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A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. No photonic machine offering programmability over all its quantum gates has demonstrated quantum computational advantage: previous machines1,2 were largely restricted to static gate sequences. Earlier photonic demonstrations were also vulnerable to spoofing3, in which classical heuristics produce samples, without direct simulation, lying closer to the ideal distribution than do samples from the quantum hardware. Here we report quantum computational advantage using Borealis, a photonic processor offering dynamic programmability on all gates implemented. We carry out Gaussian boson sampling4 (GBS) on 216 squeezed modes entangled with three-dimensional connectivity5, using a time-multiplexed and photon-number-resolving architecture. On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution, whereas Borealis requires only 36 μs. This runtime advantage is over 50 million times as extreme as that reported from earlier photonic machines. Ours constitutes a very large GBS experiment, registering events with up to 219 photons and a mean photon number of 125. This work is a critical milestone on the path to a practical quantum computer, validating key technological features of photonics as a platform for this goal.

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 that require 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 programmable quantum 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. A system for realizing many-photon quantum circuits is presented, comprising a programmable nanophotonic chip operating at room temperature, interfaced with a fully automated control system.

We investigate the coexistence of clock synchronization protocols with quantum signals in a common single-mode optical fiber. By measuring optical noise between 1500 nm to 1620 nm we demonstrate a potential for up to 100 quantum, 100 GHz wide channels coexisting with the classical synchronization signals. Both “White Rabbit” and pulsed laser-based synchronization protocols were characterized and compared. We establish a theoretical limit of the fiber link length for coexisting quantum and classical channels. The maximal fiber length is below approximately 100 km for off-the-shelf optical transceivers and can be significantly improved by taking advantage of quantum receivers.

Quantum phenomena such as entanglement can improve fundamental limits on the sensitivity of a measurement probe. In optical interferometry, a probe consisting of $N$ entangled photons provides up to a $\sqrt{N}$ enhancement in phase sensitivity compared to a classical probe of the same energy. Here, we employ high-gain parametric down-conversion sources and photon-number-resolving detectors to perform interferometry with heralded quantum probes of sizes up to $N=8$ (i.e. measuring up to 16-photon coincidences). Our probes are created by injecting heralded photon-number states into an interferometer, and in principle provide quantum-enhanced phase sensitivity even in the presence of significant optical loss. Our work paves the way towards quantum-enhanced interferometry using large entangled photonic states., Comment: 15 pages, 9 figures; includes Supplemental Material

We show strong evidence—from both fluorescence and transmittance measurements—that entangled two-photon absorption cross sections are several orders of magnitude lower than many prior reports have claimed.

To calibrate an optical transition edge sensor, for each pulse of the light source (e.g., pulsed laser), one must determine the ratio of the expected number of photons that deposit energy and the expected number of photons created by the laser. Based on the estimated pulse height generated by each energy deposit, we form a pulse height spectrum with features corresponding to different numbers of deposited photons. We model the number of photons that deposit energy per laser pulse as a realization of a Poisson process, and the observed pulse height spectrum with a mixture model method. For each candidate feature set, we determine the expected number of photons that deposit energy per pulse and its associated uncertainty based on the mixture model weights corresponding to that candidate feature set. From training data, we select the optimal feature set according to an uncertainty minimization criterion. We then determine the expected number of photons that deposit energy per pulse and its associated uncertainty for test data that are independent of the training data. Our uncertainty budget accounts for random measurement errors, systematic effects due to mismodeling feature shapes in our mixture model, and possible imperfections in our feature set selection method.

