Linear optical quantum computing in a single spatial mode

Information processing at the speed of light

In recent years, quantum computing has made significant strides, particularly in light-based technology. The introduction of quantum photonic chips has ushered in an era marked by scalability, stability, and cost-effectiveness, paving the way for innovative possibilities within compact footprints. This article provides a comprehensive exploration of photonic quantum computing, covering key aspects such as encoding information in photons, the merits of photonic qubits, and essential photonic device components including light squeezers, quantum light sources, interferometers, photodetectors, and waveguides. The article also examines photonic quantum communication and internet, and its implications for secure systems, detailing implementations such as quantum key distribution and long-distance communication. Emerging trends in quantum communication and essential reconfigurable elements for advancing photonic quantum internet are discussed. The review further navigates the path towards establishing scalable and fault-tolerant photonic quantum computers, highlighting quantum computational advantages achieved using photons. Additionally, the discussion extends to programmable photonic circuits, integrated photonics and transformative applications. Lastly, the review addresses prospects, implications, and challenges in photonic quantum computing, offering valuable insights into current advancements and promising future directions in this technology.

Programmable Photonic Quantum Circuits with Ultrafast Time-Bin Encoding

We propose a quantum information processing platform that utilizes the ultrafast time-bin encoding of photons. This approach offers a pathway to scalability by leveraging the inherent phase stability of collinear temporal interferometric networks at the femtosecond-to-picosecond timescale. The proposed architecture encodes information in ultrafast temporal bins processed using optically induced nonlinearities and birefringent materials while keeping photons in a single spatial mode. We demonstrate the potential for scalable photonic quantum information processing through two independent experiments that showcase the platform's programmability and scalability, respectively. The scheme's programmability is demonstrated in the first experiment, where we successfully program 362 different unitary transformations in up to eight dimensions in a temporal circuit. In the second experiment, we show the scalability of ultrafast time-bin encoding by building a passive optical network, with increasing circuit depth, of up to 36 optical modes. In each experiment, fidelities exceed 97%, while the interferometric phase remains passively stable for several days.

Experimental Implementation of the Optical Fractional Fourier Transform in the Time-Frequency Domain

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of optical signals in their time-frequency degree of freedom bypasses the digitization step and presents an opportunity to enhance many protocols in quantum and classical communication, sensing, and computing. In this Letter, we present the experimental realization of the fractional Fourier transform in the time-frequency domain using an atomic quantum-optical memory system with processing capabilities. Our scheme performs the operation by imposing programmable interleaved spectral and temporal phases. We have verified the FrFT by analyses of chroncyclic Wigner functions measured via a shot-noise limited homodyne detector. Our results hold prospects for achieving temporal-mode sorting, processing, and superresolved parameter estimation.

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.

Electro-Optic Fourier Transform Chronometry of Pulsed Quantum Light

The power spectrum of an optical field can be acquired without a spectrally resolving detector by means of Fourier-transform spectrometry, based on measuring the temporal autocorrelation of the optical field. Analogously, we here perform temporal envelope measurements of ultrashort optical pulses without time resolved detection. We introduce the technique of Fourier transform chronometry, where the temporal envelope is acquired by measuring the frequency autocorrelation of the optical field in a linear interferometer. We apply our technique, which is the time-frequency conjugate measurement to Fourier-transform spectrometry, to experimentally measure the pulse envelope of classical and single-photon light pulses.

Transverse Mode-Encoded Quantum Gate on a Silicon Photonic Chip

As an important degree of freedom (d.o.f.) in photonic integrated circuits, the orthogonal transverse mode provides a promising and flexible way to increase communication capability, for both classical and quantum information processing. To construct large-scale on-chip multimode multi-d.o.f.s quantum systems, a transverse mode-encoded controlled-NOT (CNOT) gate is necessary. Here, with the help of our new transverse mode-dependent directional coupler and attenuator, we demonstrate the first multimode implementation of a 2-qubit quantum gate. The ability of the gate is demonstrated by entangling two separated transverse mode qubits with an average fidelity of 0.89±0.02 and the achievement of 10 standard deviations of violations in the quantum nonlocality verification. In addition, a fidelity of 0.82±0.01 is obtained from quantum process tomography used to completely characterize the CNOT gate. Our work paves the way for universal transverse mode-encoded quantum operations and large-scale multimode multi-d.o.f.s quantum systems.

