Quantum circuit simulator (QCS) is essential for designing quantum algorithms because it assists researchers in understanding how quantum operations work without access to expensive quantum computers. Traditional array-based QCSs suffer from exponential time and memory complexities. To address this problem, Decision Diagram (DD) was introduced to compress simulation data by exploring the circuit regularity. However, for irregular circuit structures, DD-based simulation incurs significant runtime and memory overhead. To overcome this challenge, we present FlatDD, a high-performance QCS that capitalizes on the strength of both DD- and array-based approaches. FlatDD parallelizes the simulation workload at multiple levels and leverages an efficient caching technique to reuse historical results. To further enhance the simulation performance for deep circuits, FlatDD introduces a gate-fusion algorithm to reduce the computational cost. Compared to state-of-the-art QCSs on commonly used quantum circuits, FlatDD achieves 34.81× speed-up and 1.93× memory reduction.
Quantum circuit simulator (QCS) is essential for designing quantum algorithms because it assists researchers in understanding how quantum operations work without access to expensive quantum computers. Traditional array-based QCSs suffer from exponential time and memory complexities. To address this problem, Decision Diagram (DD) was introduced to compress simulation data by exploring the circuit regularity. However, for irregular circuit structures, DD-based simulation incurs significant runtime and memory overhead. To overcome this challenge, we present FlatDD, a high-performance QCS that capitalizes on the strength of both DD- and array-based approaches. FlatDD parallelizes the simulation workload at multiple levels and leverages an efficient caching technique to reuse historical results. To further enhance the simulation performance for deep circuits, FlatDD introduces a gate-fusion algorithm to reduce the computational cost. Compared to state-of-the-art QCSs on commonly used quantum circuits, FlatDD achieves 34.81× speed-up and 1.93× memory reduction.
Quantum circuit simulator (QCS) is essential for designing quantum algorithms because it assists researchers in understanding how quantum operations work without access to expensive quantum computers. Traditional array-based QCSs suffer from exponential time and memory complexities. To address this problem, Decision Diagram (DD) was introduced to compress simulation data by exploring the circuit regularity. However, for irregular circuit structures, DD-based simulation incurs significant runtime and memory overhead. To overcome this challenge, we present FlatDD, a parallel QCS that capitalizes on the strength of both DD- and array-based approaches. FlatDD parallelizes the simulation workload at multiple levels and leverages caching to reuse historical results. To further enhance the simulation performance for deep circuits, FlatDD introduces a gate-fusion algorithm to reduce the computational cost. Compared to state-of-the-art QCSs on commonly used quantum circuits, FlatDD achieves 54.35 × speed-up and 1.91 × memory reduction.
Quantum circuit simulation (QCS) plays an important role in the designs and analysis of a quantum algorithm, as it assists researchers in understanding how quantum operations work without accessing expensive quantum computers. Despite many QCS methods, they are largely limited to simulating one input at a time. However, many simulation-driven quantum computing applications, such as testing and verification, require simulating multiple inputs to reason a quantum algorithm under different scenarios. We refer to this type of QCS as batch quantum circuit simulation (BQCS). In this paper, we present BQSim, a GPU-accelerated batch quantum circuit simulator. BQSim is inspired by the state-of-the-art decision diagram (DD) that can compactly represent quantum gate matrices, but overcomes its limitation of CPU-centric simulation. Specifically, BQSim uses DD to optimize a quantum circuit for reduced BQCS computation and converts DD to a GPU-efficient data structure. Additionally, BQSim employs a task graph-based execution strategy to minimize repetitive kernel call overhead and efficiently overlap kernel execution with data movement. Compared with three state-of-the-art quantum circuit simulators, cuQuantum, Qiskit Aer, and FlatDD, BQSim is 3.25×, 159.06×, and 311.42× faster on average.
Classical simulation remains essential for the development of quantum algorithms; however, traditional matrix-based methods struggle with scalability. While the Fast Tensor Decision Diagram (FTDD) framework offers a hybrid approach by combining the strengths of Tensor Networks and Decision Diagrams (DDs) for memory-efficient simulation, its core operations are often bottlenecked by memory management structures. Our primary motivation is to address the high computational and spatial cost associated with the hash tables, as well as to simplify the complexity of the simulation workflow. This work introduces systematic, low-level optimizations to the framework. Our main contribution is the enhancement of the memory management layer for the internal tables. We implemented a node reuse mechanism and designed a controlled strategy for hash table growth. These improvements minimize the memory footprint and reduce the costly hashing overhead inherent in DD-based simulators. We performed a thorough experimental analysis using a diverse set of quantum circuits, which were characterized by well-established metrics. Experimental results demonstrate that our enhancements improve the tool's performance and scalability. Notably, these advancements enable the simulation of complex circuits, such as Quantum Fourier Transform, with hundreds of qubits, on a standard server with 2-Tb of memory.
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.
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.
Since people became aware of the power of quantum phenomena in the domain of traditional computation, a great number of complex problems that were once considered intractable in the classical world have been tackled. The downsides of quantum supremacy are its high cost and unpredictability. In order to obtain a stronger control over quantum interactions(by reducing its noise) and reduce its cost, numerous researchers are relying on quantum simulators running on classical computers. The critical obstacle facing classical computers in the task of quantum simulation is its limited memory space. Quantum simulation intrinsically models the state evolution of quantum subsystems, i.e., qubits. Qubits are mathematically constructed in Hilbert space whose size grows exponentially with its number. Consequently, the scalability of the straightforward statevector approach is limited. It has been proven effective to adopt decision diagrams to mitigate the memory cost issue in various fields. In recent years, researchers have adapted decision diagrams into different forms for representing quantum states and performing quantum calculations efficiently. This leads to the study of decision diagram based quantum simulation. However, their advantage of memory efficiency does not let it replace the mainstream statevector and tensor network based approaches. We argue the reason is the lack of effective parallelization strategies in performing calculations on decision diagrams. In this work, we explore several strategies for parallelizing decision diagram operations with the focus on leveraging them for quantum simulations. The target is to find the optimal parallelization strategies and improve the performance of decision diagram based quantum simulation. Based on the experiment results, our proposed 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.