Heralded high-dimensional photon–photon quantum gate

Strong coupling between light and matter is the foundation of promising quantum photonic devices such as deterministic single photon sources, single atom lasers, and photonic quantum gates, which consist of an atom and a photonic cavity. Unlike atom-based systems, a strong coupling unit based on an emitter-plasmonic nanocavity system has the potential to bring these devices to the microchip scale at ambient conditions. However, efficiently and precisely positioning a single or a few emitters into a plasmonic nanocavity is challenging. In addition, placing a strong coupling unit on a designated substrate location is a demanding task. Here, fluorophore-modified DNA strands are utilized to drive the formation of particle-on-film plasmonic nanocavities and simultaneously integrate the fluorophores into the high field region of the nanocavities. High cavity yield and fluorophore coupling yield are demonstrated. This method is then combined with e-beam lithography to position the strong coupling units on designated locations of a substrate. Furthermore, polariton energy under the detuning of fluorophore embedded nanocavities can fit into a model consisting of three sets of two-level systems, implying vibronic modes may be involved in the strong coupling. Our system makes strong coupling units more practical on the microchip scale and at ambient conditions and provides a stable platform for investigating fluorophore-plasmonic nanocavity interaction.

Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.

Abstract: This chapter explores the design and development of photonic processors for ultra-fast data processing in high-performance computing (HPC) environments. By leveraging light instead of electricity for computation, photonic processors offer significant advantages in terms of speed, bandwidth, and energy efficiency. The chapter covers advancements in photonic materials, device engineering, and optical interconnects that enable scalable photonic systems for real-world applications, including AI, machine learning, and quantum computing. Key topics include the integration of photonic processors with quantum communication networks, the role of photonic multiplexing in parallel data processing, and innovations such as all-optical neurons for neuromorphic computing. The chapter also addresses current challenges, including phase sensitivity and the development of photonic quantum gates, offering solutions for scaling photonic computing to meet the demands of HPC and quantum networks. Keywords: photonic processors, high-performance computing, ultra-fast data processing, optical interconnects, photonic materials, quantum communication, AI, machine learning, photonic multiplexing, neuromorphic computing, phase sensitivity, quantum gates, scalable systems.

Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.

We investigate the use of nanocrystal quantum dots as a versatile quantum bus element for preparing various quantum resources for use in photonic quantum technologies. The ability to Stark tune nanocrystal quantum dots allows an important degree of control over the cavity QED interaction. Using this property along with the bi-exciton transition, we demonstrate a photonic CNOT interaction between two logical photonic qubits comprising two cavity field modes each. We find the CNOT interaction to be a robust generator of photonic Bell states, even with relatively large bi-exciton losses. These results are discussed in light of the current state-of-the-art of both microcavity fabrication and recent advances in nanocrystal quantum dot technology. Overall, we find that such a scheme should be feasible in the near future with appropriate refinements to both nanocrystal fabrication technology and micro-cavity design. Such a gate could serve as an active element in photonic-based quantum technologies.

A high-fidelity source of identical single photons is essential for numerous\nquantum technologies such as quantum repeaters and optical quantum information\nprocessing. Hallmarks thereof are a near-unity single-photon purity, near-unity\nindistinguishability of consecutively emitted photons, and high brightness\nthrough a near-unity number of photons per time bin. In order to embed such\nsources in quantum networks, optical fiber integration is essential but\ncomplicated by cryogenic compatability and noise. Here we demonstrate a\nresonantly pumped, quantum dot (QD) based, transmission operated, single-mode\nfiber coupled single photon source with a purity of 97%, indistinguishability\nof 90%, and a brightness of 17%. This is achieved by deploying a unique\nmicropillar cavity design in a closed-cycle cryostat, which is operated using a\nthrough-fiber cross-polarization technique to remove the pump laser light from\nthe resonantly scattered single photons. These results pave the way for fully\nfiber integrated photonic quantum networks, as our technology is equally\napplicable for cavity-QED based photonic quantum gates.\n

The two or more degrees of freedoms (DOFs) of photon systems are very useful in hyperparallel photonic quantum computing to accomplish more quantum logic gate operations with less resource, and depress photonic dissipation noise in quantum information processing. We present some flexible and adjustable schemes for hybrid hyper-controlled-not (hyper-CNOT) gates assisted by low-Q cavities, on the two-photon systems in both the spatial-mode and the polarization DOFs. These hybrid spatial-polarization hyper-CNOT gates consume less quantum resource and are more robust against photonic dissipation noise, compared with the integration of two cascaded CNOT gates in one DOF. Besides, simultaneous counter-propagation of two photons economize extremely the operation time in the whole process of our schemes. Moreover, these quantum logic gates are more feasible for fast quantum operations in the weak-coupling region of the low-Q cavities with current experimental technology, which are much different from strong-coupling cases of the high-Q ones.

