With the rapid evolution of quantum computing, digital quantum simulations are essential for quantum algorithm verification, quantum error analysis, and new quantum applications. However, the exponential increase in memory overhead and operation time is challenging issues that have not been solved for years. We propose a novel approach that provides more qubits and faster quantum operations with smaller memory than before. Our method selectively tracks realized quantum states using a reduced quantum state representation scheme instead of loading the entire quantum states into memory. This method dramatically reduces memory space ensuring fast quantum computations without compromising the global quantum states. Furthermore, our empirical evaluation reveals that our proposed idea outperforms traditional methods for various algorithms. We verified that the Grover algorithm supports up to 55 qubits and the surface code algorithm supports up to 85 qubits in 512 GB memory on a single computational node, which is against the previous studies that support only between 35 qubits and 49 qubits.
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