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.
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.
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.
Since quantum computers can solve important problems faster than classical computers, many resources have gone into the development of this technology in recent decades. Despite the tremendous progress that has already been made toward the development of quantum computers, they are still an emerging technology, which restricts access and reliability. Thus, research on quantum algorithms still heavily relies on quantum circuit simulators that run on classical hardware. However, simulating the execution of a quantum computer on conventional hardware is exponentially difficult, which is also the reason why quantum computing is an interesting technology in the first place. Particularly complex is noise-aware simulation of quantum computers, i.e., the consideration of noise effects that are common in today’s quantum hardware during quantum circuit simulation. In this work, we investigate the use of decision diagrams for this task. To this end, we present two distinct approaches for noise-aware quantum circuit simulation, investigate how they can be realized using decision diagrams, and implement decision diagram-based solutions for each of the presented noise-aware simulation schemes. In an extensive evaluation, we unveil potential for further improvements and also demonstrate substantial speed-ups compared to the current state of the art.
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.
Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on conventional machines are significantly relied on to perform quantum computing research. The straightforward array-based simulators require a tremendous amount of memory that increases exponentially with respect to the number of qubits. To mitigate such computing resource concerns, decision diagram based simulators were proposed that can efficiently exploit data redundancies in quantum states and operations. In this paper, we study two classes of quantum circuits on which the state-of-the-art decision diagram based simulators failed to perform well in terms of simulation time. We also propose a simple and powerful reorder trick to boost the simulation of such quantum circuits. Preliminary evaluation results demonstrate the usefulness of the proposed trick. Especially, for the Quantum Phase Estimation circuits, the proposed trick achieved speedups up to 313.6x compared to a state-of-the-art approach that relies on an auxiliary tool to optimize simulation order.
Quantum computers promise to solve important problems faster than conventional computers ever could. Underneath is a fundamentally different computational primitive that introduces new challenges for the development of software tools that aid designers of corresponding quantum algorithms. The different computational primitives render classical simulation of quantum circuits particularly challenging. While the logic simulation of conventional circuits is comparatively simple with linear complexity with respect to the number of gates, quantum circuit simulation has to deal with the exponential memory requirements to represent quantum states on non-quantum hardware with respect to the number of qubits. Decision Diagrams (DDs) address this challenge through exploitation of redundancies in matrices and vectors to provide significantly more compact representations in many cases. Moreover, the probabilistic nature of quantum computations enables another angle to tackle the complexity: Quantum algorithms are resistant to some degree against small inaccuracies in the quantum state as these only lead to small changes in the outcome probabilities. We propose to exploit this resistance against (small) errors to gain even more compact decision diagrams. In this work, we investigate the potential of approximation in quantum circuit simulation in detail. To this end, we first present four dedicated schemes that exploit the error resistance and efficiently approximate quantum states represented by decision diagrams. Subsequently, we propose two simulation strategies that utilize those approximations schemes in order to improve the efficiency of DD-based quantum circuit simulation, while, at the same time, allowing the user to control the resulting degradation in accuracy. We empirically show that the proposed approximation schemes reduce the size of decision diagrams substantially and also analytically prove the effect of multiple approximations on the attained accuracy. Eventually, this enables speed-ups of the resulting approximate quantum circuit simulation of up to several orders of magnitudes—again, while controlling the fidelity of the result.
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups, e.g., for integer factorization or database search. However, since physical realizations of quantum computers are in their infancy, a significant amount of research in this domain still relies on simulations of quantum computations on conventional machines. This causes a significant complexity which current state-of-the-art simulators try to tackle with a rather straight forward array-based representation and by applying massive hardware power. There also exist solutions based on decision diagrams (i.e., graph-based approaches) that try to tackle the exponential complexity by exploiting redundancies in quantum states and operations. However, these existing approaches do not fully exploit redundancies that are actually present. In this paper, we revisit the basics of quantum computation, investigate how corresponding quantum states and quantum operations can be represented even more compactly, and, eventually, simulated in a more efficient fashion. This leads to a new graph-based simulation approach which outperforms state-of-the-art simulators (array-based as well as graph-based). Experimental evaluations show that the proposed solution is capable of simulating quantum computations for more qubits than before, and in significantly less run-time (several magnitudes faster compared to previously proposed simulators). An implementation of the proposed simulator is publicly available online at http://iic.jku.at/eda/research/quantum_simulation.