Direct measurement of ultrafast temporal wavefunctions

The large capacity and robustness of information encoding in the temporal mode of photons is important in quantum information processing, in which characterizing temporal quantum states with high usability and time resolution is essential. We propose and demonstrate a direct measurement method of temporal complex wavefunctions for weak light at a single-photon level with subpicosecond time resolution. Our direct measurement is realized by ultrafast metrology of the interference between the light under test and self-generated monochromatic reference light; no external reference light or complicated post-processing algorithms are required. Hence, this method is versatile and potentially widely applicable for temporal state characterization.

Two-photon interference: the Hong-Ou-Mandel effect

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

Temporal mode transformations by sequential time and frequency phase modulation for applications in quantum information science

Controlling the temporal mode shape of quantum light pulses has wide ranging application to quantum information science and technology. Techniques have been developed to control the bandwidth, allow shifting in the time and frequency domains, and perform mode-selective beam-splitter-like transformations. However, there is no present scheme to perform targeted multimode unitary transformations on temporal modes. Here we present a practical approach to realize general transformations for temporal modes. We show theoretically that any unitary transformation on temporal modes can be performed using a series of phase operations in the time and frequency domains. Numerical simulations show that several key transformations on temporal modes can be performed with greater than 95% fidelity using experimentally feasible specifications.

Sequential generation of linear cluster states from a single photon emitter

Light states composed of multiple entangled photons—such as cluster states—are essential for developing and scaling-up quantum computing networks. Photonic cluster states can be obtained from single-photon sources and entangling gates, but so far this has only been done with probabilistic sources constrained to intrinsically low efficiencies, and an increasing hardware overhead. Here, we report the resource-efficient generation of polarization-encoded, individually-addressable photons in linear cluster states occupying a single spatial mode. We employ a single entangling-gate in a fiber loop configuration to sequentially entangle an ever-growing stream of photons originating from the currently most efficient single-photon source technology—a semiconductor quantum dot. With this apparatus, we demonstrate the generation of linear cluster states up to four photons in a single-mode fiber. The reported architecture can be programmed for linear-cluster states of any number of photons, that are required for photonic one-way quantum computing schemes.

Generating photonic cluster states using a single non-heralded source and a single entangling gate would optimise scalability and reduce resource overhead. Here, the authors generate up to 4-photon cluster states using a quantum dot coupled to a fibre loop, with a fourfold generation rate of 10 Hz.

Generation of multiphoton quantum states on silicon

Multiphoton quantum states play a critical role in emerging quantum technologies and greatly improve our fundamental understanding of the quantum world. Integrated photonics is well recognized as an attractive technology offering great promise for the generation of photonic quantum states with high-brightness, tunability, stability, and scalability. Herein, we demonstrate the generation of multiphoton quantum states using a single-silicon nanophotonic waveguide. The detected four-photon rate reaches 0.34 Hz even with a low-pump power of 600 μW. This multiphoton quantum state is also qualified with multiphoton quantum interference, as well as quantum state tomography. For the generated four-photon states, the quantum interference visibilities are greater than 95%, and the fidelity is 0.78 ± 0.02. Furthermore, such a multiphoton quantum source is fully compatible with the on-chip processes of quantum manipulation, as well as quantum detection, which is helpful for the realization of large-scale quantum photonic integrated circuits (QPICs) and shows great potential for research in the area of multiphoton quantum science.

Terahertz-bandwidth switching of heralded single photons

Optically induced ultrafast switching of single photons is demonstrated by rotating the photon polarization via the Kerr effect in a commercially available single-mode fiber. A switching efficiency of 97% is achieved with a ∼1.7  ps switching time and signal-to-noise ratio of ∼800. Preservation of the single-photon properties is confirmed by measuring no significant increase in the second-order autocorrelation function g⁽²⁾(0). These values are attained with only nanojoule-level pump energies that are produced by a laser oscillator with 80 MHz repetition rate. The results highlight a simple device capable of both high-bandwidth operations and preservation of single-photon properties for applications in photonic quantum processing and ultrafast time-gating or switching.

Photonic quantum information processing: a review

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

Multiplexed storage and real-time manipulation based on a multiple degree-of-freedom quantum memory

The faithful storage and coherent manipulation of quantum states with matter-systems would enable the realization of large-scale quantum networks based on quantum repeaters. To achieve useful communication rates, highly multimode quantum memories are required to construct a multiplexed quantum repeater. Here, we present a demonstration of on-demand storage of orbital-angular-momentum states with weak coherent pulses at the single-photon-level in a rare-earth-ion-doped crystal. Through the combination of this spatial degree-of-freedom (DOF) with temporal and spectral degrees of freedom, we create a multiple-DOF memory with high multimode capacity. This device can serve as a quantum mode converter with high fidelity, which is a fundamental requirement for the construction of a multiplexed quantum repeater. This device further enables essentially arbitrary spectral and temporal manipulations of spatial-qutrit-encoded photonic pulses in real time. Therefore, the developed quantum memory can serve as a building block for scalable photonic quantum information processing architectures.