Quantum simulations are becoming an essential tool for studying complex phenomena, e.g. quantum topology, quantum information transfer, and relativistic wave equations, beyond the limitations of analytical computations and experimental observations. To date, the primary resources used in proof-of-principle experiments are collections of qubits, coherent states or multiple single-particle Fock states. Here we show the first quantum simulation performed using genuine higher-order Fock states, with two or more indistinguishable particles occupying the same bosonic mode. This was implemented by interfering pairs of Fock states with up to five photons on an interferometer, and measuring the output states with photon-number-resolving detectors. Already this resource-efficient demonstration reveals new topological matter, simulates non-linear systems and elucidates a perfect quantum transfer mechanism which can be used to transport Majorana fermions., Comment: New text and results. 19 pages, 13 figures, supplementary material

We measure the detection efficiency of single-photon detectors at wavelengths near 851 nm and 1533.6 nm. We investigate the spatial uniformity of one free-space-coupled single-photon avalanche diode and present a comparison between fusion-spliced and connectorized fiber-coupled single-photon detectors. We find that our expanded relative uncertainty for a single measurement of the detection efficiency is as low as 0.70% for fiber-coupled measurements at 1533.6 nm and as high as 1.78% for our free-space characterization at 851.7 nm. The detection-efficiency determination includes corrections for afterpulsing, dark count, and count-rate effects of the single-photon detector with the detection efficiency interpolated to operation at a specified detected count rate.

Excitation with entangled photon pairs may lead to an increase in the efficiency of two-photon absorption at low photon flux. The corresponding process, entangled two-photon absorption (E2PA), has been investigated in numerous theoretical and experimental studies. However, significant ambiguity and inconsistency remain in the literature about the absolute values of E2PA cross sections. Here, we use a fluorescence-based registration scheme to experimentally determine upper bounds on the cross sections for six fluorophores. These bounds are up to 4 orders of magnitude lower than the smallest published cross section. For two samples that have been studied by others, Rhodamine 6G and 9R-S, we measure upper bounds 4 and 5 orders of magnitude lower than the previously reported cross sections.

As quantum network technology is in the research and development phase, it is essential that robust quantum metrology protocols and procedures based on entanglement distribution be established. To enable that, it will be necessary to develop tools, metrics and measurement methods to characterize quantum network components, both individually, and in their interactions with classical and quantum networks. We present our efforts towards metrology of quantum networks and review a few metrology tools that are already available for quantum component characterization.

We demonstrate the preservation of time-energy entanglement of near-IR photons through thick biological media ($\leq$1.55 mm) and tissue ($\leq$ 235 $\mu$m) at room temperature. Using a Franson-type interferometer, we demonstrate interferometric contrast of over 0.9 in skim milk, 2% milk, and chicken tissue. This work supports the many proposed opportunities for nonclassical light in biological imaging and analyses from sub-shot noise measurements to entanglement-enhanced fluorescence imaging, clearly indicating that the entanglement characteristics of photons can be maintained even after propagation through thick, turbid biological samples., Comment: 13 pages, 4 figures, 1 table

Two-photon absorption rates may be enhanced with energy-time entangled states of light. Using a sensitive transmittance measurement we find no evidence of this enhancement, in disagreement with previously reported results.

Techniques to control the spectro-temporal properties of quantum states of light at ultrafast time scales are crucial for numerous applications in quantum information science. In this work, we report an all-optical time lens for quantum signals based on Bragg-scattering four-wave mixing with picosecond resolution. Our system achieves a temporal magnification factor of 158 with single-photon level inputs, which is sufficient to overcome the intrinsic timing jitter of superconducting nanowire single-photon detectors. We demonstrate discrimination of two terahertz-bandwidth, single-photon-level pulses with 2.1 ps resolution (electronic jitter corrected resolution of 1.25 ps). We draw on elegant tools from Fourier optics to further show that the time-lens framework can be extended to perform complex unitary spectro-temporal transformations by imparting optimized temporal and spectral phase profiles to the input waveforms. Using numerical optimization techniques, we show that a four-stage transformation can realize an efficient temporal mode sorter that demultiplexes 10 Hermite–Gaussian (HG) modes. Our time-lens-based framework represents a new toolkit for arbitrary spectro-temporal processing of single photons, with applications in temporal mode quantum processing, high-dimensional quantum key distribution, temporal mode matching for quantum networks, and quantum-enhanced sensing with time-frequency entangled states.

