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arXiv:2410.17876

Fast classical simulation of qubit-qudit hybrid systems

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

Published Oct 23, 2024• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2410.17876

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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.
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 TTT-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.
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 .
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum circuits are essential for determining the problem size at which quantum solutions outperform classical methods. In this work, we present a novel hybrid simulation approach, forming a hybrid of a fullstate and a Clifford simulator, specifically designed to address the computational challenges associated with the time evolution of quantum chemistry Hamiltonians. Our method focuses on the efficient emulation of multi-qubit rotations, a critical component of Trotterized Hamiltonian evolution. By optimizing the representation and execution of multi-qubit operations leveraging the Pauli frame, our approach significantly reduces the computational cost of simulating quantum circuits, enabling more efficient simulations. Beyond its impact on chemistry applications, our emulation strategy has broad implications for any computational workload that relies heavily on multi-qubit rotations. By increasing the efficiency of quantum simulations, our method facilitates more accurate and cost-effective studies of complex quantum systems. We quantify the performance improvements and computational savings for this emulation strategy, and we obtain a speedup of a factor ≈18\approx 18≈18 (≈22\approx 22≈22 with MPI) for our evaluated chemistry Hamiltonians with 24 qubits. Thus, we evaluate our integration of this emulation strategy into the Intel Quantum SDK, further bridging the gap between theoretical algorithm development and practical quantum software implementations.
Quantum circuit simulation is essential for researchers to develop and evaluate novel quantum algorithms with classical computers. Although full-state quantum circuit simulations are widely utilized for prototyping and debugging, they are computationally intensive due to the exponential growth in simulation time as the system size grows. To address the performance bottlenecks associated with conventional gate-by-gate simulation, this work refines the block-by-block simulation paradigm through blocking optimization, taking into account the architectural characteristics of hardware. The primary contribution of this research is the gate block search algorithm (GBSA), which efficiently groups the maximum number of quantum gates into gate blocks. This grouping technique enhances data reuse and reduces redundant memory accesses and I/O overhead during gate application. The proposed method is evaluated using both gate-level and circuit-level benchmarks on an AMD 64-core processor. Compared to conventional gate-by-gate simulators, such as QuEST and AerSimulator, the proposed approach achieves up to a 4.7× speedup in CPU execution and a 2.9× speedup in SSD-based scenarios. Furthermore, it can lead to a remarkable 46× reduction in memory and I/O traffic. These results indicate that the proposed block-based simulation strategy substantially improves the efficiency of quantum circuit simulation and can be readily adapted to multi-device environments, thereby supporting the rapid development of next-generation quantum algorithms.
Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access to quantum hardware remains too limited to meet the demand, simulating quantum circuits on conventional computers satisfies many needs. We advance Schrödinger-style simulation of quantum circuits that is useful standalone and as a building block in layered simulation algorithms, both cases are illustrated in our results. Our algorithmic contributions show how to simulate multiple quantum gates at once, how to avoid floating-point multiplies, how to best use data-level and thread-level parallelism as well as CPU cache, and how to leverage these optimizations by reordering circuit gates. While not described previously, these techniques implemented by us supported published high-performance distributed simulations up to 64 qubits. To show additional impact, we benchmark our simulator against Microsoft, IBM and Google simulators on hard circuits from Google.