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Asia and South Pacific Design Automation Conference (ASP-DAC)

Concurrency in DD-based Quantum Circuit Simulation

Stefan Hillmich, Alwin Zulehner, Robert Wille

Published Jan 1, 2020• 16 citations
Publisher

Abstract

Despite recent progress in physical implementations of quantum computers, a significant amount of research still depends on simulating quantum computations on classical computers. Here, most state-of-the-art simulators rely on array-based approaches which are perfectly suited for acceleration through concurrency using multi- or many-core processors. However, those methods have exponential memory complexities and, hence, become infeasible if the considered quantum circuits are too large. To address this drawback, complementary approaches based on decision diagrams (called DD-based simulation) have been proposed which provide more compact representations in many cases. While this allows to simulate quantum circuits that could not be simulated before, it is unclear whether DD-based simulation also allows for similar acceleration through concurrency as array-based approaches. In this work, we investigate this issue. The resulting findings provide a better understanding about when DD-based simulation can be accelerated through concurrent executions of sub-tasks and when not.

DOI
10.1109/asp-dac47756.2020.9045711

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Despite recent progress in physical implementations of quantum computers, a significant amount of research still depends on simulating quantum computations on classical computers. Here, most state-of-the-art simulators rely on array-based approaches which are perfectly suited for acceleration through concurrency using multi- or many-core processors. However, those methods have exponential memory complexities and, hence, become infeasible if the considered quantum circuits are too large. To address this drawback, complementary approaches based on decision diagrams (called DD-based simulation) have been proposed which provide more compact representations in many cases. While this allows to simulate quantum circuits that could not be simulated before, it is unclear whether DD-based simulation also allows for similar acceleration through concurrency as array-based approaches. In this work, we investigate this issue. The resulting findings provide a better understanding about when DD-based simulation can be accelerated through concurrent executions of sub-tasks and when not.
Despite the recent progress in the physical implementation of quantum computers, a significant amount of research still depends on the use of quantum circuit simulators running on classical hardware. While there are several techniques for quantum circuit simulation, many state-of-the-art simulators rely on an array-based simulation approach. However, this array-based approach has exponential memory complexity with respect to the number of simulated qubits. To address this drawback, complementary approaches based on decision diagrams have been proposed. While these approaches allow simulating circuits that could not be simulated before, they come with their own drawbacks. Unfortunately, no detailed case study has been conducted to date, which compares those complementary approaches and their respective strengths and weaknesses. In this work, we are addressing this by providing a survey on both approaches as well as a detailed case study on their respective performances.
By using quantum mechanical effects, quantum computers promise significant speedups in solving problems intractable for conventional computers. However, despite recent progress they remain limited in scaling and availability---making quantum software and hardware development heavily reliant on quantum simulators running on conventional hardware. However, most of those simulators mimic perfect quantum computers and, hence, ignore the fragile nature of quantum mechanical effects which frequently yield to decoherence errors in real quantum devices. Considering those errors during the simulation is complex, but necessary in order to tailor quantum algorithms for specific devices. Thus far, most state-of-the-art simulators considering decoherence errors rely on (exponentially) large array representations. As an alternative, simulators based on decision diagrams have been shown very promising for simulation of quantum circuits in general, but have not supported decoherence errors yet. In this work, we are closing this gap. We investigate how the consideration of decoherence errors affects the simulation performance of approaches based on decision diagrams and propose advanced solutions to mitigate negative effects. Experiments confirm that this yields improvements of several orders of magnitudes compared to a naive consideration of errors.
Recent years have seen unprecedented advance in the design and control of quantum computers. Nonetheless, their applicability is still restricted and access remains expensive. Therefore, a substantial amount of quantum algorithms research still relies on simulating quantum circuits on classical hardware. However, due to the sheer complexity of simulating real quantum computers, many simulators unrealistically simplify the problem and instead simulate perfect quantum hardware, i.e., they do not consider errors caused by the fragile nature of quantum systems. Stochastic quantum simulation provides a conceptually suitable solution to this problem: physically motivated errors are applied in a probabilistic fashion throughout the simulation. In this work, we propose to use decision diagrams, as well as concurrent executions, to substantially reduce resource-requirements-which are still daunting—for stochastic quantum circuit simulation. Backed up by rigorous theory, empirical studies show that this approach allows for a substantially faster and much more scalable simulation for certain quantum circuits.
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Recent technological advancements show promise in leveraging quantum mechanical phenomena for computation. This brings substantial speed-ups to problems that are once considered to be intractable in the classical world. However, the physical realization of quantum computers is still far away from us, and a majority of research work is done using quantum simulators running on classical computers. Classical computers face a critical obstacle in simulating quantum algorithms. Quantum states reside in a Hilbert space whose size grows exponentially to the number of subsystems, i.e., qubits. As a result, the straightforward statevector approach does not scale due to the exponential growth of the memory requirement. Decision diagrams have gained attention in recent years for representing quantum states and operations in quantum simulations. The main advantage of this approach is its ability to exploit redundancy. However, mainstream quantum simulators still rely on statevectors or tensor networks. We consider the absence of decision diagrams due to the lack of parallelization strategies. This work explores several strategies for parallelizing decision diagram operations, specifically for quantum simulations. We propose optimal parallelization strategies. Based on the experiment results, our parallelization strategy achieves a 2-3 times faster simulation of Grover’s algorithm and random circuits than the state-of-the-art single-thread DD-based simulator DDSIM.
Quantum computing is gaining considerable momentum through the recent progress in physical realizations of quantum computers. This led to rather sophisticated design flows in which the originally specified quantum functionality is compiled through different abstractions. This increasingly raises the question whether the respectively resulting quantum circuits indeed realize the originally intended function. Accordingly, efficient methods for equivalence checking are gaining importance. However, existing solutions still suffer from significant shortcomings such as their exponential worst case performance and an increased effort to obtain counterexamples in case of non-equivalence. In this work, we propose an improved DD-based equivalence checking approach which addresses these shortcomings. To this end, we utilize decision diagrams and exploit the fact that quantum operations are inherently reversible - allowing for dedicated strategies that keep the overhead moderate in many cases. Experimental results confirm that the proposed strategies lead to substantial speed-ups - allowing to perform equivalence checking of quantum circuits factors or even magnitudes faster than the state of the art.