Noisy Quantum Computing (QC) simulation on a classical machine is very time consuming since it requires Monte Carlo simulation with a large number of error-injection trials to model the effect of random noises. Orthogonal to existing QC simulation optimizations, we aim to accelerate the simulation by eliminating the redundant computation among those Monte Carlo simulation trials. We observe that the intermediate states of many trials can often be the same. Once these states are computed in one trial, they can be temporarily stored and reused in other trials. However, storing such states will consume significant memory space. To leverage the shared intermediate states without introducing too much storage overhead, we propose to statically generate and analyze the Monte Carlo simulation simulation trials before the actual simulation. Those trials are reordered to maximize the overlapped computation between two consecutive trials. The states that cannot be reused in follow-up simulation are dropped, so that we only need to store a few states. Experiment results show that the proposed optimization scheme can save on average 80% computation with only a small number of state vectors stored. In addition, the proposed simulation scheme demonstrates great scalability as more computation can be saved with more simulation trials or on future QC devices with reduced error rates.
Noisy Quantum Computing (QC) simulation on a classical machine is very time consuming since it requires Monte Carlo simulation with a large number of error-injection trials to model the effect of random noises. Orthogonal to existing QC simulation optimizations, we aim to accelerate the simulation by eliminating the redundant computation among those Monte Carlo simulation trials. We observe that the intermediate states of many trials can often be the same. Once these states are computed in one trial, they can be temporarily stored and reused in other trials. However, storing such states will consume significant memory space. To leverage the shared intermediate states without introducing too much storage overhead, we propose to statically generate and analyze the Monte Carlo simulation simulation trials before the actual simulation. Those trials are reordered to maximize the overlapped computation between two consecutive trials. The states that cannot be reused in follow-up simulation are dropped, so that we only need to store a few states. Experiment results show that the proposed optimization scheme can save on average 80% computation with only a small number of state vectors stored. In addition, the proposed simulation scheme demonstrates great scalability as more computation can be saved with more simulation trials or on future QC devices with reduced error rates.
As quantum devices continue to improve in scale and precision, a central challenge is how to effectively utilize noisy hardware for meaningful computation. Most existing approaches aim to recover noiseless circuit outputs from noisy ones through error mitigation or correction. Here, we show that noisy quantum devices can be directly leveraged as computational resources to enhance the classical simulation of quantum circuits. We introduce the Noisy-device-enhanced Classical Simulation (NDE-CS) protocol, which improves stabilizer-based classical Monte Carlo simulation methods by incorporating data obtained from noisy quantum hardware. Specifically, NDE-CS uses noisy executions of a target circuit together with noisy Clifford circuits to learn how the target circuit can be expressed in terms of Clifford circuits under realistic noise. The same learned relation can then be reused in the noiseless Clifford limit, enabling accurate estimation of ideal expectation values with substantially reduced sampling cost. Numerical simulations on Trotterized Ising circuits demonstrate that NDE-CS achieves orders-of-magnitude reductions in sampling cost compared to the underlying purely classical Monte Carlo approaches from which it is derived, while maintaining the same accuracy. We also compare NDE-CS with Sparse Pauli Dynamics (SPD), a powerful classical framework capable of simulating quantum circuits at previously inaccessible scales, and provide an example where the cost of SPD scales exponentially with system size, while NDE-CS scales much more favorably. These results establish NDE-CS as a scalable hybrid simulation approach for quantum circuits, where noise can be harnessed as a computational asset.
To realize the full potential of quantum computers, we must mitigate qubit errors by developing noise-aware algorithms, compilers, and architectures.Thus, simulating quantum programs on highperformance computing (HPC) systems with different noise models is a de facto tool researchers use.Unfortunately, noisy simulators iteratively execute a similar circuit for thousands of trials, thereby incurring significant performance overheads.To address this, we propose a noisy simulation technique called Tree-Based Quantum Circuit Simulation (TQSim) 1 .TQSim exploits the reusability of intermediate results during the noisy simulation, reducing computation.TQSim dynamically partitions a circuit into several subcircuits.It then reuses the intermediate results from these subcircuits during computation.Compared to a noisy Qulacsbased baseline simulator, TQSim achieves a speedup of up to 3.89× for noisy simulations.TQSim is designed to be efficient with multinode setups while also maintaining tight fidelity bounds.
