QuantumInformation.jl---a Julia package for numerical computation in quantum information theory

Numerical investigations are an important research tool in quantum information theory. There already exists a wide range of computational tools for quantum information theory implemented in various programming languages. However, there is little effort in implementing this kind of tools in the Julia language. Julia is a modern programming language designed for numerical computation with excellent support for vector and matrix algebra, extended type system that allows for implementation of elegant application interfaces and support for parallel and distributed computing. QuantumInformation.jl is a new quantum information theory library implemented in Julia that provides functions for creating and analyzing quantum states, and for creating quantum operations in various representations. An additional feature of the library is a collection of functions for sampling random quantum states and operations such as unitary operations and generic quantum channels.Comment: 32 pages, 8 figure

RosneT: a block tensor algebra library for out-of-core quantum computing simulation

With recent Quantum Devices showing increasing capabilities to perform controlled operations, further development on Quantum Algorithms may benefit from Quantum Simulations on classical hardware. Among important applications one finds verification and debugging of Quantum Algorithms, and elucidating the frontier for real Quantum Advantage of new devices [1]. Tensor Networks are regarded as an efficient numerical representation of a Quantum Circuit, but exponential growth forces tensors to be distributed among computing nodes. A number of methods and libraries have appeared recently to implement Quantum Simulators with Tensor Networks [2], [3] intended for HPC clusters. In this work we develop a Python library called RosneT using a task-based programming model able to extend all tensor operations into distributed systems, and prepared for existing and upcoming Exascale supercomputers. It is compatible with the Python ecosystem, and offers a simple programming interface for developers

Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables

A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only problems of commuting variables have efficient generators. We develop an implementation for problems of noncommuting problems that creates the relaxation to be solved by SDPA -- a high-performance solver that runs in a distributed environment. We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of the resulting relaxations. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in Python. The tool helps solve problems such as finding the ground state energy or testing quantum correlations.Comment: 17 pages, 3 figures, 1 table, 2 algorithms, the algorithm is available at http://peterwittek.github.io/ncpol2sdpa

Validating Quantum-Classical Programming Models with Tensor Network Simulations

The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work we consider time-periodically modulated quantum systems which are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a non-trivial computational task. To go beyond the current size limits, we use the quantum trajectory method which unravels master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long 'leaps' forward in time, and is numerically exact in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, $\{\eta_1, \eta_2,...,\eta_n\}$, one could propagate a quantum trajectory (with $\eta_i$'s as norm thresholds) in a numerically exact way. %Since the quantum trajectory method falls into the class of standard sampling problems, performance of the algorithm %can be substantially improved by implementing it on a computer cluster. By using a scalable $N$-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with $N = 2000$ states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed