Linear Optical Quantum Computing Research Articles

Quantum circuit mapping for universal and scalable computing in MZI-based integrated photonics.

Linear optical quantum computing (LOQC) offers a quantum computation paradigm based on well-established and robust technology and flexible environmental conditions following DiVincenzo's criteria. Within this framework, integrated photonics can be utilized to achieve gate-based quantum computing, defining qubits by path-encoding, quantum gates through the use of Mach-Zehnder interferometers (MZIs), and measurements through single-photon detectors. In particular, universal two-qubit gates can be achieved by suitable structures of MZIs together with post-selection or heralding. The most resource-efficient choice is given by the post-selected Controlled-Z (CZ) gate. However, this implementation is characterized by a design which has a non-regular structure and cannot be cascaded. This limits the implementation of large-scale LOQC. Starting from these issues, we suggest an approach to move toward a universal and scalable LOQC on the integrated photonic platform. First of all, choosing the post-selected CZ as a universal two-qubit gate, we extend the path-encoded dual-rail qubit to a triplet of waveguides, composed of an auxiliary waveguide and the pair of waveguides corresponding to the qubit basis states. Additionally, we introduce a swap photonic network that maps the regularly-labeled structure of the new path-encoded qubits to the structure needed for the post-selected CZ. We also discuss the optical swap gate that allows the connection of non-nearest neighbor path-encoded qubits. In this way, we can deterministically exchange the locations of the qubits and execute controlled quantum gates between any path-encoded qubits. Next, by truncating the auxiliary waveguides after any post-selected CZ, we find that it is possible to cascade this optical gate when it acts on different pairs that share only one qubit. Finally, we show the Bell state and the Greenberger-Horne-Zeilinger (GHZ) state generation circuits implementing the regular structure, the cascading procedure of post-selected CZ and the optical swap.

Basic study on linear optical quantum computers with liquid crystal devices

A basic experiment on 2-bit quantum calculations related to the Deutsch–Jozsa algorithm on a linear optical quantum computer using a liquid crystal (LC) device as a linear optical element was investigated. By controlling the phase of each of the two split laser beams and checking the number of photons at the output, it is possible to determine if the input bits are “not equal” or “not uniform.” The phase of the laser light was controlled using an LC device and a half-wave plate, and changes in the interference state of the output light and the number of photons were observed. The voltage application to the LC device is set at the input bit. As a result, the interference state changed according to the input bit, and changes in the number of photons were observed.

Gigahertz Detection Rates and Dynamic Photon-Number Resolution with Superconducting Nanowire Arrays.

Superconducting nanowire single-photon detectors (SNSPDs) have enabled the realization of several quantum optics technologies thanks to their high system detection efficiency (SDE), low dark counts, and fast recovery time. However, the widespread use of linear optical quantum computing, quasi-deterministic single-photon sources, and quantum repeaters requires even faster detectors that can also distinguish between different photon-number states. Here, we present an SNSPD array composed of 14 independent pixels, achieving an SDE of 90% in the telecommunications band. By reading each pixel of the array independently, we show detection of telecommunication photons at 1.5 GHz with 45% absolute SDE. We exploit the dynamic photon-number resolution of the array to demonstrate accurate state reconstruction for a wide range of light inputs, including operation with long-duration light pulses, as obtained with some cavity-based sources. We show two-photon and three-photon fidelities of 74% and 57%, respectively, which represent state-of-the-art results for fiber-coupled SNSPDs.

Splitting phonons: Building a platform for linear mechanical quantum computing

Linear optical quantum computing provides a desirable approach to quantum computing, with only a short list of required computational elements. The similarity between photons and phonons points to the interesting potential for linear mechanical quantum computing using phonons in place of photons. Although single-phonon sources and detectors have been demonstrated, a phononic beam splitter element remains an outstanding requirement. Here we demonstrate such an element, using two superconducting qubits to fully characterize a beam splitter with single phonons. We further use the beam splitter to demonstrate two-phonon interference, a requirement for two-qubit gates in linear computing. This advances a new solid-state system for implementing linear quantum computing, further providing straightforward conversion between itinerant phonons and superconducting qubits.

