Quantum generative adversarial learning in photonics.

Quantum generative adversarial networks (QGANs), an intersection of quantum computing and machine learning, have attracted widespread attention due to their potential advantages over classical analogs. However, in the current era of noisy intermediate-scale quantum (NISQ) computing, it is essential to investigate whether QGANs can perform learning tasks on near-term quantum devices usually affected by noise and even defects. In this Letter, using a programmable silicon quantum photonic chip, we experimentally demonstrate the QGAN model in photonics for the first time to our knowledge and investigate the effects of noise and defects on its performance. Our results show that QGANs can generate high-quality quantum data with a fidelity higher than 90%, even under conditions where up to half of the generator's phase shifters are damaged, or all of the generator and discriminator's phase shifters are subjected to phase noise up to 0.04π. Our work sheds light on the feasibility of implementing QGANs on the NISQ-era quantum hardware.

Experimental quantum natural gradient optimization in photonics.

Variational quantum algorithms (VQAs) combining the advantages of parameterized quantum circuits and classical optimizers, promise practical quantum applications in the noisy intermediate-scale quantum era. The performance of VQAs heavily depends on the optimization method. Compared with gradient-free and ordinary gradient descent methods, the quantum natural gradient (QNG), which mirrors the geometric structure of the parameter space, can achieve faster convergence and avoid local minima more easily, thereby reducing the cost of circuit executions. We utilized a fully programmable photonic chip to experimentally estimate the QNG in photonics for the first time, to the best of our knowledge. We obtained the dissociation curve of the He-H+ cation and achieved chemical accuracy, verifying the outperformance of QNG optimization on a photonic device. Our work opens up a vista of utilizing QNG in photonics to implement practical near-term quantum applications.

Variational Quantum Process Tomography of Non-Unitaries.

Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of dimensionality. On the other hand, non-unitary operators are more realistic cases. In this work, we put forward a variational quantum process tomography method based on the supervised quantum machine learning framework. It approximates the unknown non-unitary quantum process utilizing a relatively shallow depth parametric quantum circuit and fewer input states. Numerically, we verified our method by reconstructing the non-unitary quantum mappings up to eight qubits in two cases: the weighted sum of the randomly generated quantum circuits and the imaginary time evolution of the Heisenberg XXZ spin chain Hamiltonian. Results show that those quantum processes could be reconstructed with high fidelities (>99%) and shallow depth parametric quantum circuits (d≤8), while the number of input states required is at least two orders of magnitude less than the demands of the standard quantum process tomography. Our work shows the potential of the variational quantum process tomography method in characterizing non-unitary operators.

Variational Entanglement-Assisted Quantum Process Tomography with Arbitrary Ancillary Qubits.

Quantum process tomography is a pivotal technique in fully characterizing quantum dynamics. However, exponential scaling of the Hilbert space with the increasing system size extremely restrains its experimental implementations. Here, we put forward a more efficient, flexible, and error-mitigated method: variational entanglement-assisted quantum process tomography with arbitrary ancillary qubits. Numerically, we simulate up to eight-qubit quantum processes and show that this tomography with m ancillary qubits (0≤m≤n) alleviates the exponential costs on state preparation (from 4^{n} to 2^{n-m}), measurement settings (at least a 1 order of magnitude reduction), and data postprocessing (efficient and robust parameter optimization). Experimentally, we first demonstrate our method on a silicon photonic chip by rebuilding randomly generated one-qubit and two-qubit unitary quantum processes. Further using the error mitigation method, two-qubit quantum processes can be rebuilt with average gate fidelity enhanced from 92.38% to 95.56%. Our Letter provides an efficient and practical approach to process tomography on the noisy quantum computing platforms.

Continuous-time quantum walk based centrality testing on weighted graphs.

