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QQ: Is 2-bit Enough? Exploiting Quantization to Enhance Computation and Memory Efficiency in Quantum Simulation

Hyoju Seo, Seokhyeon Lee, Yongtae Kim

Published Oct 26, 2025• 1 citation
Publisher

Abstract

Quantum computer simulations are essential for validating quantum algorithms but face significant computational and memory challenges due to massive floating-point arithmetic with complex numbers. In this paper, we propose a Quantization for Quantum computer simulation (QQ), an integer-based quantization scheme that considerably reduces these overheads while maintaining simulation accuracy. By exploiting the structure of quantum gate matrices, the proposed method separates real and imaginary components, eliminating zero-value operations. Across 25 quantum benchmark circuits, our quantization scheme reduces matrix-vector multiplications and additions by up to 50% and 66.7%, respectively, leading to energy savings of up to 400,834× compared to conventional quantum simulations. It also maintains simulation fidelity above 0.99 for most benchmark circuits, with over half preserving accuracy even at 2-bit precision. Additionally, it reduces memory usage by up to 93.75%, enabling scalable and efficient quantum computer simulations.

DOI
10.1109/iccad66269.2025.11240726

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Quantum computer simulations are essential for validating quantum algorithms but face significant computational and memory challenges due to massive floating-point arithmetic with complex numbers. In this paper, we propose a Quantization for Quantum computer simulation (QQ), an integer-based quantization scheme that considerably reduces these overheads while maintaining simulation accuracy. By exploiting the structure of quantum gate matrices, the proposed method separates real and imaginary components, eliminating zero-value operations. Across 25 quantum benchmark circuits, our quantization scheme reduces matrix-vector multiplications and additions by up to 50% and 66.7%, respectively, leading to energy savings of up to 400,834× compared to conventional quantum simulations. It also maintains simulation fidelity above 0.99 for most benchmark circuits, with over half preserving accuracy even at 2-bit precision. Additionally, it reduces memory usage by up to 93.75%, enabling scalable and efficient quantum computer simulations.
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Quantum computing holds immense promise for solving complex problems beyond the reach of classical computers. However, the realization of practical quantum computers faces significant challenges, including its inherent noise and error rates. To address these challenges and explore the capabilities of quantum computers, accurate and efficient quantum computer simulations are essential. This paper presents a novel quantum computer simulation framework designed to accommodate a wide range of custom reduced precision floating-point formats. Leveraging our proposed quantum computation algorithm, our framework enables the quantum computer simulations using exceptionally low precision floating-point numbers, while maintaining high accuracy levels. Through a systematic analysis, we explore the impact of floating-point precision on the accuracy of the quantum computer simulation, providing optimized bit-widths tailored for floating-point numbers. Particularly, using our proposed quantum computation algorithm, our framework achieves quantum state vector outcomes comparable to full-precision quantum simulations, even with extremely low precision floating-point formats ranging from 4 to 6 bits. Overall, these findings highlight the viability of precision reduction techniques in enhancing the efficiency of quantum computer simulations.
There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around 90%90\%90% reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to special structure in the algorithm or even in the underlying problem. We thus introduce a new simulation method that exploits this sparsity to reduce memory usage and simulation runtime. Moreover, our prototype implementation includes optimizations such as gate (re)scheduling, which amortizes data structure accesses and reduces memory usage. To benchmark our implementation, we run quantum algorithms for factoring, for computing integer and elliptic curve discrete logarithms, and for chemistry. Our simulator successfully runs a factoring instance of a 20-bit number using 102 qubits, and elliptic curve discrete logarithm over a 10-bit curve with 110 qubits. While previous work needed a supercomputer to simulate such instances of factoring, our approach succeeds in less than four minutes using a single core and less than 100 MB of memory. To the best of our knowledge, we are the first to fully simulate a quantum algorithm to compute elliptic curve discrete logarithms.
Noisy intermediate-scale quantum (NISQ) computers face significant reliability challenges because they are vulnerable to quantum noise, which severely limits their fidelity in quantum applications. In particular, deep circuits with a large number of quantum gates are susceptible to errors as they are more likely to lose their states in a deep circuit. In this paper, we propose a quantum circuit for square root operation that generates correct results on NISQ devices. The square root operation is used in many applications such as complex number computations, computer graphics, etc. While there have been limited studies on quantum square root circuits, none of them can be implemented on NISQ devices. In this work, we simplify the structure of an exact quantum square root circuit and reduce the number of quantum gates. The proposed design reduces the complexity of the square root circuit while maintaining the same level of precision in outputs. In addition, we exploit approximate computing to simplify the circuit further and run it on a real quantum computer. Approximate computing is used in classical computers to enhance the power and/or performance in exchange for accuracy. We exploit approximate computing for a different purpose, which is reducing the depth as well as the number of quantum gates in the square root circuit. To validate the effectiveness of our approach, we conduct experiments on an IBM quantum computer, where our circuit produces meaningful results. Furthermore, we present examples of error-resilient applications to demonstrate the validity of our approximate circuit.
As quantum computing technology continues to develop, the need for research into novel quantum algorithms is growing. However, such algorithms cannot yet be reliably tested on actual quantum hardware, which is still limited in several ways, including qubit coherence times, connectivity, and available qubits. To facilitate the development of novel algorithms despite this, simulators on classical computing systems are used to verify the correctness of an algorithm, and study its behaviour under different error models. In general, this involves operating on a memory space that grows exponentially with the number of qubits. In this work, we introduce quantum circuit transformations that allow for the construction of parameterised circuits for quantum algorithms. The parameterised circuits are in an ideal form to be processed by quantum compilation tools, such that the circuit can be partially evaluated prior to simulation, and a smaller specialised circuit can be constructed by eliminating fixed input qubits. We show significant reduction in the number of qubits for various quantum arithmetic circuits. Divide-by-n-bits quantum integer dividers are used as an example demonstration. It is shown that the complexity reduces from 4n+2 to 3n+2 qubits in the specialised versions. For quantum algorithms involving divide-by-8 arithmetic operations, a reduction by 28=256 in required memory is achieved for classical simulation, reducing the memory required from 137 GB to 0.53 GB.