Quantum computers are becoming practical for computing numerous applications. However, simulating quantum computing on classical computers is still demanding yet useful because current quantum computers are limited because of computer resources, hardware limits, instability, and noises. Improving quantum computing simulation performance in classical computers will contribute to the development of quantum computers and their algorithms. Quantum computing simulations on classical computers require long performance times, especially for quantum circuits with a large number of qubits or when simulating a large number of shots for noise simulations or circuits with intermediate measures. Graphical processing units (GPU) are suitable to accelerate quantum computer simulations by exploiting their computational power and high bandwidth memory and they have a large advantage in simulating relatively larger qubits circuits. However, GPUs are inefficient at simulating multi-shots runs with noises because the randomness prevents highly parallelization. In addition, GPUs have a disadvantage in simulating circuits with a small number of qubits because of the large overheads in GPU kernel execution. In this paper, we introduce optimization techniques for multi-shot simulations on GPUs. We gather multiple shots of simulations into a single GPU kernel execution to reduce overheads by scheduling randomness caused by noises. In addition, we introduce shot-branching that reduces calculations and memory usage for multi-shot simulations. By using these techniques, we speed up x10 from previous implementations.
Quantum computing has shown great potential in addressing traditional computational challenges, but due to its high error rates and noise issues, classical simulation has become an essential tool for verifying its performance. However, the superposition and entanglement properties of quantum systems pose significant challenges for simulation, especially when memory is limited. Although circuit cutting methods can decompose large-scale quantum circuits into smaller computational tasks to reduce computational load, previous research primarily focused on their application to quantum computers, without fully considering their effectiveness in quantum circuit simulation. This study fills that gap by proposing an optimization scheme based on a heuristic cutting algorithm and subcircuit state vector reuse to address memory limitations in simulations. By incorporating global computational cost considerations and an integer programming model, the heuristic method proposed in this paper not only optimizes the cutting process but also combines subcircuit state vector reuse to reduce redundant calculations and memory usage. Experimental results show that compared to current popular circuit cutting methods, the proposed approach significantly improves simulation speed while reducing memory requirements, effectively addressing the challenges in quantum circuit simulation. The overall average speedup achieved 46%.
With the development of quantum computing, quantum processor demonstrates the potential supremacy in specific applications, such as Grover's database search and popular quantum neural networks (QNNs). For better calibrating the quantum algorithms and machines, quantum circuit simulation on classical computers becomes crucial. However, as the number of quantum bits (qubits) increases, the memory requirement grows exponentially. In order to reduce memory usage and accelerate simulation, we propose a multi-level optimization, namely Mera, by exploring memory and computation redundancy. First, for a large number of sparse quantum gates, we propose two compressed structures for low-level full-state simulation. The corresponding gate operations are designed for practical implementations, which are relieved from the longtime compression and decompression. Second, for the dense Hadamard gate, which is definitely used to construct the superposition, we design a customized structure for significant memory saving as a regularity-oriented simulation. Meanwhile, an ondemand amplitude updating process is optimized for execution acceleration. Experiments show that our compressed structures increase the number of qubits from 17 to 35, and achieve up to6.9×acceleration for QNN.
Quantum simulations on noisy hardware are often designed as if the machine were ideal, with device limitations considered only after the basis and measurement plan have been chosen. We instead use information about the physical problem and the device at an earlier stage, to decide which states and evolution times should form a compact simulation basis. Because the target problem remains unchanged, the method adapts only the representation used to solve it. Tests on many-body and molecular models show that this approach can reveal useful directions that ordinary time evolution misses, while also exposing an important limitation: some of these directions can become too similar to estimate reliably. Realistic device data further show that hardware response can change the preferred states and evolution times before execution. Across seven acquisition days, a four-qubit experiment shows a median 54\% reduction in projected-energy error from problem-informed time choices relative to uniform sampling under matched hardware conditions. These results provide a proof of principle for simulation-basis design as a practical interface between quantum algorithms and the hardware that executes them.