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 .
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 .
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× to 1000× faster than the state-of-the-art simulator for simulating multi-level quantum systems with various benchmark circuits.
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on multi-level, qudit, systems offers a range of advantages, including expanded gate sets, higher information density, and improved computational efficiency, which might play a key role in overcoming not only the limitations of classical machines but also of current qubit-based quantum devices. However, working with qudits faces challenges not only in experimental control but particularly in algorithm development and quantum software. In this work, we introduce MQT Qudits, an open-source tool, which, as part of the Munich Quantum Toolkit (MQT), is built to assist in designing and implementing applications for mixed-dimensional qudit devices. We specify a standardized language for mixed-dimension systems and discuss circuit specification, compilation to hardware gate sets, efficient circuit simulation, and open challenges. MQT Qudits is available at github.com/cda-tum/mqt-qudits and on pypi at pypi.org/project/mqt.qudits.
Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently introduced Clifford Augmented Matrix Product State (CAMPS) method offer scalability and efficiency by combining both tensor network and stabilizer simulation techniques and leveraging their complementary advantages. This hybrid simulation method has indeed demonstrated significant improvements in simulation performance for qubit circuits. Our work generalises the CAMPS method to higher quantum degrees of freedom -- qudit simulation, resulting in a generalised CAMPS (GCAMPS). Benchmarking this extended simulator on quantum systems with three degrees of freedom, i.e. qutrits, we show that similar to the case of qubits, qutrit systems also benefit from a comparable speedup using these techniques. Indeed, we see a greater improvement with qutrit simulation compared to qubit simulation on the same T-doped random Clifford benchmarking circuit as a result of the increased difficulty of conventional qutrit simulation using tensor networks. This extension allows for the classical simulation of problems that were previously intractable without access to a quantum device and will open new avenues to study complex many-body physics and to develop efficient methods for quantum information processing.
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.
The use of classical computers to simulate quantum computing has been successful in aiding the study of quantum algorithms and circuits that are too complex to examine analytically. Current implementations of quantum computing simulators are limited to two-level quantum systems. Recent advances in high-dimensional quantum computing systems have demonstrated the viability of working with multi-level superposition and entanglement. These advances allow an agile increase in the number of dimensions of the system while maintaining quantum entanglement, achieving higher encoding of information and making quantum algorithms less vulnerable to decoherence and computational errors. In this paper, we introduce QuantumSkynet, a novel high-dimensional cloud-based quantum computing simulator. This platform allows simulations of qudit-based quantum algorithms. We also propose a unified generalization of high-dimensional quantum gates, which are available for simulations in QuantumSkynet. Finally, we report simulations and their results for qudit-based versions of the Deutsch--Jozsa and quantum phase estimation algorithms using QuantumSkynet.
Developing state-of-the-art classical simulators of quantum circuits is of utmost importance to test and evaluate early quantum technology and understand the true potential of full-blown error-corrected quantum computers. In the past few years, multiple theoretical and numerical advances have continuously pushed the boundary of what is classically simulable, hence the development of a plethora of tools which are often limited to a specific purpose or designed for a particular hardware (e.g. CPUs vs. GPUs). Moreover, such tools are typically developed using tailored languages and syntax, which makes it hard to compare results from, and create hybrid approaches using, different simulation techniques. To support unified and optimized use of these techniques across platforms, we developed HybridQ , a highly extensible platform designed to provide a common framework to integrate multiple state-of-the-art techniques to run on a variety of hardware. The philosophy behind its development has been driven by three main pillars: Easy to Use, Easy to Extend, and Use the Best Available Technology. The powerful tools of HybridQ allow users to manipulate, develop, and extend noiseless and noisy circuits for different hardware architectures. HybridQ supports large-scale high-performance computing (HPC) simulations, automatically balancing workload among different processor nodes and enabling the use of multiple backends to maximize parallel efficiency. Everything is then glued together by a simple and expressive language that allows seamless switching from one technique to another as well as from one hardware to the next, without the need to write lengthy translations, thus greatly simplifying the development of new hybrid algorithms and techniques.