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IEEE Software

Fast Classical Simulation of Qubit-Qudit Hybrid Systems: Optimizing Efficiency in Classical Simulation of Multilevel Quantum Systems [Focus: Quantum Software and Its Engineering]

Haemanth Velmurugan, Arnav Das, Turbasu Chatterjee, Amit Saha, Anupam Chattopadhyay, Amlan Chakrabarti

Published Feb 5, 2025• 0 citations
Publisher

Abstract

Simulating quantum circuits is a computationally intensive task. Here, we adopt a block simulation methodology applicable to qubit-qudit hybrid systems, which is approximately 10× to 1000× faster than the state-of-the-art simulator for simulating multilevel quantum systems.
DOI
10.1109/ms.2025.3537804

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Simulating quantum circuits is a computationally intensive task that relies heavily on tensor products and matrix multiplications, which can be inefficient. Recent advancements, eliminate the need for tensor products and matrix multiplications, offering significant improvements in efficiency and parallelization. Extending these optimizations, we adopt a block-simulation methodology applicable to qubit-qudit hybrid systems. This method interprets the statevector as a collection of blocks and applies gates without computing the entire circuit unitary. Our method, a spiritual successor of the simulator QuDiet \cite{Chatterjee_2023}, utilizes this block-simulation method, thereby gaining major improvements over the simulation methods used by its predecessor. We exhibit that the proposed method is approximately 10×\times× to 1000×\times× faster than the state-of-the-art simulator for simulating multi-level quantum systems with various benchmark circuits.
We present a comprehensive study of quantum simulation methods and quantum simulators for classical computers. We first study an exhaustive set of 150+ simulators and quantum libraries. Then, we short-list the simulators that are actively maintained and enable simulation of quantum algorithms for more than 10 qubits. As a result, we realize that most efficient and actively maintained simulators have been developed after 2010. We also provide a taxonomy of the most important simulation methods, namely Schrodinger-based, Feynman path integrals, Heisenberg-based, and hybrid methods. We observe that most simulators fall in the category of Schrodinger-based approaches. However, there are a few efficient simulators belonging to other categories. We also make note that quantum frameworks form their own class of software tools that provide more flexibility for algorithm designers with a choice of simulators/simulation method. Another contribution of this study includes the use and classification of optimization methods used in a variety of simulators. We observe that some state-of-the-art simulators utilize a combination of software and hardware optimization techniques to scale up the simulation of quantum circuits. We summarize this study by providing a roadmap for future research that can further enhance the use of quantum simulators in education and research.
Abstract In recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state‐of‐the‐art classical simulators are only limited to binary quantum systems, which restrict the classical simulation of higher‐dimensional quantum computing systems. Through recent developments in higher‐dimensional quantum computing systems, it is realised that implementing qudits improves the overall performance of a quantum algorithm by increasing memory space and reducing the asymptotic complexity of a quantum circuit. Hence, in this article, QuDiet , a state‐of‐the‐art user‐friendly python‐based higher‐dimensional quantum computing simulator is introduced. QuDiet offers multi‐valued logic operations by utilising generalised quantum gates with an abstraction so that any naive user can simulate qudit systems with ease as compared to the existing ones. Various benchmark quantum circuits is simulated in QuDiet and show the considerable speedup in simulation time as compared to the other simulators without loss in precision. Finally, QuDiet provides a full qubit‐qudit hybrid quantum simulator package with quantum circuit templates of well‐known quantum algorithms for fast prototyping and simulation. Comprehensive simulation up to 20 qutrits circuit on depth 80 on QuDiet was successfully achieved. The complete code and packages of QuDiet is available at https://github.com/LegacYFTw/QuDiet .
Optimizing for a classification problem with a 0-1 loss function is an NP-hard problem [1] even for a simple binary classification task. As Preskill stated “We don't expect a quantum computer to solve worst case instances of NP-hard problems, but it might find better approximate solution or find it faster” [2]. Hybrid Quantum Classical Platforms harness the full capacity of Near-Term Quantum Computers. In this study, a focus is given on the variational circuits based approach accomplishing various machine learning tasks. We will survey a variety of experimental demonstrations conducted on actual quantum hardware and actively developing simulation software, anticipated to have a broad range of real-world applications in this increasingly growing field.
Quantum computers promise to solve several categories of problems faster than classical computers ever could. Current research mostly focuses on qubits, i.e., systems where the unit of information can assume only two levels. However, the underlying physics of most (if not all) of the technological platforms supports more than two levels, commonly referred to as qudits. Performing computations with qudits increases the overall complexity while, at the same time, reducing the number of operations and providing a lower error rate. Furthermore, qudits with different number of levels can be mixed in one system to ease the experimental control and keep representations as compact as possible. Exploiting these capabilities requires dedicated software support to tackle the increased complexity in an automated and efficient fashion. In this paper, we present a qudit simulator that handles mixed-dimensional systems based on Decision Diagrams (DDs). More precisely, we discuss the type of decision diagram introduced as underlying data structure as well as the resulting implementation. Experimental evaluations demonstrate that the proposed solution is capable of efficiently simulating mixed-dimensional quantum circuits, with specific use cases including more than 100 qudits in one circuit. The source code of the simulator is available via github.com/cda-tdum/MiSiM under the MIT license.
Qudit-based quantum computation offers unique advantages over qubit-based systems in terms of noise mitigation capabilities as well as algorithmic complexity improvements. However, the software ecosystem for multi-state quantum systems is severely limited. In this paper, we highlight a quantum workflow for describing and compiling qudit systems. We investigate the design and implementation of a quantum compiler for qudit systems. We also explore several key theoretical properties of qudit computing as well as efficient optimization techniques. Finally, we provide demonstrations using physical quantum computers as well as simulations of the proposed quantum toolchain.