successfully retrieves any arbitrary phase with one ternary digit of precision.