Quantum frequency combs from chip-scale integrated sources are promising candidates for scalable and robust quantum information processing (QIP). However, to use these quantum combs for frequency domain QIP, demonstration of entanglement in the frequency basis, showing that the entangled photons are in a coherent superposition of multiple frequency bins, is required. We present a verification of qubit and qutrit frequency-bin entanglement using an on-chip quantum frequency comb with 40 mode pairs, through a two-photon interference measurement that is based on electro-optic phase modulation. Our demonstrations provide an important contribution in establishing integrated optical microresonators as a source for high-dimensional frequency-bin encoded quantum computing, as well as dense quantum key distribution.

The probabilistic nature of single-photon sources and photon-photon interactions encourages encoding as much quantum information as possible in every photon for the purpose of photonic quantum information processing. Here, by encoding highdimensional units of information (qudits) in time and frequency degrees of freedom using on-chip sources, we report deterministic two-qudit gates in a single photon with fidelities exceeding 0.90 in the computational basis. Constructing a two-qudit modulo SUM gate, we generate and measure a single-photon state with nonseparability between time and frequency qudits. We then employ this SUM operation on two frequency-bin entangled photons-each carrying two 32-dimensional qudits-to realize a four-party high-dimensional Greenberger-Horne-Zeilinger state, occupying a Hilbert space equivalent to that of 20 qubits. Although highdimensional coding alone is ultimately not scalable for universal quantum computing, our design shows the potential of deterministic optical quantum operations in large encoding spaces for practical and compact quantum information processing protocols.

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.

We investigate the time-frequency signatures of an on-chip biphoton frequency comb (BFC) generated from a silicon nitride microring resonator. Using a Franson interferometer, we examine, for the first time, the multifrequency nature of the photon pair source in a time entanglement measurement scheme; having multiple frequency modes from the BFC results in a modulation of the interference pattern. This measurement together with a Schmidt mode decomposition shows that the generated continuous variable energy-time entangled state spans multiple pair-wise modes. Additionally, we demonstrate nonlocal dispersion cancellation, a foundational concept in time-energy entanglement, suggesting the potential of the chip-scale BFC for large-alphabet quantum key distribution. © 2017 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited. Quantum information processing (QIP) promises to improve the security of our communications as well as to solve some algorithms with exponential complexity in polynomial time [1]. The fundamental unit of quantum information is based on a superposition of two states, the so-called qubit. It has been proposed to extend this concept to a superposition of many states (known as a high-dimensional state) for higher density information encodings, fault-tolerant quantum computing, and even for secure protocols in dense quantum key distribution.Entangled photon pairs have been demonstrated as one of the most promising platforms for implementing QIP systems. In recent years, generation of entangled photons on chip has gained attention because of its reduced cost and compatibility with semiconductor foundries [2][3][4][5]. Despite Biphoton Frequency Combs (BFC) have been generated using cavity-filtered broadband biphotons [6] and cavity-enhanced spontaneous parametric down conversion [7], it was only recently that on-chip microresonators have been used to generate entangled photons in the form of a BFC [8][9][10]. These demonstrations suggest the use of chip-scale sources for high-dimensional quantum processing [11][12][13]. However, studies such as [4, 9, 10] only focused on single sideband pairs-the multifrequency nature of their sources (important for high-dimensional quantum processing) was not explored. In this Letter, we present the first examination of the time-frequency signatures of an on-chip BFC generated from a silicon nitride microring resonator. Through Franson interferometry and a demonstration of nonlocal dispersion compensation, we are able to examine the multifrequency nature of our photon-pair source. Figure 1 is a depiction of our experimental setup. To generate our BFC, we use a tunable continuous-wave (CW) laser to pump a microring at the resonance located at the frequency ω p (λ p ∼ 1550.9 nm). Through spontaneous four-wave mixing process, two pump photons decay int...