On-chip generation of time-and wavelength-division multiplexed multiple time-bin entanglement

Optical quantum states based on entangled photons are the key resource in quantum-information science. The realization of multiplexed multiple entanglement are necessary for developing high-capacity quantum information process. Silicon-on-insulator (SOI) has recently become a leading platform for generating and processing of non-classical optical states. In this work, by combining the wavelength- and time-division multiplexing technologies, we demonstrate a multiplexing time-bin entangled photon pair source based on a silicon nanowire waveguide and distribute entangled photons into 3(time) × 14(wavelength) channels independently. The indistinguishability of photon pairs in each time channel is confirmed by a fourfold Hong-Ou-Mandal quantum interference. Our work paves a new and promising way to achieve a high capacity quantum communication and to generate a multiple-photon non-classical state.

Universal Quantum Computing with Measurement-Induced Continuous-Variable Gate Sequence in a Loop-Based Architecture

We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically processed in a nested loop by an electrically programmable gate sequence. This architecture can process any input state and an arbitrary number of modes with almost minimum resources, and offers a universal gate set for both qubits and continuous variables. Furthermore, quantum computing can be performed fault tolerantly by a known scheme for encoding a qubit in an infinite-dimensional Hilbert space of a single light mode.

Time-Bin-Encoded Boson Sampling with a Single-Photon Device

Boson sampling is a problem strongly believed to be intractable for classical computers, but can be naturally solved on a specialized photonic quantum simulator. Here, we implement the first time-bin-encoded boson sampling using a highly indistinguishable (∼94%) single-photon source based on a single quantum-dot-micropillar device. The protocol requires only one single-photon source, two detectors, and a loop-based interferometer for an arbitrary number of photons. The single-photon pulse train is time-bin encoded and deterministically injected into an electrically programmable multimode network. The observed three- and four-photon boson sampling rates are 18.8 and 0.2 Hz, respectively, which are more than 100 times faster than previous experiments based on parametric down-conversion.

Spectrally Engineering Photonic Entanglement with a Time Lens

A time lens, which can be used to reshape the spectral and temporal properties of light, requires the ultrafast manipulation of optical signals and presents a significant challenge for single-photon application. In this work, we construct a time lens based on dispersion and sum-frequency generation to spectrally engineer single photons from an entangled pair. The strong frequency anticorrelations between photons produced from spontaneous parametric down-conversion are converted to positive correlations after the time lens, consistent with a negative-magnification system. The temporal imaging of single photons enables new techniques for time-frequency quantum state engineering.

A fully programmable 100-spin coherent Ising machine with all-to-all connections

Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.

Near-Transform-Limited Single Photons from an Efficient Solid-State Quantum Emitter

By pulsed s-shell resonant excitation of a single quantum dot-micropillar system, we generate long streams of 1000 near-transform-limited single photons with high mutual indistinguishability. The Hong-Ou-Mandel interference of two photons is measured as a function of their emission time separation varying from 13 ns to 14.7  μs, where the visibility slightly drops from 95.9(2)% to a plateau of 92.1(5)% through a slow dephasing process occurring at a time scale of 0.7  μs. A temporal and spectral analysis reveals the pulsed resonance fluorescence single photons are close to the transform limit, which are readily useful for multiphoton entanglement and interferometry experiments.

A multiplexed light-matter interface for fibre-based quantum networks

Processing and distributing quantum information using photons through fibre-optic or free-space links are essential for building future quantum networks. The scalability needed for such networks can be achieved by employing photonic quantum states that are multiplexed into time and/or frequency, and light-matter interfaces that are able to store and process such states with large time-bandwidth product and multimode capacities. Despite important progress in developing such devices, the demonstration of these capabilities using non-classical light remains challenging. Here, employing the atomic frequency comb quantum memory protocol in a cryogenically cooled erbium-doped optical fibre, we report the quantum storage of heralded single photons at a telecom-wavelength (1.53 μm) with a time-bandwidth product approaching 800. Furthermore, we demonstrate frequency-multimode storage and memory-based spectral-temporal photon manipulation. Notably, our demonstrations rely on fully integrated quantum technologies operating at telecommunication wavelengths. With improved storage efficiency, our light-matter interface may become a useful tool in future quantum networks.

