Photonic Quantum Computing Research Articles

Belief propagation with quantum messages for quantum-enhanced classical communications

For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal “joint-detection receiver” that acts collectively on long codeword-blocks of modulated pulses; an effect often termed “superadditive capacity”. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of “belief-propagation with quantum messages” (BPQM). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best “classical” approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.

Boosting Photonic Quantum Computation with Moderate Nonlinearity

Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic clusters using probabilistic linear-optics gates. Although strong single-photon nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shifts smaller than $\pi$) to boost photonic quantum computing and significantly reduce its resources overhead. The key element in our scheme is a nonlinear router that preferentially directs photonic wavepackets to different output ports depending on their intensity. As a relevant example, we analyze the nonlinearity provided by Rydberg blockade in atomic ensembles, in which the trade-off between the nonlinearity and the accompanying loss is well understood. We present protocols for efficient Bell measurement and GHZ-state preparation -- both key elements in the construction of cluster states, as well as for the CNOT gate and quantum factorization. Given the large number of entangling operations involved in fault-tolerant MBQC, the increase in success probability provided by our protocols already at moderate nonlinearity can result in a dramatic reduction in the required resources.

Tunable quantum interference using a topological source of indistinguishable photon pairs

Sources of quantum light, in particular correlated photon pairs that are indistinguishable for all degrees of freedom, are the fundamental resource for photonic quantum computation and simulation. Although such sources have been recently realized using integrated photonics, they offer limited ability to tune the spectral and temporal correlations between generated photons because they rely on a single component, such as a ring resonator. Here, we demonstrate a tunable source of indistinguishable photon pairs using dual-pump spontaneous four-wave mixing in a topological system comprising a two-dimensional array of resonators. We exploit the linear dispersion of the topological edge states to tune the spectral bandwidth (by about 3.5×), and thereby, to tune quantum interference between generated photons by tuning the two pump frequencies. We demonstrate energy−time entanglement and, using numerical simulations, confirm the topological robustness of our source. Our results could lead to tunable, frequency-multiplexed quantum light sources for photonic quantum technologies.

Harmonizing continuous noise to build a modular photonic quantum computer

Harmonizing continuous noise to build a modular photonic quantum computer

Quantum circuits with many photons on a programmable nanophotonic chip.

Growing interest in quantum computing for practical applications has led to a surge in the availability of programmable machines for executing quantum algorithms1,2. Present-day photonic quantum computers3-7 have been limited either to non-deterministic operation, low photon numbers and rates, or fixed random gate sequences. Here we introduce a full-stack hardware-software system for executing many-photon quantum circuit operations using integrated nanophotonics: a programmable chip, operating at room temperature and interfaced with a fully automated control system. The system enables remote users to execute quantum algorithms thatrequire up to eight modes of strongly squeezed vacuum initialized as two-mode squeezed states in single temporal modes, a fully general and programmable four-mode interferometer, and photon number-resolving readout on all outputs. Detection of multi-photon events with photon numbers and rates exceeding any previous programmablequantum optical demonstration is made possible by strong squeezing and high sampling rates. We verify the non-classicality of the device output, and use the platform to carry out proof-of-principle demonstrations of three quantum algorithms: Gaussian boson sampling, molecular vibronic spectra and graph similarity8. These demonstrations validate the platform as a launchpad for scaling photonic technologies for quantum information processing.

Integrated photon-pair sources with nonlinear optics

Assisted by the rapid development of photonic integrated circuits, scalable and versatile chip-based quantum light sources with nonlinear optics are increasingly tangible for real-world applications. In this review, we introduce the basic concepts behind parametric photon pair sources and discuss the current state-of-the-art photon pair generation in detail but also highlight future perspectives in hybrid integration, novel waveguide structures, and on-chip multiplexing. The advances in near-deterministic integrated photon pair sources are deemed to pave the way for the realization of large-scale quantum photonic integrated circuits for applications, including quantum telecommunication, quantum sensing, quantum metrology, and photonic quantum computing.

Multi-dimensional q-deformed bosonic Newton oscillators and the related q-calculus, q-coherent states, and Hermite q-polynomials

The multi-dimensional q-deformed bosonic Newton oscillator algebra with SU(d)-symmetry is considered. In this framework, we first introduce some new properties concerning the q-deformed calculus related to the algebra, and we then discuss possible consequences of applying these deformed oscillators in some quantum optical issues such as in the construction of coherent states and their effects on the photon statistics. Second, we investigate the role of q-deformation on both the energy levels and the wave functions of the bosonic Newton oscillators by constructing the q-deformed Hermite polynomials. The results obtained in this work might have some implications for studies on quantum information based technologies such as in photonic quantum computing.