Quantum Light Source Based on Semiconductor Quantum Dots: A Review

Quantum light sources that generate single photons and entangled photons have important applications in the fields of secure quantum communication and linear optical quantum computing. Self-assembled semiconductor quantum dots, also known as “artificial atoms”, have discrete energy-level structures due to electronic confinement in all three spatial dimensions. It has the advantages of high stability, high brightness, deterministic, and tunable emission wavelength, and is easy to integrate into an optical microcavity with a high-quality factor, which can realize a high-performance quantum light source. In this paper, we first introduce the generation principles, properties, and applications of single-photon sources in the field of quantum information and then present implementations and development of quantum light sources in self-assembled semiconductor quantum dot materials. Finally, we conclude with an outlook on the future development of semiconductor quantum dot quantum light sources.

Linear Optical Quantum Computation with Frequency-Comb Qubits and Passive Devices.

We propose a linear optical quantum computation scheme using time-frequency degrees of freedom. In this scheme, a qubit is encoded in single-photon frequency combs, and manipulation of the qubits is performed using time-resolving detectors, beam splitters, and optical interleavers. This scheme does not require active devices such as high-speed switches and electro-optic modulators and is robust against temporal and spectral errors, which are mainly caused by the detectors' finite resolution. We show that current technologies almost meet the requirements for fault-tolerant quantum computation.

A Software Platform for Programmable Linear Optical Quantum Computer

A Software Platform for Programmable Linear Optical Quantum Computer

Исследование направленных ответвителей для реализации квантовых операций над кубитами

In this work, nanophotonic circuits with directional couplers are studied, which, along with phase shifters, are one of the main elements for creating circuits of a linear optical quantum computer. Directional couplers are two closely spaced waveguides, were made of silicon nitride. The subject of the study was the splitting ratio of directional couplers at a wavelength of 914 nm at room (300 K) and helium (3 K) temperatures. On the basis of experimental data, the coupling length at which all the power from one waveguide passes into another was extracted, and the refractive indices of silicon nitride at room (300 K) and helium temperatures (3 K) were found. The results of the work are of great importance in the design and manufacture of fully integrated quantum optical microcircuits with superconducting detectors operating at helium temperatures.

Spectrally-Pure Integrated Telecom-Band Photon Sources in Silicon

We demonstrate theoretically the direct (filter-free) generation of spectrally uncorrelated photon pairs, and consequently high-purity heralded single photons at telecommunication wavelengths, in SOI (silicon-on-insulator) nanowaveguides via spontaneous four-wave mixing (SFWM). The inherent strong waveguide dispersion in such high-index contrast structures is employed for discrete-band phase-matching in order to suppress the pair spectral correlations, and to produce photons in the fundamental spatial mode for easy in-out coupling to single-mode optical fibers. Additionally, by optimizing the source parameters like waveguide length, dispersion and pump bandwidth, the group-velocity of generated photons is also engineered to further eliminate spectral correlations. Extensive numerical mode simulations for various waveguide widths are used to design intrinsically pure photon sources via joint spectral amplitude (JSA) engineering. Purity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;$</tex-math></inline-formula> 95% is shown to be achievable in a silica-clad SOI waveguide with a cross-section 220 × 600 nm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> for typical values of length and pump bandwidth. The wavelength of these heralded single photons can be tuned in the range of 1266–1363 nm ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> O-band) by varying the pump wavelength. Considering the high accuracy provided by silicon nanofabrication techniques, the feasibility of generating single photons across the wavelength range 1333–1425 nm (E-band) and 1437–1510 nm (S-band) for slightly different waveguide widths (625 nm & 650 nm) is also demonstrated. These filter-free integrated photon sources could be important for large-scale linear optical quantum computation (LOQC) and long-distance fiber-optic quantum key distribution (QKD) networks.

All-Photonic Architecture for Scalable Quantum Computing with Greenberger-Horne-Zeilinger States

Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss. Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states. Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches and on-off detectors. We concatenate topological quantum error correction code with three-qubit repetition codes and estimate that our architecture can tolerate remarkably high photon-loss rate of $11.5 \%$; this makes a drastic change that is at least an order higher than those of known proposals. Further, considering three-photon GHZ states as resources, we estimate the resource overheads to perform gate operations with an accuracy of $10^{-6}~(10^{-15})$ to be $2.0\times10^6~(5.6\times10^7)$. Compared to other all-photonic schemes, our architecture is also resource-efficient. In addition, the resource overhead can be even further improved if larger GHZ states are available. Given its striking enhancement in the photon loss threshold and the recent progress in generating multiphoton entanglement, our scheme will make scalable photonic quantum computing a step closer to reality.

