Simulations for quantum computing typically involve the computation of a large number of eigenvalues of large matrices. This effort focuses on optimization of these calculations using algorithms tailored to the specific characteristics of typical matrices found in these simulations. Currently, computations which heretofore required over 30 hours of simulation time have been reduced to less than 3 hours.
Simulations for quantum computing typically involve the computation of a large number of eigenvalues of large matrices. This effort focuses on optimization of these calculations using algorithms tailored to the specific characteristics of typical matrices found in these simulations. Currently, computations which heretofore required over 30 hours of simulation time have been reduced to less than 3 hours.
The design and understanding of quantum-dot cellular automata (QCA) networks has been largely influenced by limitations in the approximation methods used in common design tools. In some cases, such limitations have led to unrealistic selections of clock zones which are not feasible for nanoscale QCA implementations given current fabrication constraints on clocking electrodes. A better understanding of the behaviour of larger QCA networks of perhaps tens to hundreds of QCA devices is needed. One approach is by investigating the low energy spectrum; however, diagonalization of the system Hamiltonian even in the 2-state approximation is impractical beyond 20 or so devices. In this work, we present a methodology for understanding the spectrum of the full network in terms of contributions from components of the network. We show that important features of the low energy spectrum can be attributed to specific critical components, and present one scheme for decomposing the network into these components. In addition, we address the question of computing the low energy spectrum of large QCA networks. A method based on basis reduction which naturally emerges from the component decomposition is successfully applied to a 49 cell XOR gate with results compared against a density matrix renormalization group implementation.
Quantum computing has the potential to revolutionize the field of computing, but with hardware and algorithms unlike any in use today. Due to the primitive state of existing quantum hardware, simulation is one of the most effective methods for studying quantum computing issues. Our team previously developed a general-purpose simulator capable of modeling arbitrary quantum algorithms executing on any hardware device. The simulator performs over a thousand matrix multiplications per step as part of its operations. To improve the simulator performance, optimizations were designed to dynamically restructure the problem. The resulting calculations were then distributed across a cluster. These enhancements reduced both the order of the simulator operations and the memory overhead, achieving an overall performance improvement of 99.94% from the initial implementation of a key quantum algorithm, reducing the simulator run time for this algorithm from two days on a single processor to under two minutes on a cluster.
Quantum-dot cellular automata (QDCA) hold great potential to produce the next generation of computer hardware, but their development is hindered by computationally intensive simulations. Our research therefore focuses on rewriting one such simulation to run parallel calculations on a graphics processing unit (GPU). We have decreased execution time from 33 hours 11 minutes to 1 hour 39 minutes, but current progress has shown that further gains are possible. The calculation of eigenvectors holds particular promise for acceleration. Our research has two components: testing MATLAB’s algorithm for these calculations and creating a C-based algorithm to improve on MATLAB’s execution time. MATLAB requires 0.2352 +/- 0.0074 seconds to execute this function, while our function requires 0.0674 +/- 0.0143 seconds. Further, our function’s iterative and many-threaded nature makes it ideal for parallel implementation in the CUDA language, which is expected to further increase execution speed. At the time of this writing, implementation is ongoing. Our presentation shall focus on our functions’ efficiency increases over their MATLAB counterparts, and the application of GPUs’ immense computational power to QDCA device simulation.
This paper proposes a novel approach to quantum algorithm design by leveraging the principles of cellular automata (CA). The core idea is to utilize CA as a hardware abstraction layer for quantum computation, mimicking the evolution rules of qubits. This allows for a parallelized design and optimization of quantum algorithms. Specifically, quantum gates are mapped to CA rules, enabling the simulation of qubit superposition and entanglement through cellular interactions and information transfer. This work explores the theoretical framework and outlines a methodology for designing quantum algorithms using CA, focusing on the potential for enhanced computational efficiency and scalability. The design methodology includes defining the CA grid, encoding quantum states into cellular configurations, translating quantum gates into CA rule updates, and analyzing the resulting algorithm execution. The presented framework offers a fundamentally different perspective on quantum algorithm development, potentially bridging the gap between classical algorithmic design and the unique characteristics of quantum systems. Further research will focus on exploring specific quantum algorithms and evaluating the performance of the CA-based approach.
The advancements in classical computational components such as CPUs and GPUs have had a reverberating impact on the democratization of computational power available, with the field of computational chemistry reaping significant benefits from the propulsion of the limits of systems studied. The accurate prediction of chemical properties and reaction dynamics through computational simulation is now a centerpiece of modern chemical research, significantly accelerating discoveries research areas of materials science and drug development, as well as industrially relevant processes such as the emission of aldehydes from soft foams, flame retardants and pyrolysis and the carbonylation of epoxides. These achievements of computational chemistry still are overshadowed in the face of fundamental bottlenecks where classical methods remain constrained by the exponential scaling when treating large and/or strongly correlated quantum many-body systems. This innate computational complexity often constitutes chemically accurate calculations based on first principles impractical, or plain impossible, for systems beyond modest sizes. Quantum computing offers a potential pathway around these limitations, originally formally formulated by David Deutsch as a tool for simulating quantum systems, with the first quantum algorithms indicating speed-ups compared to classical counterparts arising from Peter Shor and Lov Grover for the prime factorization of an integer number and unstructured search respectively. Relying on fundamental theorems by Claude Shannon, it has been demonstrated that through the use of error-correcting codes fault-tolerant quantum computers are able to safeguard information against noise and decoherence, strongly indicating towards exponential speedups in solving central computational chemistry problems, such as determining ground state energies or reaction pathways of chemical systems. Substantial strides in experimental quantum computing over the past decade, including proof-of-principle demonstrations of quantum error correction, mean to bring full-scale fault-tolerant quantum computing within the grasp of humanity. The breakthroughs needed to attain scalable, error-corrected quantum computation with capabilities exceeding those of classical methods in real-world scenarios is likely still some years away. While striving to address the engineering challenges standing in the way of achieving fault tolerant quantum computing, substantial effort has been focused toward developing and benchmarking hybrid algorithms tailored for the Noisy Intermediate- Scale Quantum (NISQ) devices, available now to researchers. These hybrid quantum-classical algorithms, with the most notable being the Variational Quantum Eigensolver (VQE), allow the probing of quantum computing’s utility in computational chemistry even in the face of significant hardware noise and limited coherence times. The work presented in this thesis introduces several key additions the VQE framework, geared especially towards to NISQ hardware, where the mindful use of available resources is imperative. First, the implementation of the Conjugate Model Search optimizer is described, an optimization method that integrates simple models that are surrogate to the original function, combined with conjugate gradient optimization to navigate effectively parameter landscapes typical of variational algorithms, prone to noise. Second, this thesis contains the proposal and extensive study of a hyperparameter tuning procedure employing genetic algorithms, allowing for comprehensive simulation benchmarks that augment the robustness and efficiency of VQE implementations with respect to convergence time through real wall-time models of quantum processors. Continuing, a bridge is presented between quantum simulation and quantum chemistry, through qubit-to-fermion mappings of existing quantum gates, further enabling the direct and accurate modeling of chemical systems on trapped atom quantum hardware with the added arsenal provided by techniques designed for qubit architectures. Additionally, experimental data contained in this thesis include detailed benchmarking data collected from state-of-the-art trapped ion quantum processors available at the Johannes Gutenberg Universität Mainz, demonstrating the actual viability and performance of various methodologies for extracting results. Lastly, the state of VQE is examined, as it served as a springboard for a plethora of advancements in the development of quantum computing hardware, as well as the direction the field of simulation of computational quantum chemistry via quantum devices is headed towards in the coming years.