Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization problem is in general nonconvex, the method can converge to suboptimal parameter values that do not yield the minimum eigenvalue. In this work, we address this shortcoming by adopting the concept of variational adiabatic quantum computing (VAQC) as a procedure to improve VQE. In VAQC, the ground state of a continuously parameterized Hamiltonian is approximated via a parameterized quantum circuit. We discuss some basic theory of VAQC to motivate the development of a hybrid quantum-classical homotopy continuation method. The proposed method has parallels with a predictor-corrector method for numerical integration of differential equations. While there are theoretical limitations to the procedure, we see in practice that VAQC can successfully find good initial circuit parameters to initialize VQE. We demonstrate this with two examples from quantum chemistry. Through these examples, we provide empirical evidence that VAQC, combined with other techniques (an adaptive termination criteria for the classical optimizer and a variance-based resampling method for the expectation evaluation), can provide more accurate solutions than “plain” VQE, for the same amount of effort.

Quantum Fourier transform to estimate drive cycles

Drive cycles in vehicle systems are important determinants for energy consumption, emissions, and safety. Estimating the frequency of the drive cycle quickly is important for control applications related to fuel efficiency, emission reduction and improving safety. Quantum computing has established the computational efficiency that can be gained. A drive cycle frequency estimation algorithm based on the quantum Fourier transform is exponentially faster than the classical Fourier transform. The algorithm is applied on real world data set. We evaluate the method using a quantum computing simulator, demonstrating remarkable consistency with the results from the classical Fourier transform. Current quantum computers are noisy, a simple method is proposed to mitigate the impact of the noise. The method is evaluated on a 15 qubit IBM-q quantum computer. The proposed method for a noisy quantum computer is still faster than the classical Fourier transform.

Quantum Computing for Dealing with Inaccurate Knowledge Related to the Certainty Factors Model

In this paper, we illustrate that inaccurate knowledge can be efficiently implemented in a quantum environment. For this purpose, we analyse the correlation between certainty factors and quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point of view. Next, we introduce some basic aspects of quantum computing, and we pay special attention to quantum rule-based systems. In this context, a specific use case was built: an inferential network for testing the behaviour of the certainty factors approach in a quantum environment. After the design and execution of the experiments, the corresponding analysis of the obtained results was performed in three different scenarios: (1) inaccuracy in declarative knowledge, or imprecision, (2) inaccuracy in procedural knowledge, or uncertainty, and (3) inaccuracy in both declarative and procedural knowledge. This paper, as stated in the conclusions, is intended to pave the way for future quantum implementations of well-established methods for handling inaccurate knowledge.

Edge Caching in Fog-Based Sensor Networks through Deep Learning-Associated Quantum Computing Framework

Fog computing (FC) based sensor networks have emerged as a propitious archetype for next-generation wireless communication technology with caching, communication, and storage capacity services in the edge. Mobile edge computing (MEC) is a new era of digital communication and has a rising demand for intelligent devices and applications. It faces performance deterioration and quality of service (QoS) degradation problems, especially in the Internet of Things (IoT) based scenarios. Therefore, existing caching strategies need to be enhanced to augment the cache hit ratio and manage the limited storage to accelerate content deliveries. Alternatively, quantum computing (QC) appears to be a prospect of more or less every typical computing problem. The framework is basically a merger of a deep learning (DL) agent deployed at the network edge with a quantum memory module (QMM). Firstly, the DL agent prioritizes caching contents via self organizing maps (SOMs) algorithm, and secondly, the prioritized contents are stored in QMM using a Two-Level Spin Quantum Phenomenon (TLSQP). After selecting the most appropriate lattice map (32 × 32) in 750,000 iterations using SOMs, the data points below the dark blue region are mapped onto the data frame to get the videos. These videos are considered a high priority for trending according to the input parameters provided in the dataset. Similarly, the light-blue color region is also mapped to get medium-prioritized content. After the SOMs algorithm’s training, the topographic error (TE) value together with quantization error (QE) value (i.e., 0.0000235) plotted the most appropriate map after 750,000 iterations. In addition, the power of QC is due to the inherent quantum parallelism (QP) associated with the superposition and entanglement principles. A quantum computer taking “n” qubits that can be stored and execute 2n presumable combinations of qubits simultaneously reduces the utilization of resources compared to conventional computing. It can be analyzed that the cache hit ratio will be improved by ranking the content, removing redundant and least important content, storing the content having high and medium prioritization using QP efficiently, and delivering precise results. The experiments for content prioritization are conducted using Google Colab, and IBM’s Quantum Experience is considered to simulate the quantum phenomena.

Quantum computing formulation of some classical Hadamard matrix searching methods and its implementation on a quantum computer

Finding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order is a hard problem that can be solved by a quantum computer. Due to the limitation on the number of qubits and connections in current quantum processors, only low order H-matrix search of orders 2 and 4 were implementable by previous method. In this paper, we show that by adopting classical searching techniques of the H-matrices, we can formulate new quantum computing methods for finding higher order ones. We present some results of finding H-matrices of order up to more than one hundred and a prototypical experiment of the classical-quantum resource balancing method that yields a 92-order H-matrix previously found by Jet Propulsion Laboratory researchers in 1961 using a mainframe computer. Since the exactness of the solutions can be verified by an orthogonality test performed in polynomial time; which is untypical for optimization of hard problems, the proposed method can potentially be used for demonstrating practical quantum supremacy in the near future.

Analysis of Carleman Linearization of Lattice Boltzmann

We explore the Carleman linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible fluid with the Bhatnagar Gross and Krook equilibrium function. Under this assumption, the error in the velocities is proportional to the square of the Mach number. Then, we showcase the Carleman linearization technique for the system under study. We compute an upper bound to the number of variables as a function of the order of the Carleman linearization. We study both collision and streaming steps of the lattice Boltzmann formulation under Carleman linearization. We analytically show why linearizing the collision step sacrifices the exactness of streaming in lattice Boltzmann, while also contributing to the blow up in the number of Carleman variables in the classical algorithm. The error arising from Carleman linearization has been shown analytically and numerically to improve exponentially with the Carleman linearization order. This bodes well for the development of a corresponding quantum computing algorithm based on the Lattice Boltzmann equation.