Search

The quantum to classical transition (QCT) is one of the central mysteries in quantum physics. This process is generally interpreted as state collapse from measurement or decoherence from interacting with the environment. Here we define the quantumness of a Hamiltonian by the free energy difference between its quantum and classical descriptions, which vanishes during QCT. We apply this criterion to the many-body Rabi model and study its scaling law across the phase transition, finding that not only the temperature and Planck constant, but also all the model parameters are important for this transition. We show that the Jaynes-Cummings and anti Jaynes-Cummings models exhibit greater quantumness than the Rabi model. Moreover, we show that the rotating wave and anti-rotating wave terms in this model have opposite quantumness in QCT. We demonstrate that the quantumness may be enhanced or suppressed at the critical point. Finally, we estimate the quantumness of the Rabi model in current trapped ion experiments. The quantumness provides an important tool to characterize the QCT in a vast number of many-body models., Comment: 6 pages, 5 figures

Variational quantum algorithms, which consist of optimal parameterized quantum circuits, are promising for demonstrating quantum advantages in the noisy intermediate-scale quantum (NISQ) era. Apart from classical computational resources, different kinds of quantum resources have their contributions to the process of computing, such as information scrambling and entanglement. Characterizing the relation between the complexity of specific problems and quantum resources consumed by solving these problems is helpful for us to understand the structure of VQAs in the context of quantum information processing. In this work, we focus on the quantum approximate optimization algorithm (QAOA), which aims to solve combinatorial optimization problems. We study information scrambling and entanglement in QAOA circuits, respectively, and discover that for a harder problem, more quantum resource is required for the QAOA circuit to obtain the solution in most cases. We note that in the future, our results can be used to benchmark the complexity of quantum many-body problems by information scrambling or entanglement accumulation in the computing process., Comment: 11 pages, 12 figures

Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel. Our CSB method is insensitive to state-preparation and measurement errors, and importantly, can benchmark universal gates and is scalable to many-qubit systems. Unlike standard randomized schemes, CSB can provide direct noise information for both target native gates and circuit fragments, allowing benchmarking and calibration of global entangling gates and frequently used modules in quantum algorithms like Trotterized Hamiltonian evolution operator in quantum simulation., Comment: 14 pages, 5 figures, Published version

The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate application-level quantum advantages in the noisy intermediate-scale quantum(NISQ) processors with shallow circuit depth. Since the core of QAOA is the computation of expectation values of the problem Hamiltonian, an important practical question is whether we can find an efficient classical algorithm to solve quantum mean value in the case of general shallow quantum circuits. Here, we present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits in most optimization problems except for complete graph case. Numerical tests in Max-cut, graph coloring and Sherrington-Kirkpatrick model problems, compared to the state-of-the-art method, shows orders of magnitude performance improvement. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.

Existing deep convolutional neural networks (CNNs) generate massive interlayer feature data during network inference. To maintain real-time processing in embedded systems, large on-chip memory is required to buffer the interlayer feature maps. In this paper, we propose an efficient hardware accelerator with an interlayer feature compression technique to significantly reduce the required on-chip memory size and off-chip memory access bandwidth. The accelerator compresses interlayer feature maps through transforming the stored data into frequency domain using hardware-implemented 8x8 discrete cosine transform (DCT). The high-frequency components are removed after the DCT through quantization. Sparse matrix compression is utilized to further compress the interlayer feature maps. The on-chip memory allocation scheme is designed to support dynamic configuration of the feature map buffer size and scratch pad size according to different network-layer requirements. The hardware accelerator combines compression, decompression, and CNN acceleration into one computing stream, achieving minimal compressing and processing delay. A prototype accelerator is implemented on an FPGA platform and also synthesized in TSMC 28-nm COMS technology. It achieves 403GOPS peak throughput and 1.4x~3.3x interlayer feature map reduction by adding light hardware area overhead, making it a promising hardware accelerator for intelligent IoT devices.

In a graph $G$, a vertex dominates itself and its neighbors. A subset $S\subseteq V(G)$ is said to be a double dominating set of $G$ if $S$ dominates every vertex of $G$ at least twice. The double domination number $\gamma_{\times 2}(G)$ is the minimum cardinality of a double dominating set of $G$. We show that if $G$ is a maximal outerplanar graph on $n\geq 3$ vertices, then $\gamma_{\times 2}(G)\leq \lfloor \frac{2n}{3}\rfloor$. Further, if $n\geq 4$, then $\gamma_{\times 2}(G)\leq \min \{\lfloor \frac{n+t}{2}\rfloor, n-t\}$, where $t$ is the number of vertices of degree $2$ in $G$. These bounds are shown to be tight. In addition, we also study the case that $G$ is a striped maximal outerplanar graph.