We propose a novel scheme for high fidelity photonic controlled phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of Rydberg blockade and optical cavities effectively enhances the optical non-linearity created by the strong Rydberg interaction and thereby reduces the requirements for photonic quantum gates. The resulting gate can be implemented with cavities of moderate finesse which allows for highly efficient processing of quantum information encoded in photons. As a particular example of this, we show how the gate can be employed to increase the communication rate of quantum repeaters based on atomic ensembles.

We present a simple technique to reduce the emission rate of higher-order photon events from pulsed spontaneous parametric down-conversion. The technique uses extra-cavity control over a mode locked ultrafast laser to simultaneously increase repetition rate and reduce the energy of each pulse from the pump beam. We apply our scheme to a photonic quantum gate, showing improvements in the non-classical interference visibility for 2-photon and 4-photon experiments, and in the quantum-gate fidelity and entangled state production in the 2-photon case.

Quantum dots in optical nanocavities are interesting as a test-bed for fundamental studies of light–matter interaction (cavity quantum electrodynamics, QED), as well as an integrated platform for information processing. As a result of the strong field localization inside sub-cubic-wavelength volumes, these dots enable very large emitter–field interaction strengths. In addition to their use in the study of new regimes of cavity QED, they can also be employed to build devices for quantum information processing, such as ultrafast quantum gates, non-classical light sources, and spin–photon interfaces. Beside quantum information systems, many classical information processing devices, such as lasers and modulators, benefit greatly from the enhanced light–matter interaction in such structures. This chapter gives an introduction to quantum dots, photonic crystal resonators, cavity QED, and quantum optics on this platform, as well as possible device applications.

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

The photon's frequency degree of freedom, being compatible with mature telecom infrastructure, offers large potential for the stable and controllable realization of photonic quantum processing applications such as the quantum internet. The Hong–Ou–Mandel effect, as a two‐photon interference phenomenon, serves as a central building block for such frameworks. A key element yet missing to enable meaningful frequency‐based implementations as well as scalability in the number of processed photons, is the demonstration of the Hong–Ou–Mandel effect between independently created photons of different frequencies. The experimental implementation of bosonic and fermionic frequency domain Hong–Ou–Mandel interference between independently generated single photons is reported here, with measured visibilities of 74.31% ± 3.56% and 86.44% ± 8.27%, respectively. This is achieved through a scalable photonic frequency circuit that creates two post‐selected pure single photons, which undergo frequency mixing at an electro‐optic phase modulator. The system is on‐the‐fly reconfigurable allowing to probe bosonic and fermionic Hong–Ou–Mandel interference in the same experimental setup. The work demonstrates the versatility of frequency domain processing and its scalability toward higher photon numbers, which enables new quantum gate concepts as well as the establishment of frequency‐based large‐scale quantum networks.

Quantum computers may offer significant computational advantages over classical counterparts, revolutionizing the technology landscape in the near future. When networked together, the advantage of quantum computing may be further amplified, and there may emerge innovative applications. Among various active explorations on distributed quantum computing, multiqubit quantum gates between distant networked quantum computers are of particular interest because they offer operational advantages of efficiency and fidelity. Here we report the first experimental demonstration of quantum teleportation for a Toffoli gate, which is a commonly used multiqubit quantum gate, across three spatially distributed parties within a photonic quantum network. Employing the Hofmann method, we estimate the fidelity of the teleported Toffoli gate to be at least 0.706 ± 0.131. This successful demonstration of the quantum teleportation of a Toffoli gate constitutes a critical step toward the ultimate realization of distributed quantum computation.

The unique success story of semiconductor physics and technology relies on the ability to highly integrate micro- and nanometer sized functional units on a single chip. Within the last few years single nanostructures, e.g., individual and coupled pairs of quantum dots and single molecules moved more and more into the focus of many research groups to study the exciting physics and to exploit their tremendous potential for device applications. The full advantage of their superior properties can be utilized if a controlled positioning or growth of the nanostructure inside a more complex device structure can be realized, thereby defining precise coupling between the microscopic nanostructure and the macroscopic periphery. single-photon sources coupled quantum-dot gates single quantum-dot tunneling diodes. electroluminescence of single electrically-driven molecules at room temperature controlling quantum-dot emission by integration of semiconductor nanomembranes onto piezoelectric actuators controlled coupling of individual self-assembled quantum dots to plasmonic nanoantennas quantum light emission of two lateral tunnel-coupled (In,Ga)As/GaAs quantum dots controlled by a tunable static electric field realization of vertically stacked and laterally ordered InP and InAs quantum dots for quantum gate applications development of site-controlled SiGe islands on patterned Si(001) and realization of tunneling diodes ultrafast transient reflection spectroscopy of a single self-assembled GaAs quantum dot. We hope that this collection of ideas and results of controlled positioning of single nanostructures stimulates many fascinating experiments and clever applications of quantum objects. We wish to thank all people involved in the research group for their excellent work, the DFG for the financial support and Wiley for the opportunity to publish this volume. On behalf of all applicants being funded by DFG over the years, M. Lippitz and P. Michler Stuttgart, March 2012