Modeling Complex Quantum Dynamics: Evolution of Numerical Algorithms in the HPC Context

Abstract

Due to complexity of the systems and processes it addresses, the development of computational quantum physics is influenced by the progress in computing technology. Here we overview the evolution, from the late 1980s to the current year 2020, of the algorithms used to simulate dynamics of quantum systems. We put the emphasis on implementation aspects and computational resource scaling with the model size and propagation time. Our minireview is based on a literature survey and our experience in implementing different types of algorithms.

Qibo: a framework for quantum simulation with hardware acceleration

“…The simulation of circuit-based quantum processors is already implemented by several research collaborations and companies. Some notable examples of simulation software which are based on linear algebra approach are Cirq [19] and TensorFlow quantum (TFQ) [20] from Google, Qiskit from IBM Q [21], PyQuil from Rigetti [22], Intel-QS (qHipster) from Intel [23], QCGPU [24] and Qulacs [25], among others [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. While the simulation techniques and hardware-specific configurations are well defined for each simulation software, despite the availability of recent implementations based on field programmable gate arrays [46,47], there are no simulation tools that can take full advantage of hardware acceleration in single and double precision computations, through a simple interface which allows the user to switch from multithreading CPU, single GPU, and distributed multi-GPU/CPU setups.…”

Transition from ergodic to many-body localization regimes in open quantum systems in terms of the neural-network ansatz

“…The complexity of the description of a state of a many-body system grows exponentially with the number 𝑁 of system's components, e.g., spin or qubits, so that the corresponding model becomes intractable already for relatively small values of 𝑁 . The development of the computational many-body physics is the story of a constant search for new methods to compactify the description of quantum states at the price of restricting them to a subset which is constrained by some conditions [2], f.e., by area laws [3,4].…”

“…Open many-body open quantum systems are especially challenging to deal with computationally. Due to the growth of the number of parameters (needed to describe the state of an open system) as the square of the corresponding Hilbert space dimension, description of open quantum states by density matrices requires substantially more computational resource as compared to the states of Hamiltonian systems [2].…”

“…Numerical solution of the Lindblad master equation [10], commonly used to model evolution of open quantum systems, becomes a challenge already for 𝑁 = 10 spins/qubits. Equally, the exact diagonalization of the Lindblad equation in order to find its stationary state -and thus to compute the asymptotic state of the corresponding model -becomes a problem starting 𝑁 = 8 spins (if no further constraints are imposed so that the dimension of the Hilbert space can be reduced) [2]. It therefore would be beneficial to implement the machine learning techniques to model open quantum many-body states.…”

Emulating Quantum Dynamics with Neural Networks via Knowledge Distillation

“…The underlying motivation for focusing on quantum dynamics emulation tools is their use in simulating quantum systems and role in the design process of quantum devices, such as qubits and sensors 28 . Specifically, modeling devices that are embedded in an environment requires challenging predictions of open quantum system dynamics 29,30 .…”