Four‐Photon Greenberger–Horne–Zeilinger Entanglement via Collective Two‐Photon Coherence in Doppler‐Broadened Atoms

AbstractBright, entangled multiphoton sources based on atom–photon interactions are an essential requirement in the realization of several quantum information and quantum computation schemes based on photonic quantum systems. Here, a four‐photon polarization‐entangled Greenberger–Horne–Zeilinger (GHZ) state obtained from Doppler‐broadened atomic ensembles of 87Rb atoms is experimentally demonstrated. Owing to collective two‐photon coherence in the Doppler‐broadened cascade‐type atomic system, the setup enables the generation of robust four‐photon GHZ states with a fidelity of 82.1% and a measured four‐photon average coincidence rate of 0.58 s−1. It is believed that the generation of such bright and stable multiphoton GHZ states from atomic media is an important step toward realizing photonic quantum computation and practical quantum networks based on atom–photon interactions.

Single-shot number-resolved detection of microwave photons with error mitigation

Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, however, require not only detecting the presence of any photons, but distinguishing the number present with a single shot. Here, we implement a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators which make up the bits in the binary decomposition of the photon number. Our protocol consists of successive, independent measurements of each bit by entangling the ancilla with the cavity, then reading out and resetting the ancilla. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in ensembles of measurements, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from $13.5\%$ to $1.1\%$. We also show that the mitigation is efficiently scalable to an $M$-mode system provided that the errors are independent and sufficiently small. Our work motivates the development of new algorithms that utilize single-shot, high-fidelity PNR detectors.

Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into states of light and the modern tools for their generation. Here we propose such a design for a scalable fault-tolerant photonic quantum computer informed by the latest developments in theory and technology. Central to our architecture is the generation and manipulation of three-dimensional resource states comprising both bosonic qubits and squeezed vacuum states. The proposal exploits state-of-the-art procedures for the non-deterministic generation of bosonic qubits combined with the strengths of continuous-variable quantum computation, namely the implementation of Clifford gates using easy-to-generate squeezed states. Moreover, the architecture is based on two-dimensional integrated photonic chips used to produce a qubit cluster state in one temporal and two spatial dimensions. By reducing the experimental challenges as compared to existing architectures and by enabling room-temperature quantum computation, our design opens the door to scalable fabrication and operation, which may allow photonics to leap-frog other platforms on the path to a quantum computer with millions of qubits.

Fiber-compatible photonic feed-forward with 99% fidelity.

Both photonic quantum computation and the establishment of a quantum internet require fiber-based measurement and feed-forward in order to be compatible with existing infrastructure. Here we present a fiber-compatible scheme for measurement and feed-forward, whose performance is benchmarked by carrying out remote preparation of single-photon polarization states at telecom-wavelengths. The result of a projective measurement on one photon deterministically controls the path a second photon takes with ultrafast optical switches. By placing well-calibrated bulk passive polarization optics in the paths, we achieve a measurement and feed-forward fidelity of (99.0 ± 1)%, after correcting for other experimental errors. Our methods are useful for photonic quantum experiments including computing, communication, and teleportation.

Dispersion cancellation in a quantum interferometer with independent single photons.

A key technique to perform proper quantum information processing is to get a high visibility quantum interference between independent single photons. One of the crucial elements that affects the quantum interference is a group velocity dispersion that occurs when single photons pass through a dispersive medium. We theoretically and experimentally demonstrate that an effect of group velocity dispersion on the two-photon interference can be cancelled if two independent single photons experience the same amount of pulse broadening. This dispersion cancellation effect can be applied to a multi-path linear interferometer with multiple independent single photons. As multi-path quantum interferometers are at the heart of quantum communication, photonic quantum computing, and boson sampling applications, our work should find wide applicability in quantum information science.

Quantum photonic computer technology for solving complex computational problems of high availability systems

We consider the problem of calculating the approximate value (estimate) of the permanent of a square matrix over the field of real numbers using a photonic quantum computer that sampling bosons from a given distribution. It is pointed out that it is possible to effectively solve this problem for the following three classes of matrices: symmetric matrices which eigenvalues do not exceed 1 in absolute value; orthogonal matrices; doubly stochastic matrices. For the last two classes, we are talking about evaluating the square of the permanent. The mathematical basis for solving the problem is the formula, which represents the permanent of the Hermitian matrix as the mathematical expectation of some random variable which values are equal to the products of the powers of the eigenvalues of the Hermitian matrix. And the corresponding probabilities with which these products are accepted as values of a random variable are also completely determined by the same Hermitian matrix. This circumstance allows using the methods of probability theory in order to solve the problem of permanent estimation.

Quantum computational advantage using photons.

Quantum computers promise to perform certain tasks that are believed to be intractable to classical computers. Boson sampling is such a task and is considered a strong candidate to demonstrate the quantum computational advantage. We performed Gaussian boson sampling by sending 50 indistinguishable single-mode squeezed states into a 100-mode ultralow-loss interferometer with full connectivity and random matrix-the whole optical setup is phase-locked-and sampling the output using 100 high-efficiency single-photon detectors. The obtained samples were validated against plausible hypotheses exploiting thermal states, distinguishable photons, and uniform distribution. The photonic quantum computer, Jiuzhang, generates up to 76 output photon clicks, which yields an output state-space dimension of 1030 and a sampling rate that is faster than using the state-of-the-art simulation strategy and supercomputers by a factor of ~1014.

Universal fault-tolerant measurement-based quantum computation

Certain physical systems that one might consider for fault-tolerant quantum computing where qubits do not readily interact, for instance photons, are better suited for measurement-based quantum-computational protocols. Here we propose a measurement-based model for universal quantum computation that simulates the braiding and fusion of Majorana modes. To derive our model we develop a general framework that maps any scheme of fault-tolerant quantum computation with stabilizer codes into the measurement-based picture. As such, our framework gives an explicit way of producing fault-tolerant models of universal quantum computation with linear optics using protocols developed using the stabilizer formalism. Given the remarkable fault-tolerant properties that Majorana modes promise, the main example we present offers a robust and resource efficient proposal for photonic quantum computation.

Truncated Metallo-Dielectric Omnidirectional Reflector: Collecting Single Photons in the Fundamental Gaussian Mode with 95% Efficiency

We propose a novel antenna structure which funnels single photons from a single emitter with unprecedented efficiency into a low-divergence fundamental Gaussian mode. Our device relies on the concept of creating an omnidirectional photonic bandgap to inhibit unwanted large-angle emission and to enhance small-angle defect-guided-mode emission. The new photon collection strategy is intuitively illustrated, rigorously verified and optimized by implementing an efficient body-of-revolution finite-difference time-domain method for in-plane dipole emitters. We investigate a few antenna designs to cover various boundary conditions posed by fabrication processes or material restrictions and theoretically demonstrate that collection efficiencies into the fundamental Gaussian mode exceeding 95% are achievable. Our antennas are broadband, insensitive to fabrication imperfections and compatible with a variety of solid-state emitters such as organic molecules, quantum dots and defect centers in diamond. Unidirectional and low-divergence Gaussian-mode emission from a single emitter may enable the realization of a variety of photonic quantum computer architectures as well as highly efficient light-matter interfaces.

Training Gaussian boson sampling distributions

Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed which rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing ingredient for developing new algorithms. In this work, we derive analytical gradient formulas for the GBS distribution, which can be used to train devices using standard methods based on gradient descent. We introduce a parametrization of the distribution that allows the gradient to be estimated by sampling from the same device that is being optimized. In the case of training using a Kullback-Leibler divergence or log-likelihood cost function, we show that gradients can be computed classically, leading to fast training. We illustrate these results with numerical experiments in stochastic optimization and unsupervised learning. As a particular example, we introduce the variational Ising solver, a hybrid algorithm for training GBS devices to sample ground states of a classical Ising model with high probability.

Cost-reduced all-Gaussian universality with the Gottesman-Kitaev-Preskill code: Resource-theoretic approach to cost analysis

The Gottesman-Kitaev-Preskill (GKP) quantum error-correcting code has emerged as a key technique in achieving fault-tolerant quantum computation using photonic systems. Whereas [Baragiola et al., Phys. Rev. Lett. 123, 200502 (2019)] showed that experimentally tractable Gaussian operations combined with preparing a GKP codeword $\lvert 0\rangle$ suffice to implement universal quantum computation, this implementation scheme involves a distillation of a logical magic state $\lvert H\rangle$ of the GKP code, which inevitably imposes a trade-off between implementation cost and fidelity. In contrast, we propose a scheme of preparing $\lvert H\rangle$ directly and combining Gaussian operations only with $\lvert H\rangle$ to achieve the universality without this magic state distillation. In addition, we develop an analytical method to obtain bounds of fundamental limit on transformation between $\lvert H\rangle$ and $\lvert 0\rangle$, finding an application of quantum resource theories to cost analysis of quantum computation with the GKP code. Our results lead to an essential reduction of required non-Gaussian resources for photonic fault-tolerant quantum computation compared to the previous scheme.

Applications of near-term photonic quantum computers: software and algorithms

Gaussian boson sampling (GBS) is a near-term platform for photonic quantum computing. Recent efforts have led to the discovery of GBS algorithms with applications to graph-based problems, point processes, and molecular vibronic spectra in chemistry. The development of dedicated quantum software is a key enabler in permitting users to program devices and implement algorithms. In this work, we introduce a new applications layer for the Strawberry Fields photonic quantum computing library. The applications layer provides users with the necessary tools to design and implement algorithms using GBS with only a few lines of code. This paper serves a dual role as an introduction to the software, supported with example code, and also a review of the current state of the art in GBS algorithms.

Point processes with Gaussian boson sampling.

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of quantum computing to statistical modeling by establishing a connection between point processes and Gaussian boson sampling, an algorithm for photonic quantum computers. We show that Gaussian boson sampling can be used to implement a class of point processes based on hard-to-compute matrix functions which, in general, are intractable to simulate classically. We also discuss situations where polynomial-time classical methods exist. This leads to a family of efficient quantum-inspired point processes, including a fast classical algorithm for permanental point processes. We investigate the statistical properties of point processes based on Gaussian boson sampling and reveal their defining property: like bosons that bunch together, they generate collections of points that form clusters. Finally, we analyze properties of these point processes for homogeneous and inhomogeneous state spaces, describe methods to control cluster location, and illustrate how to encode correlation matrices.