The authors show a quantum state tomography scheme with excitation counting for bosonic systems

We report demonstrations of both quadrature squeezed vacuum and photon number difference squeezing generated in an integrated nanophotonic device. Squeezed light is generated via strongly driven spontaneous four-wave mixing below threshold in silicon nitride microring resonators. The generated light is characterized with both homodyne detection and direct measurements of photon statistics using photon number-resolving transition edge sensors. We measure $1.0(1)$~dB of broadband quadrature squeezing (${\sim}4$~dB inferred on-chip) and $1.5(3)$~dB of photon number difference squeezing (${\sim}7$~dB inferred on-chip). Nearly-single temporal mode operation is achieved, with measured raw unheralded second-order correlations $g^{(2)}$ as high as $1.95(1)$. Multi-photon events of over 10 photons are directly detected with rates exceeding any previous quantum optical demonstration using integrated nanophotonics. These results will have an enabling impact on scaling continuous variable quantum technology., Comment: Minor revisions, and Fig. 5 corrected; Now published in Science Advances

Characterization of quantum states and detectors is a key task in rapidly emerging optical quantum science and technology. First, we introduce and experimentally demonstrate a noise-robust quantum state characterization protocol using photon-number-resolving (PNR) measurements. Unlike conventional continuous variable state tomography methods, our method utilizes computationally efficient semi-definite programming (SDP) and can be used to accurately reconstruct the state even after loss a known loss. The protocol is demonstrated for a weak coherent state as well as a single-photon Fock state. Next, we propose a method for characterizing a photodetector by directly reconstructing the Wigner functions of the detector’s Positive-Operator-Value-Measure (POVM) elements via weak-field homodyne technique. We also report our experimental progress on characterizing a superconducting transition-edge sensor for PNR measurements.

Improvements in temporal resolution of single-photon detectors enable increased data rates and transmission distances for both classical and quantum optical communication systems, higher spatial resolution in laser ranging, and observation of shorter-lived fluorophores in biomedical imaging. In recent years, superconducting nanowire single-photon detectors (SNSPDs) have emerged as the most efficient time-resolving single-photon-counting detectors available in the near-infrared, but understanding of the fundamental limits of timing resolution in these devices has been limited due to a lack of investigations into the timescales involved in the detection process. We introduce an experimental technique to probe the detection latency in SNSPDs and show that the key to achieving low timing jitter is the use of materials with low latency. By using a specialized niobium nitride SNSPD we demonstrate that the system temporal resolution can be as good as 2.6 ± 0.2 ps for visible wavelengths and 4.3 ± 0.2 ps at 1,550 nm. Knowledge about detection latency provides a guideline to reduce the timing jitter of niobium nitride superconducting nanowire single-photon detectors. A timing jitter of 2.6 ps at visible wavelength and 4.3 ps at 1,550 nm is achieved.

We have developed an entangled photon pair source based on a domain-engineered, type-II periodically poled lithium niobate crystal that produces signal and idler photons at 1533 nm and 1567 nm. We characterized the spectral correlations of the generated entangled photons using fiber-assisted signal-photon spectroscopy. We observed interference between the two down-conversion paths after erasing polarization distinguishability of the down-converted photons. The observed interference signature is closely related to the spectral correlations between photons in a Hong- Ou-Mandel interferometer. These measurements suggest good indistinguishability between the two downconversion paths, which is required for high entanglement visibility.

Integrating single-photon detectors on an electro-optic, second-order nonlinear medium opens the field for new complex photonic circuits. We present our detection efficiency results on evanescently coupled SNSPDs and TESs on titanium in-diffused lithium niobate waveguides.

We present our measurements of the detection efficiency of free-space and fiber-coupled single-photon detectors at wavelengths near 851 nm and 1533.6 nm. We investigate the spatial uniformity of one free-space-coupled silicon single-photon avalanche diode (SPAD) and present a comparison between fusion-spliced and connectorized fiber-coupled single-photon detectors. We find that our expanded relative uncertainty for a single measurement of the detection efficiency is as low as 0.7 % for fiber-coupled measurements at 1533.6 nm and as high as 1.8 % for our free-space characterization at 851.8 nm.

We present a detailed study of two-photon absorption in some common fluorescent molecules with excitation by entangled photon pairs. Using fluorescence and transmittance measurements, we set an upper bound on the absorption cross sections.

Two-photon microscopy (TPM) with entangled photons may provide significant enhancements over classical TPM. Though previously little explored, here we demonstrate via a unique Franson interferometer, the robust maintenance of entanglement through millimeters of bio-samples.

The quantum statistical fluctuations of the electromagnetic field establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric down-conversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling and quantum networks., 9 pages, 6 figures, added more discussions

The quantum theory of electromagnetic radiation predicts characteristic statistical fluctuations for light sources as diverse as sunlight, laser radiation, and molecule fluorescence. Indeed, these underlying statistical fluctuations of light are associated with the fundamental physical processes behind their generation. In this contribution, we experimentally demonstrate that the manipulation of the quantum electromagnetic fluctuations of two-mode squeezed vacuum states leads to a family of quantum-correlated multiphoton states with tunable mean photon numbers and degree of correlation. Our technique relies on the use of conditional measurements to engineer the excitation mode of the field through the simultaneous subtraction of photons from two-mode squeezed vacuum states. The experimental generation of nonclassical multiphoton states by means of photon subtraction unveils novel mechanisms to control fundamental properties of light. As a remarkable example, we demonstrate the engineering of a quantum state of light with up to ten photons, exhibiting nearly Poissonian photon statistics, that constitutes an important step towards the generation of entangled lasers. Our technique enables a robust protocol to prepare quantum states with multiple photons in high-dimensional spaces and, as such, it constitutes a novel platform for exploring quantum phenomena in mesoscopic systems.

Claude Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure., 10 Figures

We use pulsed spontaneous parametric down-conversion in KTiOPO 4, with a Gaussian phase-matching function and a transform-limited Gaussian pump, to achieve near-unity spectral purity in heralded single photons at telecommunication wavelength. Theory shows that these phase-matching and pump conditions are sufficient to ensure that a biphoton state with a circularly symmetric joint spectral intensity profile is transform limited and factorable. We verify the heralded-state spectral purity in a four-fold coincidence measurement by performing Hong-Ou-Mandel interference between two independently generated heralded photons. With a mild spectral filter we obtain an interference visibility of 98.4±1.1% which corresponds to a heralded-state purity of 99.2%. Our heralded photon source is potentially an essential resource for measurement-based quantum information processing and quantum network applications.

Transition-edge sensors (TES) are photon-number resolving calorimetric spectrometers with near unit efficiency. Their recovery time, which is on the order of microseconds, limits the number resolving ability and timing accuracy in high photon-flux conditions. This is usually addressed by pulsing the light source or discarding overlapping signals, thereby limiting its applicability. We present an approach to assign detection times to overlapping detection events in the regime of low signal-to-noise ratio, as in the case of TES detection of near-infrared radiation. We use a two-level discriminator, inherently robust against noise, to coarsely locate pulses in time, and timestamp individual photoevents by fitting to a heuristic model. As an example, we measure the second-order time correlation of a coherent source in a single spatial mode using a single TES detector., 6 pages, 8 figures

We measure the detection efficiency of single-photon detectors at wavelengths near 851 nm and 1533.6 nm. We investigate the spatial uniformity of one free-space-coupled single-photon avalanche diode and present a comparison between fusion-spliced and connectorized fiber-coupled single-photon detectors. We find that our expanded relative uncertainty for a single measurement of the detection efficiency is as low as 0.70% for fiber-coupled measurements at 1533.6 nm and as high as 1.78% for our free-space characterization at 851.7 nm. The detection-efficiency determination includes corrections for afterpulsing, dark count, and count-rate effects of the single-photon detector with the detection efficiency interpolated to operation at a specified detected count rate.