High-dimensional optical quantum logic in large operational spaces

Imany, Poolad; Jaramillo-Villegas, José A.; Alshaykh, Mohammed S.; Lukens, Joseph M.; Odele, Ogaga D.; Moore, Alexandria J.; Leaird, Daniel E.; Qi, Minghao; Weiner, Andrew M.

doi:10.1038/s41534-019-0173-8

Cited by 125 publications

(71 citation statements)

References 62 publications

(75 reference statements)

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“…Recent development on photonic qudit-based quantum computing [11] provides a good test bed for our qudit RB. We suggest that quantum optics will provide a good test by exploiting different photonic degrees of freedom, for example orbital angular-momentum [16], frequency [46,47], and time [47].…”

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confidence: 99%

Randomized benchmarking for qudit Clifford gates

Jafarzadeh

Sanders

et al. 2020

New J. Phys.

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We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending singleand multi-qubit URB to single-and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications.Quantum computing and quantum communication typically focuse on quantum information encoded and processed with quantum bit (qubit) strings, but replacing qubits by higher-dimensional qudit strings [1,2] can be advantageous [3] for quantum simulation [4], quantum algorithms [5-7], quantum error correction [8-10], universal optics-based quantum computation [11], quantum communication [12, 13] and fault-tolerant quantum computation [14, 15]. Qudit quantum-information process could reduce space requirements and exploit natural properties such as orbital angular momentum for photons [16], superconductors [4] and neutral atoms [17]. Specifically, quantum computing on higher-dimensional systems can be more efficient than on qubits [7,14,18]. Ultimate success of quantum computing, both qubitand qudit-based, depends on being scalable, which, in turn, requires components meeting fault-tolerance conditions [19].Unitary-gate randomized benchmarking (URB) is the preferred technique to characterize unitary-gate performance due to its efficiency [20,21], which is robust against state-preparation-and-measurement (SPAM) errors and exponentially superior to the alternative of quantum process tomography (QPT) [22,23]. URB estimates average fidelity between real and ideal implementation of all 24 Clifford gates in C 2 , which normalizes the Pauli group

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confidence: 99%

Randomized benchmarking for qudit Clifford gates

Jafarzadeh

Sanders

et al. 2020

New J. Phys.

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“…For Step (i) we choose to work with frequency and time DoF in photons, since we can take advantage of their inherent high dimensionality to encode more quantum information in a single qudit. For example, our group has recently demonstrated a two‐photon four‐party GHZ state by encoding two 32 dimensional qudits in each photon . In addition, the recipe of constructing high‐dimensional quantum gate, though still relatively limited, has been proposed and experimentally realized on both time‐bin and frequency‐bin platforms.…”

Section: Discussionmentioning

confidence: 99%

“…Indeed, several benefits of qudits, including higher information coding capacity, stronger non‐locality, and enhanced security, have been proposed . Various techniques have demonstrated the required hardware to generate and process qudits by utilizing different degrees of freedom (DoFs) in photons, including orbital angular momentum, time‐bin, frequency‐bin, and hybrid time‐frequency bin encoding . Performing quantum simulation and computation with qudits have also been proposed, but the implementation of a functional quantum algorithm (such as PEA) has not yet been realized on any qudit‐based platform.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we experimentally realize a proof‐of‐principle qudit‐based PEA on a photonic platform by encoding two qutrits in a single photon, where the frequency DoF carries one qutrit as the control register, and the time DoF carries another qutrit as the target register. By working with two DoFs in a photon, the controlled‐unitary operation required by the PEA is realized within a single photon, thus circumventing the undesirable, probabilistic photon‐photon interaction . Our qutrit‐based implementation is tested on diagonal 3 × 3 unitary matrices.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Phase Estimation with Time‐Frequency Qudits in a Single Photon

Alshaykh

et al. 2019

Adv Quantum Tech

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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.

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“…This makes a BS-FWM frequency beam splitter (FBS) compatible with the typical free spectral range (FSR) of integrated microresonators and also with dense wavelength division multiplexing (DWDM) components aligned to the ITU grid. Previously, EOMs have been used in combina-tion with integrated sources to generate high-dimensional time-frequency entangled states [28][29][30]. Together with pulse shaping and bulk single-photon sources, EOMs have also been used to create frequency-bin entangled states and to demonstrate two-photon HOM-type interference with modes separated by up to 25 GHz [31][32][33][34][35][36][37].…”

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confidence: 99%

Frequency-Domain Quantum Interference with Correlated Photons from an Integrated Microresonator

et al. 2020

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Frequency encoding of quantum information together with fiber and integrated photonic technologies can significantly reduce the complexity and resource requirements for realizing all-photonic quantum networks. The key challenge for such frequency domain processing of single photons is to realize coherent and selective interactions between quantum optical fields of different frequencies over a range of bandwidths. Here, we report frequency-domain Hong-Ou-Mandel interference with spectrally distinct photons generated from a chip-based microresonator. We use four-wave mixing to implement an active 'frequency beam-splitter' and achieve interference visibilities of 0.95 ± 0.02. Our work establishes four-wave mixing as a tool for selective high-fidelity two-photon operations in the frequency domain which, combined with integrated single-photon sources, provides a building block for frequency-multiplexed photonic quantum networks.

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High-dimensional optical quantum logic in large operational spaces

Cited by 125 publications

References 62 publications

Randomized benchmarking for qudit Clifford gates

Randomized benchmarking for qudit Clifford gates

Quantum Phase Estimation with Time‐Frequency Qudits in a Single Photon

Frequency-Domain Quantum Interference with Correlated Photons from an Integrated Microresonator

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