Scalable networks for processing and distribution of quantum information using photons can be achieved by using multiplexed quantum states. Here, the authors report frequency-multimode storage and spectral-temporal photon manipulation of heralded single photons at telecom wavelength, in a fully integrated setting.

On-Demand Single Photons with High Extraction Efficiency and Near-Unity Indistinguishability from a Resonantly Driven Quantum Dot in a Micropillar

Scalable photonic quantum technologies require on-demand single-photon sources with simultaneously high levels of purity, indistinguishability, and efficiency. These key features, however, have only been demonstrated separately in previous experiments. Here, by s-shell pulsed resonant excitation of a Purcell-enhanced quantum dot-micropillar system, we deterministically generate resonance fluorescence single photons which, at π pulse excitation, have an extraction efficiency of 66%, single-photon purity of 99.1%, and photon indistinguishability of 98.5%. Such a single-photon source for the first time combines the features of high efficiency and near-perfect levels of purity and indistinguishabilty, and thus opens the way to multiphoton experiments with semiconductor quantum dots.

Harnessing click detectors for the genuine characterization of light states

The key requirement for harnessing the quantum properties of light is the capability to detect and count individual photons. Of particular interest are photon-number-resolving detectors, which allow one to determine whether a state of light is classical or genuinely quantum. Existing schemes for addressing this challenge rely on a proportional conversion of photons to electrons. As such, they are capable of correctly characterizing small photon fluxes, yet are limited by uncertainties in the conversion rate. In this work, we employ a divide-and-conquer approach to infallibly discerning non-classicality of states of light. This is achieved by transforming the incident fields into uniform spatial distributions that readily lend themselves for characterization by standard on-off detectors. Since the exact statistics of the light stream in multiplexed on-off detectors are click statistics, our technique is freely scalable to accommodate-in principle-arbitrarily large photon fluxes. Our experiments pave the way towards genuine integrated photon-number-resolving detection for advanced on-chip photonic quantum networks.

Experimental demonstration of high fidelity entanglement distribution over decoherence channels via qubit transduction

Quantum coherence and entanglement, which are essential resources for quantum information, are often degraded and lost due to decoherence. Here, we report a proof-of-principle experimental demonstration of high fidelity entanglement distribution over decoherence channels via qubit transduction. By unitarily switching the initial qubit encoding to another, which is insensitive to particular forms of decoherence, we have demonstrated that it is possible to avoid the effect of decoherence completely. In particular, we demonstrate high-fidelity distribution of photonic polarization entanglement over quantum channels with two types of decoherence, amplitude damping and polarization-mode dispersion, via qubit transduction between polarization qubits and dual-rail qubits. These results represent a significant breakthrough in quantum communication over decoherence channels as the protocol is input-state independent, requires no ancillary photons and symmetries, and has near-unity success probability.

Continuous-variable quantum computing in optical time-frequency modes using quantum memories

We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate, and measure two-dimensional cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that are a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures.

Strain-optic active control for quantum integrated photonics

We present a practical method for active phase control on a photonic chip that has immediate applications in quantum photonics. Our approach uses strain-optic modification of the refractive index of individual waveguides, effected by a millimeter-scale mechanical actuator. The resulting phase change of propagating optical fields is rapid and polarization-dependent, enabling quantum applications that require active control and polarization encoding. We demonstrate strain-optic control of non-classical states of light in silica, showing the generation of 2-photon polarisation N00N states by manipulating Hong-Ou-Mandel interference. We also demonstrate switching times of a few microseconds, which are sufficient for silica-based feed-forward control of photonic quantum states.

Counterfactual entanglement distribution without transmitting any particles

To date, all schemes for entanglement distribution needed to send entangled particles or a separable mediating particle among distant participants. Here, we propose a counterfactual protocol for entanglement distribution against the traditional forms, that is, two distant particles can be entangled with no physical particles travel between the two remote participants. We also present an alternative scheme for realizing the counterfactual photonic entangled state distribution using Michelson-type interferometer and self-assembled GaAs/InAs quantum dot embedded in a optical microcavity. The numerical analysis about the effect of experimental imperfections on the performance of the scheme shows that the entanglement distribution may be implementable with high fidelity.