ABSTRACT We review existing classical simulation methods for performing fermionic Gaussian operations and develop new methods to address the gap by adhering to the fundamental theoretical framework established by Bravyi [Quantum Info. Comput. 5, 216 (2005)] for the most general fermionic Gaussian processes. Throughout this attempt, the focus remains on the unified approach that can be applied to generic fermionic Gaussian operations. This is beneficial since the selection of simulation methods has often been based on an ad hoc choice, heavily influenced by the specific model and circumstances, rather than on a systematic approach.
ABSTRACT We review existing classical simulation methods for performing fermionic Gaussian operations and develop new methods to address the gap by adhering to the fundamental theoretical framework established by Bravyi [Quantum Info. Comput. 5, 216 (2005)] for the most general fermionic Gaussian processes. Throughout this attempt, the focus remains on the unified approach that can be applied to generic fermionic Gaussian operations. This is beneficial since the selection of simulation methods has often been based on an ad hoc choice, heavily influenced by the specific model and circumstances, rather than on a systematic approach.
We review existing classical simulation methods for performing fermionic Gaussian operations and develop new methods to address the gap by adhering to the fundamental theoretical framework established by Bravyi [Quantum Info. Comput. 5, 216 (2005)] for the most general fermionic Gaussian processes. Throughout this attempt, the focus remains on the unified approach that can be applied to generic fermionic Gaussian operations. This is beneficial since the selection of simulation methods has often been based on an ad hoc choice, heavily influenced by the specific model and circumstances, rather than on a systematic approach.
In the effort to develop useful quantum computers, simulating quantum machines with conventional classical computing resources is a key capability. Such simulations will always face limits, preventing the emulation of quantum computers at substantial scale; however, by pushing the envelope through optimal choices of algorithms and hardware, the value of simulator tools can be maximized. This work reviews state-of-the-art numerical simulation methods, i.e., classical algorithms that emulate quantum computer evolution under specific operations. We focus on the mainstream state-vector and tensor-network paradigms, while briefly mentioning alternative methods. Moreover, we review the diverse applications of simulation across different facets of quantum computer development, including understanding the fundamental differences between quantum and classical computations, exploring algorithmic design for quantum advantage, predicting quantum processor performance at the design stage, and efficiently characterizing fabricated devices for rapid iterations. This review complements recent surveys of current tools and implementations; here, we aim to provide readers with an essential understanding of the theoretical basis of classical simulation methods, a detailed discussion of their advantages and limitations, and an overview of the demands and challenges arising from practical use cases.
We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.
This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale numerical simulations. Quantum critical phenomena in fermionic systems have attracted decades of extensive research efforts, partially lured by their exotic properties and potential technology applications, and partially awakened by the profound and universal fundamental principles that govern these quantum critical systems. Due to the complex and non-perturbative nature, these systems face the most difficult and challenging problems in the study of modern condensed matter physics, and many important fundamental problems remain open. Recently, new developments in model design and algorithm improvements enabled unbiased large-scale numerical solutions to be achieved in the close vicinity of these quantum critical points, which paves a new pathway towards achieving controlled conclusions through combined efforts of theoretical and numerical studies, as well as possible theoretical guidance for experiments in heavy-fermion compounds, Cu-based and Fe-based superconductors, ultra-cold fermionic atomic gas, twisted graphene layers, etc, where signatures of fermionic quantum criticality exist.
Quantum networks in their most general configuration consist of nodes, containing sources, detectors, memories, and logic gates, connected by both quantum and classical channels. Quantum networks leverage the unique properties of quantum mechanics to enable "beyond classical" communication, sensing, and computing protocols. The research community has recently emphasized computational simulation of these networks as an approach to gauging their performance, understanding their properties, and considering the impact of technical standards. Despite this, the implications of quantum networks in military contexts with limited resources remains underexplored. We review a recently introduced quantum network simulation framework that we developed, named QuanTACT, that is specifically tailored for integration into existing tactical simulation tools, such as the Extendable Mobile Ad hoc Network Emulator (EMANE). The QuanTACT framework is built from the SQUANCH quantum network simulation tool by adding quantum channel models for optical fiber and various subroutines required for entanglement-based QKD simulation such as key sifting, information reconciliation, and privacy amplification. Our choice of SQUANCH as opposed to other quantum network simulation tools is due to the agent-based model utilized by SQUANCH which allows for fully parallelized simulations with multiple agents running their own processes. This distributed architecture is, by design, consistent with EMANE and facilitates future integration. Building off of benchmark results based on field-deployed QKD experiments, we investigate the computational scaling properties of this system for linear chains of nodes that exchange keys via an XOR operation.