Quantum teleportation of physical qubits into logical code spaces.

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.

Unconditional and Robust Quantum Metrological Advantage beyond N00N States.

Quantum metrology employs quantum resources to enhance the measurement sensitivity beyond that can be achieved classically. While multiphoton entangled N00N states can in principle beat the shot-noise limit and reach the Heisenberg limit, high N00N states are difficult to prepare and fragile to photon loss which hinders them from reaching unconditional quantum metrological advantages. Here, we combine the idea of unconventional nonlinear interferometers and stimulated emission of squeezed light, previously developed for the photonic quantum computer Jiuzhang, to propose and realize a new scheme that achieves a scalable, unconditional, and robust quantum metrological advantage. We observe a 5.8(1)-fold enhancement above the shot-noise limit in the Fisher information extracted per photon, without discounting for photon loss and imperfections, which outperforms ideal 5-N00N states. The Heisenberg-limited scaling, the robustness to external photon loss, and the ease-of-use of our method make it applicable in practical quantum metrology at a low photon flux regime.

Solving Graph Problems Using Gaussian Boson Sampling.

Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed that the generated samples from the GBS could be harnessed to enhance the classical stochastic algorithms in searching some graph features. Here, we use Jiǔzhang, a noisy intermediate-scale quantum computer, to solve graph problems. The samples are generated from a 144-mode fully connected photonic processor, with photon click up to 80 in the quantum computational advantage regime. We investigate the open question of whether the GBS enhancement over the classical stochastic algorithms persists-and how it scales-with an increasing system size on noisy quantum devices in the computationally interesting regime. We experimentally observe the presence of GBS enhancement with a large photon-click number and a robustness of the enhancement under certain noise. Our work is a step toward testing real-world problems using the existing noisy intermediate-scale quantum computers and hopes to stimulate the development of more efficient classical and quantum-inspired algorithms.

Gaussian Boson Sampling with Pseudo-Photon-Number-Resolving Detectors and Quantum Computational Advantage.

We report new Gaussian boson sampling experiments with pseudo-photon-number-resolving detection, which register up to 255 photon-click events. We consider partial photon distinguishability and develop a more complete model for the characterization of the noisy Gaussian boson sampling. In the quantum computational advantage regime, we use Bayesian tests and correlation function analysis to validate the samples against all current classical spoofing mockups. Estimating with the best classical algorithms to date, generating a single ideal sample from the same distribution on the supercomputer Frontier would take ∼600 yr using exact methods, whereas our quantum computer, Jiǔzhang 3.0, takes only 1.27 µs to produce a sample. Generating the hardest sample from the experiment using an exact algorithm would take Frontier∼3.1×10^{10} yr.

Experimental Refutation of Real-Valued Quantum Mechanics under Strict Locality Conditions.

Quantum mechanics is commonly formulated in a complex, rather than real, Hilbert space. However, whether quantum theory really needs the participation of complex numbers has been debated ever since its birth. Recently, a Bell-like test in an entanglement-swapping scenario has been proposed to distinguish standard quantum mechanics from its real-valued analog. Previous experiments have conceptually demonstrated, yet not satisfied, the central requirement of independent state preparation and measurements and leave several loopholes. Here, we implement such a Bell-like test with two separated independent sources delivering entangled photons to three separated parties under strict locality conditions that are enforced by spacelike separation of the relevant events, rapid random setting generation, and fast measurement. With the fair-sampling assumption and closed loopholes of independent source, locality, and measurement independence simultaneously, we violate the constraints of real-valued quantum mechanics by 5.30 standard deviations. Our results disprove the real-valued quantum theory to describe nature and ensure the indispensable role of complex numbers in quantum mechanics.

Robust Self-Testing of Multiparticle Entanglement.

Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Because of the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multiphoton genuinely entangled quantum states. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.

Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light.

We report phase-programmable Gaussian boson sampling (GBS) which produces up to 113 photon detection events out of a 144-mode photonic circuit. A new high-brightness and scalable quantum light source is developed, exploring the idea of stimulated emission of squeezed photons, which has simultaneously near-unity purity and efficiency. This GBS is programmable by tuning the phase of the input squeezed states. The obtained samples are efficiently validated by inferring from computationally friendly subsystems, which rules out hypotheses including distinguishable photons and thermal states. We show that our GBS experiment passes a nonclassicality test based on inequality constraints, and we reveal nontrivial genuine high-order correlations in the GBS samples, which are evidence of robustness against possible classical simulation schemes. This photonic quantum computer, Jiuzhang 2.0, yields a Hilbert space dimension up to ∼10^{43}, and a sampling rate ∼10^{24} faster than using brute-force simulation on classical supercomputers.

Cloning of Quantum Entanglement.

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.

Quantum Teleportation in High Dimensions.

Quantum teleportation allows a "disembodied" transmission of unknown quantum states between distant quantum systems. Yet, all teleportation experiments to date were limited to a two-dimensional subspace of quantized multiple levels of the quantum systems. Here, we propose a scheme for teleportation of arbitrarily high-dimensional photonic quantum states and demonstrate an example of teleporting a qutrit. Measurements over a complete set of 12 qutrit states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), which is well above both the optimal single-copy qutrit state-estimation limit of 1/2 and maximal qubit-qutrit overlap of 2/3, thus confirming a genuine and nonclassical three-dimensional teleportation. Our work will enable advanced quantum technologies in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.

Experimental demonstration of wave-particle duality relation based on coherence measure.