Geometrically robust linear optics from non-Abelian geometric phases

We construct a unified operator framework for quantum holonomies generated from bosonic systems. For a system whose Hamiltonian is bilinear in the creation and annihilation operators, we find a holonomy group determined only by a set of selected orthonormal modes obeying a stronger version of the adiabatic theorem. This photon-number independent description offers deeper insight as well as a computational advantage when compared to the standard formalism on geometric phases. In particular, a strong analogy between quantum holonomies and linear optical networks can be drawn. This relation provides an explicit recipe of how any linear optical quantum computation can be made geometrically robust in terms of adiabatic or nonadiabatic geometric phases.

非平衡光纤干涉仪的相位稳定方法研究

By using photons to carry quantum information, optical quantum information technology plays an essential role in quantum communication, quantum metrology, and linear optical quantum computing. In recent years, the unbalanced fiber interferometer has been widely applied in preparing, manipulating, and measuring photon qubits. However, the unbalanced fiber interferometer based on fiber devices is sensitive to the environment's thermal, mechanical, and acoustic noise. Thus, phase stabilization based on feedback control is essential in utilizing an unbalanced fiber interferometer. The existing phase stabilization methods typically employ a reference laser combined with optoelectronic detection, thus introducing additional noise to photon qubits. In this paper, we propose and demonstrate a feedback control method to stabilize a phase in an unbalanced fiber interferometer by combining weak coherent reference light and single photon counting. Using theoretical analysis, we realized the phase stabilization of an unbalanced fiber Michelson interferometer with an arm-length difference of about 1 m. The results showed that the jitter of the stabilized phase is less than 0.042 rad, while the visibility of single-photon interference fringes is higher than 99%.

Cavity quantum electrodynamics design with single photon emitters in hexagonal boron nitride

Hexagonal boron nitride (h-BN), a prevalent insulating crystal for dielectric and encapsulation layers in two-dimensional (2D) nanoelectronics and a structural material in 2D nanoelectromechanical systems, has also rapidly emerged as a promising platform for quantum photonics with the recent discovery of optically active defect centers and associated spin states. Combined with measured emission characteristics, here we propose and numerically investigate the cavity quantum electrodynamics scheme, incorporating these defect-enabled single photon emitters (SPEs) in h-BN microdisk resonators. The whispering-gallery nature of microdisks can support multiple families of cavity resonances with different radial and azimuthal mode indices simultaneously, overcoming the challenges in coinciding a single point defect with the maximum electric field of an optical mode both spatially and spectrally. The excellent characteristics of h-BN SPEs, including exceptional emission rate, considerably high Debye–Waller factor, and Fourier transform limited linewidth at room temperature, render strong coupling with the ratio of coupling to decay rates g/max(γ, κ) predicated as high as 500. This study not only provides insight into the emitter–cavity interaction, but also contributes toward realizing h-BN photonic components, such as low-threshold microcavity lasers and high-purity single photon sources, critical for linear optics quantum computing and quantum networking applications.

Scheme for Universal High-Dimensional Quantum Computation with Linear Optics.

Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise resilience. However, schemes to generate the resources required for high-dimensional quantum computing have so far been lacking in linear optics. Here, we show how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices. Combining our results with recent schemes for qudit Bell measurements, we show that universal linear optical quantum computing can be performed in arbitrary dimensions.

Simulation of High-Efficiency Resonant-Cavity-Enhanced GeSn Single-Photon Avalanche Photodiodes for Sensing and Optical Quantum Applications

Two novel resonant-cavity-enhanced (RCE) GeSn single-photon avalanche photodiode (SPAD) detectors are designed and simulated for high-efficiency single-photon detection at 1550 and 2000 nm wavelength at room temperature for sensing and optical quantum applications. The RCE GeSn SPAD consists of a PIPIN GeSn/Si heterostructures embedded in an optical cavity formed by a distributed Bragg reflector (DBR) and GeSn surface. The results show that high photon absorption efficiency and avalanche triggering probabilities can be achieved by careful design of DBR reflectors, GeSn absorber, doping concentrations of Si charge sheet layer and multiplication layer, which lead to a high single-photon detection efficiency (SPDE) of ~80%, which is promising for emerging quantum applications demanding high SPDE, such as linear optical quantum computing. The noise equivalent power (NEP) and dark count rate (DCR) as a function of threading dislocations density (TDD) are examined as well. It is found that the device could operate near room temperature with a similar DCR level to that of Ge SPAD operating at low temperature. A NEP of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 3\times 10^{-15}$ </tex-math></inline-formula> W/Hz <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{1/2}$ </tex-math></inline-formula> is observed from RCE GeSn SPAD for 1550 nm wavelength at room temperature. This work shows that the proposed RCE GeSn SPADs are promising candidates for high-efficiency single-photon detection in short-wave infrared (SWIR) regime for sensing and optical quantum applications.

