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arXiv:2403.06937 · Lobachevskii Journal of Mathematics

Distributed Computing Quantum Unitary Evolution

Hui‐hui Miao, Yu. I. Ozhigov

Published Jul 1, 2024• 7 citations
arXivHTMLPDF

Abstract

Abstract A distributed computing approach to solve the curse of dimensionality, caused by the complex quantum system modeling, is discussed. With the help of Cannon’s algorithm, the distributed computing transformation of numerical method for simulating quantum unitary evolution is achieved. Based on the Tavis–Cummings model, a large number of atoms are added into the optical cavity to obtain a high-dimensional quantum closed system, implemented on the supercomputer platform. The comparison of time cost and speedup of different distributed computing strategies is discussed.

DOI
10.1134/s1995080224603904

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Abstract A distributed computing approach to solve the curse of dimensionality, caused by the complex quantum system modeling, is discussed. With the help of Cannon’s algorithm, the distributed computing transformation of numerical method for simulating quantum unitary evolution is achieved. Based on the Tavis–Cummings model, a large number of atoms are added into the optical cavity to obtain a high-dimensional quantum closed system, implemented on the supercomputer platform. The comparison of time cost and speedup of different distributed computing strategies is discussed.
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 mini-review is based on a literature survey and our experience in implementing different types of algorithms on supercomputers ‘‘Lobachevskii’’ (at Lobachevskii State University of Nizhny Novgorod) and ‘‘Lomonosov 2’’ (at Moscow State University).
High Resolution Image Download MS PowerPoint Slide Various phenomena have been observed in molecule–cavity coupled systems, which are believed to hold potential for applications in transistors, lasers, and computational units, among others. However, theoretical methods for simulating molecules in optical cavities still require further development due to the complex couplings between electrons, phonons, and photons within the cavity. In this study, motivated by recent advances in quantum algorithms and quantum computing hardware, we propose a quantum computing algorithm tailored for molecules in optical cavities. Our method, based on a variational quantum algorithm and variational boson encoders, has its effectiveness validated on both quantum simulators and hardware. For aggregates within the cavity, described by the Holstein–Tavis–Cummings model, our approach demonstrates clear advantages over other quantum and classical methods, as proved by numerical benchmarks. Additionally, we apply this method to study the H 2 molecule in a cavity using a superconducting quantum computer and the Pauli–Fierz model. To enhance accuracy, we incorporate error mitigation techniques, such as readout and reference-state error mitigation, resulting in an 86% reduction in the average error.
Abstract We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open cavity quantum electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis–Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity–emitter systems on contemporary and future quantum computers.
A viable approach for building large-scale quantum computers is to interlink small-scale quantum computers with a quantum network to create a larger distributed quantum computer. When designing quantum algorithms for such a distributed quantum computer, one can make use of the added parallelization and distribution abilities inherent in the system. An added difficulty to then overcome for distributed quantum computing is that a complex control system to orchestrate the various components is required. In this work, we aim to address these issues. We explicitly define what it means for a quantum algorithm to be distributed and then present various quantum algorithms that fit the definition. We discuss potential benefits and propose a high-level scheme for controlling the system. With this, we present our software framework called Interlin-q, a simulation platform that aims to simplify designing and verifying parallel and distributed quantum algorithms. We demonstrate Interlin-q by implementing some of the discussed algorithms using Interlin-q and layout future steps for developing Interlin-q into a control system for distributed quantum computers.
This paper investigates nonlinear dynamics in the dissipative-pumped Tavis--Cummings model (TCM). Under global excitation constraints, the competition between photon decay and pumping leads to two significant effects. First, the steady-state peak population exhibits a non-monotonic plateau: contrary to the expected monotonic decay trend at high energy levels, intermediate energy levels show comparable peak populations, and this plateau gradually shifts to higher energies and broadens as the number of atoms increases. Second, the average free photon number exhibits re-entrant dynamics. Under strong pumping, the photon number experiences an initial rise and decay, then slowly increases again, exceeding the initial peak when the system is sufficiently large, with clear thresholds in both system size and pumping rate. To reveal these phenomena, we develop a distributed computing framework suitable for large Hilbert spaces to solve the Lindblad master equation. By exploiting the sparsity of the jump operator and combining it with Cannon's algorithm, we reduce the complexity of the non-unitary terms from O(MN3)\mathcal{O}(MN^3)O(MN3) to O(MN)\mathcal{O}(MN)O(MN). Furthermore, the dynamic subspace construction method effectively eliminates redundant quantum states and significantly compresses the Hilbert space. Although the scalability of unitary evolution is limited by communication overhead, the framework as a whole still achieves efficient parameter space exploration. This study demonstrates that the dissipative-pumped TCM serves as a rich platform for studying non-equilibrium nonlinear dynamics and provides a practical numerical tool for its investigation.