Wave-particle duality is a typical example of Bohr's complementarity principle that plays a significant role in quantum mechanics. Previous studies used the visibility of an interference pattern to quantify the wave property and used path information to quantify the particle property. However, coherence is the core and basis of the interference phenomenon. If we could use coherence to characterize the wave property, the understanding of wave-particle duality would be strengthened. A recent theoretical work [ Phys. Rev. Lett.116, 160406 (2016)] found two relations between quantum coherence and path information. Here, we demonstrate the new measure of wave-particle duality based on two kinds of coherence measures quantitatively for the first time. The wave property, quantified by the coherence in the l1-norm measure and the relative entropy measure, can be obtained via tomography of the target state, which is encoded in the path degree of freedom of the photons. The particle property, quantified by the path information, can be obtained via the discrimination of detector states, which is encoded in the polarization degree of freedom of the photons. Our work may deepen people's understanding of coherence and provide a new perspective regarding wave-particle duality.

12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion.

Entangled-photon sources with simultaneously near-unity heralding efficiency and indistinguishability are the fundamental elements for scalable photonic quantum technologies. We design and realize a degenerate telecommunication wavelength entangled-photon source from an ultrafast pulsed laser pumped spontaneous parametric down-conversion (SPDC), which shows simultaneously 97% heralding efficiency and 96% indistinguishability between independent single photons without narrow-band filtering. Such a beamlike and frequency-uncorrelated SPDC source allows generation of the first 12-photon genuine entanglement with a state fidelity of 0.572±0.024. We further demonstrate a blueprint of scalable scattershot boson sampling using 12 SPDC sources and a 12×12 mode interferometer for three-, four-, and five-boson sampling, which yields count rates more than 4 orders of magnitude higher than all previous SPDC experiments.

Eliminating temporal correlation in quantum-dot entangled photon source by quantum interference.

Semiconductor quantum dots, as promising solid-state platform, have exhibited deterministic photon pair generation with high polarization entanglement fidelity for quantum information applications. However, due to temporal correlation from inherently cascaded emission, photon indistinguishability is limited, which restricts their potential scalability to multi-photon experiments. Here, by utilizing quantum interferences to decouple polarization entanglement from temporal correlation, we improve four-photon Greenberger-Horne-Zeilinger (GHZ) state entanglement fidelity from (58.7±2.2)% to (75.5±2.0)%. Our work paves the way to realize scalable and high-quality multi-photon states from quantum dots.

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.

Emergence of classical objectivity of quantum Darwinism in a photonic quantum simulator.

Quantum-to-classical transition is a fundamental open question in physics frontier. Quantum decoherence theory points out that the inevitable interaction with environment is a sink carrying away quantum coherence, which is responsible for the suppression of quantum superposition in open quantum system. Recently, quantum Darwinism theory further extends the role of environment, serving as communication channel, to explain the classical objectivity emerging in quantum measurement process. Here, we used a six-photon quantum simulator to investigate classical and quantum information proliferation in quantum Darwinism process. In the simulation, many environmental photons are scattered from an observed quantum system and they are collected and used to infer the system's state. We observed redundancy of system's classical information and suppression of quantum correlation in the fragments of environmental photons. Our results experimentally show that the classical objectivity of quantum system can be established through quantum Darwinism mechanism.

Experimental Gaussian Boson sampling.

Gaussian Boson sampling (GBS) provides a highly efficient approach to make use of squeezed states from parametric down-conversion to solve a classically hard-to-solve sampling problem. The GBS protocol not only significantly enhances the photon generation probability, compared to standard Boson sampling with single photon Fock states, but also links to potential applications such as dense subgraph problems and molecular vibronic spectra. Here, we report the first experimental demonstration of GBS using squeezed-state sources with simultaneously high photon indistinguishability and collection efficiency. We implement and validate 3-, 4- and 5-photon GBS with high sampling rates of 832, 163 and 23 kHz, respectively, which is more than 4.4, 12.0, and 29.5 times faster than the previous experiments. Further, we observe a quantum speed-up on a NP-hard optimization problem when comparing with simulated thermal sampler and uniform sampler.

Time-tagged coincidence counting unit for large-scale photonic quantum computing.

Real-time analysis of single-photon coincidence is critical in photonic quantum computing. The large channel number and high counting rate foreseen in such experiments pose a big challenge for the conventional time tagged method and coincidence instruments. Here we propose a real-time time-tagged coincidence method and a data filtering solution, demonstrated by a 32-channel coincidence counting unit that has been implemented successfully on a field-programmable gate array system. The unit provides high counting rates, a tunable coincidence window, and a timing resolution of 390 ps. Beyond that, it is feasible to be scaled up to 104 channels and is thus ideally suited for channel consuming applications such as boson sampling. Based on the versatility and scalability the unit has shown, we believe that it is the turn-key solution for many single-photon coincidence counting applications in photonic quantum computing.

Statistical Analysis for Collision-free Boson Sampling.

Boson sampling is strongly believed to be intractable for classical computers but solvable with photons in linear optics, which raises widespread concern as a rapid way to demonstrate the quantum supremacy. However, due to its solution is mathematically unverifiable, how to certify the experimental results becomes a major difficulty in the boson sampling experiment. Here, we develop a statistical analysis scheme to experimentally certify the collision-free boson sampling. Numerical simulations are performed to show the feasibility and practicability of our scheme, and the effects of realistic experimental conditions are also considered, demonstrating that our proposed scheme is experimentally friendly. Moreover, our broad approach is expected to be generally applied to investigate multi-particle coherent dynamics beyond the boson sampling.