A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel

The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs efficiently on a cluster. Our implementation also improves single node performance, and is able to use multiple GPUs within a node. The scaling is close to linear using the CPU kernels, whereas the efficiency of GPU kernels improve with larger matrices. We also introduce a hybrid kernel that simultaneously uses multicore CPUs and GPUs in a distributed system. This kernel is shown to be efficient when the matrix size would not fit in the GPU memory. Larger quantum systems scale especially well with a high number nodes. The code is available under an open source license.Comment: 11 pages, 10 figure

Large-scale Classical Simulation of Quantum Systems Using the Trotter-Suzuki Decomposition

Many theoretical studies and experimental results rely on the use of numerical analysis for the solution of the Schrödinger equation. Indeed, for nontrivial quantum systems, a complete solution of the dynamics is difficult to achieve analytically. We extended the implementation of a highly optimized solver to simulate the evolution of a wave function on a 2D lattice. We also implemented the imaginary time evolution to approximate the ground state. The dynamics of the system is now described by a Hamiltonian that includes an external potential and a contact interaction term. The algorithm is based on the second-order Trotter-Suzuki approximation and it is implemented on CPU and GPU kernels that run efficiently on a cluster. We proved the accuracy of the code solving the Gross-Pitaevskii equation for a Bose-Einstein condensate and reproducing the experimental results, obtained at NIST, of the soliton dynamics in a cloud of sodium atoms. The code is available under an open source license, and it is exposed as an application program interface and a command-line interface. The code is also accessible in Python and MATLAB. Future development of the code include the extension to a 3D lattice, whereas the actual implementation can already find applications in ultracold atom physics

Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units

The split-step Fourier method is a powerful technique for solving partial differential equations and simulating ultracold atomic systems of various forms. In this body of work, we focus on several variations of this method to allow for simulations of one, two, and three-dimensional quantum systems, along with several notable methods for controlling these systems. In particular, we use quantum optimal control and shortcuts to adiabaticity to study the non-adiabatic generation of superposition states in strongly correlated one-dimensional systems, analyze chaotic vortex trajectories in two dimensions by using rotation and phase imprinting methods, and create stable, threedimensional vortex structures in Bose–Einstein condensates through artificial magnetic fields generated by the evanescent field of an optical nanofiber. We also discuss algorithmic optimizations for implementing the split-step Fourier method on graphics processing units. All computational methods present in this work are demonstrated on physical systems and have been incorporated into a state-of-the-art and open-source software suite known as GPUE, which is currently the fastest quantum simulator of its kind.Okinawa Institute of Science and Technology Graduate Universit

Neural Networks for Programming Quantum Annealers

Quantum machine learning has the potential to enable advances in artificial intelligence, such as solving problems intractable on classical computers. Some fundamental ideas behind quantum machine learning are similar to kernel methods in classical machine learning. Both process information by mapping it into high-dimensional vector spaces without explicitly calculating their numerical values. We explore a setup for performing classification on labeled classical datasets, consisting of a classical neural network connected to a quantum annealer. The neural network programs the quantum annealer's controls and thereby maps the annealer's initial states into new states in the Hilbert space. The neural network's parameters are optimized to maximize the distance of states corresponding to inputs from different classes and minimize the distance between quantum states corresponding to the same class. Recent literature showed that at least some of the "learning" is due to the quantum annealer, connecting a small linear network to a quantum annealer and using it to learn small and linearly inseparable datasets. In this study, we consider a similar but not quite the same case, where a classical fully-fledged neural network is connected with a small quantum annealer. In such a setting, the fully-fledged classical neural-network already has built-in nonlinearity and learning power, and can already handle the classification problem alone, we want to see whether an additional quantum layer could boost its performance. We simulate this system to learn several common datasets, including those for image and sound recognition. We conclude that adding a small quantum annealer does not provide a significant benefit over just using a regular (nonlinear) classical neural network.Comment: 15 pages and 9 figure

Nueva aproximación en la simulación computarizada de 1H RMN -1D

Se estudió la evolución de un sistema de dos espines en Resonancia Magnética Nuclear (RMN) 1H-1D teniendo como objetivo el análisis del acople escalar fuerte empleando la aproximación de Trotter-Suzuki (TS). Se examinó el desempeño de la aproximación comparando los espectros obtenidos con ella y los espectros 1H RMN-1D exactos, por otra parte se hizo uso de las normas matriciales para medir la distancia entre la aproximación y el sistema 1H RMN-1D exacto. Algunos de los resultados de la aproximación mostró resultados muy similares a la aproximación de acople débil, y se contempló la posibilidad de mejoría para los sistemas de espín acoplados fuertemente.PregradoQUÍMICO(A

Quantum number preserving ansätze and error mitigation studies for the variational quantum eigensolver

Computational chemistry has advanced rapidly in the last decade on the back of the progress of increased performance in CPU and GPU based computation. The prediction of reaction properties of varying chemical compounds in silico promises to speed up development in, e.g., new catalytic processes to reduce energy demand of varying known industrial used reactions. Theoretical chemistry has found ways to approximate the complexity of the underlying intractable quantum many-body problem to various degrees to achieve chemically accurate ab initio calculations for various, experimentally verified systems. Still, in theory limited by fundamental complexity theorems accurate and reliable predictions for large and/or highly correlated systems elude computational chemists today. As solving the Schrödinger equation is one of the main use cases of quantum computation, as originally envisioned by Feynman himself, computational chemistry has emerged as one of the applications of quantum computers in industry, originally motivated by potential exponential improvements in quantum phase estimation over classical counterparts. As of today, most rigorous speed ups found in quantum algorithms are only applicable for so called error-corrected quantum computers, which are not limited by local qubit decoherence in the length of the algorithms possible. Over the last decade, the size of available quantum computing hardware has steadily increased and first proof of concepts of error-correction codes have been achieved in the last year, reducing error rates below the individual error rates of qubits comprising the code. Still, fully error-corrected quantum computers in sizes that overcome the constant factor in speed up separating classical and quantum algorithms in increasing system size are a decade or more away. Meanwhile, considerable efforts have been made to find potential quantum speed ups of non-error corrected quantum systems for various applications in the noisy intermediate-scale quantum (NISQ) era. In chemistry, the variational quantum eigensolver (VQE), a family of classical-quantum hybrid algorithms, has become a topic of interest as a way of potentially solving computational chemistry problems on current quantum hardware. The main contributions of this work are: extending the VQE framework with two new potential ansätze, (1) a maximally dense first-order trotterized ansatz for the paired approximation of the electronic structure Hamiltonian, (2) a gate fabric with many favourable properties like conserving relevant quantum numbers, locality of individual operations and potential initialisation strategies mitigating plateaus of vanishing gradient during optimisation. (3) Contributions to one of largest and most complex VQE to date, including the aforementioned ansatz in paired approximation, benchmarking different error-mitigation techniques to achieve accurate results, extrapolating performance to give perspective on what is needed for NISQ devices having potential in competing with classical algorithms and (4) Simulations to find optimal ways of measuring Hamiltonians in this error-mitigated framework. (5) Furthermore a simulation of different purification error mitigation techniques and their combination under different noise models and a way of efficiently calibrating for coherent noise for one of them is part of this manuscript. We discuss the state of VQE after almost a decade after its introduction and give an outlook on computational chemistry on quantum computers in the near future