Purification of Single and Entangled Photons by Wavepacket Shaping

AbstractSingle photons and entangled photons lie at the heart of photonic quantum technologies, whose optimal performances are normally reached when the purity of the single or entangled photons is high. However, the multiphoton emission, dissipation, and decoherence in practical realizations always lead to the degradation of the single‐ and entangled‐ photon quality. The purification of single or entangled photons is thus valuable to restore the quantum states and enhance the performance of quantum technologies. The applications of wavepacket shaping, an emerging quantum optics tool to manipulate the single‐ and entangled‐ photon wavefunctions, to purify single and entangled photons are reviewed. In particular, by modulating the single photons emitted from optically excited room‐temperature quantum dots, it is shown that the fast‐decaying multiphoton emission can be eliminated to obtain a low value of g(2)(0) that is independent of the excitation power. It is also shown that the two‐photon interference and polarization entanglement of the non‐degenerate biphotons from spontaneous parametric down‐conversion can be restored after modulating the biphotons with a periodic function. The works have potential applications in long‐distance quantum communication and linear optical quantum computation.

Efficient Simulation of Loop Quantum Gravity: A Scalable Linear-Optical Approach

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is loop quantum gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spin-foam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the bounded-error quantum polynomial time class, which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers, which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer that can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.

Integrated nanophotonics for the development of fully functional quantum circuits based on on-demand single-photon emitters

In recent years, research on integrated quantum circuits has developed rapidly and exciting results have been achieved. The overarching goal of this emerging research direction in the field of modern quantum technology is the scalable integration of quantum functionality on robust chips. Such chips can work independently of one another, but it is even more interesting to develop them modularly for integration into larger quantum networks, thereby linking quantum computation and quantum communication in the same framework. In this context, the ongoing development and further optimization of integrated quantum circuits aim, inter alia, to achieve a quantum advantage in the area of quantum computing and to pave the way for multipartite quantum networks. The functionality of such chips is essentially based on single-photon operations, such as interference at beam splitters in combination with phase shifters in the field of linear optical quantum computing and Bell-state measurements for entanglement swapping in long-distance quantum networks. While individual functionalities such as CNOT gates and more complex quantum computing operations such as boson sampling in a combination of waveguide chips and external photon sources and detectors were successfully demonstrated, the field is currently facing the major challenge of integrating all necessary components monolithically on chip in order to exploit the full potential of integrated quantum nanophotonics. The present Perspective discusses the status and the present challenges of integrated quantum nanophotonics based on on-demand single-photon emitters and gives an outlook on required developments to enter the next level of fully functional quantum circuits for photonic quantum technology.

Entanglement dynamics of photonic bell states under different noisy channels

Entanglement and decoherence are two intimately related phenomena that lie at the heart of quantum information. The EPR-Bell states are the most basic quantum systems, which form the complete entangled basis of the two-particle Hilbert space, and which are important in many quantum computation schemes. The bit flip, phase flip, and bit-phase flip noise channels represent all the possible errors in quantum computation. Thus, the quantum decoherence characteristic of maximally and partially Bell entangled states under different noisy channels is studied using the concurrence. Our work is useful for linear-optical quantum computation and quantum communication schemes whose building blocks are entangled state.

Purcell-Enhanced and Indistinguishable Single-Photon Generation from Quantum Dots Coupled to On-Chip Integrated Ring Resonators.

Integrated photonic circuits provide a versatile toolbox of functionalities for advanced quantum optics applications. Here, we demonstrate an essential component of such a system in the form of a Purcell-enhanced single-photon source based on a quantum dot coupled to a robust on-chip integrated resonator. For that, we develop GaAs monolithic ring cavities based on distributed Bragg reflector ridge waveguides. Under resonant excitation conditions, we observe an over 2-fold spontaneous emission rate enhancement using Purcell effect and gain a full coherent optical control of a QD-two-level system via Rabi oscillations. Furthermore, we demonstrate an on-demand single-photon generation with strongly suppressed multiphoton emission probability as low as 1% and two-photon interference with visibility up to 95%. This integrated single-photon source can be readily scaled up, promising a realistic pathway for scalable on-chip linear optical quantum simulation, quantum computation, and quantum networks.