Centrality measure is an essential tool in network analysis and widely used in the domain of computer science, biology and sociology. Taking advantage of the speedup offered by quantum computation, various quantum centrality measures have been proposed. However, few work of quantum centrality involves weighted graphs, while the weight of edges should be considered in certain real-world networks. In this work, we extend the centrality measure based on continuous-time quantum walk to weighted graphs. We testify the feasibility and reliability of this quantum centrality using an ensemble of 41,675 graphs with various topologies and comparing with the eigenvector centrality measure. The average Vigna's correlation index of all the tested graphs with all edge weights in [1, 10] is as high as 0.967, indicating the pretty good consistency of rankings by the continuous-time quantum walk centrality and the eigenvector centrality. The intuitive consistency of the top-ranked vertices given by this quantum centrality measure and classical centrality measures is also demonstrated on large-scale weighted graphs. Moreover, the range of the continuous-time quantum walk centrality values is much bigger than that of classical centralities, which exhibits better distinguishing ability to pick the important vertices from the ones with less importance. All these results show that the centrality measure based on continuous-time quantum walk still works well on weighted graphs.

Optimization of quantum light sources and four-wave mixing based on a reconfigurable silicon ring resonator.

Being a key component on a photonic chip, the microring usually specializes in a certain nonlinear optical process and can not simultaneously meet different working conditions for different processes. Here, we theoretically and experimentally investigate a reconfigurable silicon microring resonator to act as a optimization strategy for both classical four-wave mixing and quantum light sources. Experimental results show that the four-wave mixing efficiency with continuous wave and pulsed pump can be both optimized to a high value well matching numerical analysis. A variety of quantum light sources - including the heralded single-photon source, two-photon source and multi-photon source - are demonstrated to present a high performance and their key parameters including the pair generation rates (PGR), the heralding efficiency (HE) and the coincidence-to-accidental ratio (CAR) are controllable and optimizable. Such tunable nonlinear converter is immune to fabrication variations and can be popularized to other nonlinear optical materials, providing a simple and compact post-fabrication trimming strategy for on-chip all-optical signal processing and photonic quantum technologies.

Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor.

Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.

Reconfigurable multiphoton entangled states based on quantum photonic chips.

Multipartite entanglement is one of the most prominent features of quantum mechanics and is the key ingredient in quantum information processing. Seeking for an advantageous way to generate it is of great value. Here we propose two different schemes to prepare multiphoton entangled states on a quantum photonic chip that are both based on the theory of entanglement on the graph. The first scheme is to construct graphs for multiphoton states by the network of spatially anti-bunching two-photon sources. The second one is to construct graphs by the linear beam-splitter network, which can generate W and Dicke states efficiently with simple structure. Both schemes can be scaled up in the photon number and can be reconfigured for different types of multiphoton states. This study supplies a systematic solution for the on-chip generation of multiphoton entangled states and will promote the practical development of multiphoton quantum technologies.

General-Purpose Quantum Circuit Simulator with Projected Entangled-Pair States and the Quantum Supremacy Frontier.

Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Here, we bring together many-body quantum physics and quantum computing by using a method for strongly interacting two-dimensional systems, the projected entangled-pair states, to realize an effective general-purpose simulator of quantum algorithms. The classical computing complexity of this simulator is directly related to the entanglement generation of the underlying quantum circuit rather than the number of qubits or gate operations. We apply our method to study random quantum circuits, which allows us to quantify precisely the memory usage and the time requirements of random quantum circuits. We demonstrate our method by computing one amplitude for a 7×7 lattice of qubits with depth (1+40+1) on the Tianhe-2 supercomputer.

[Effects of different application rates of humic acid compound fertilizer on pepper and its mechanism of anti-senility and incremental yield].

The effects of different application rates of humic acid compound fertilizer (HA) on the yield and physiological characteristics of pepper (Capsicum frutescens L.) were studied in this paper. The results showed that different application rates of (HA) could affect the physiological activities and yield of pepper. The nitrate reductase activity (NRA) and peroxidase (POD) activity were improved with increasing application rate, but the change rate of NRA was reduced gradually. POD activity in inorganic compound fertilizer treatment was improved significantly when the application rate of fertilizer was higher than 0.3 g.kg-1, but that in HA treatment changed smoothly. Superoxide dismutase (SOD) activity was improved significantly when the application rate of fertilizer was lower than 0.2 g.kg-1, and decreased gradually when the application rate was higher than 0.2 g.kg-1. The change of transpiration rate was consistent with that of SOD activity. The relationship between the application rate of fertilizer and the yield of pepper could be described with quadratic curve regression model. According to the equation, the highest application rate of HA should be 0.27 g.kg-1, and the highest yield of pepper could reach 165.22 g per pot.