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.
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.
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.
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% 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.
Quantum computation and optimization have recently garnered considerable attention, with a noticeable focus on their floating-point and arithmetic designs. In classical computing, numerical optimization problems are commonly employed to assess the performance of optimization algorithms before their application to real-world issues. Nevertheless, precision issues impact the performance analysis of these algorithms, and neglecting these predictable exceptions can lead to unforeseen consequences. Therefore, this study systematically organizes potential precision issues related to how the floating-point storage format impacts optimization. These issues cause the optimal solution to deviate from the theoretical value, introducing imprecision or multiple optimal values, which in turn affects the usability of optimization algorithms, the direction of the search, and the assessment of convergence levels. These analyses offer valuable insights into the practical behavior of optimization algorithms when applied to function optimization problems, aiding researchers in accurately assessing and enhancing algorithm performance. Moreover, these findings contribute to the advancement of both classical and quantum computation.
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.
Quantum computation promises to solve many hard or infeasible problems substantially faster than classical solutions. The involvement of big players like Google, IBM, Intel, Rigetti, or Microsoft furthermore led to a momentum which increases the demand for automated design methods for quantum computations. In this context, decision diagrams for quantum computation provide a major pillar as they allow to efficiently represent quantum states and quantum operations which, otherwise, have to be described in terms of exponentially large state vectors and unitary matrices. However, current decision diagrams for the quantum domain suffer from a tradeoff between accuracy and compactness, since: 1) small errors that are inevitably introduced by the limited precision of floating-point arithmetic can harm the compactness (i.e., the size of the decision diagram) significantly and 2) overcompensating these errors (to increase compactness) may lead to an information loss and introduces numerical instabilities. In this article, we describe and evaluate the effects of this tradeoff which clearly motivates the need for a solution that is perfectly accurate and compact at the same time. More precisely, we show that the tradeoff indeed weakens current design automation approaches for quantum computation (possibly leading to corrupted results or infeasible run-times). To overcome this, we propose an alternative approach that utilizes an algebraic representation of the occurring complex and irrational numbers and outline how this can be incorporated in a decision diagram which is suited for quantum computation. Evaluations show that-at the cost of an overhead which is moderate in many cases-the proposed algebraic solution indeed overcomes the tradeoff between accuracy and compactness that is present in current numerical solutions.
The advent of quantum computing has ushered in a new era of computational capabilities, promising to revolutionize the resolution of complex problems. Unlike classical computers, which rely on binary digits (bits) to process information, quantum computers utilize quantum bits (qubits) that can exist in multiple states simultaneously due to the principles of superposition and entanglement inherent in quantum mechanics. This fundamental difference allows quantum computers to perform certain calculations exponentially faster than their classical counterparts, offering profound implications for fields ranging from cryptography to material science. At the heart of this transformative potential lie quantum algorithms, specifically designed to harness the unique properties of quantum systems to tackle problems currently intractable for classical computers. Notable examples include Shor's algorithm for integer factorization, which threatens the security of widely used cryptographic schemes, and Grover's algorithm for unstructured search, which provides a quadratic speedup over classical approaches. Beyond these pioneering works, ongoing research continues to uncover new quantum algorithms capable of addressing a broad spectrum of applications. The proposed method leverages the principles of quantum mechanics to develop efficient algorithms that outperform classical approaches in solving complex computational problems. By harnessing the unique properties of quantum bits (qubits), such as superposition and entanglement, the method aims to achieve superior accuracy and efficiency in various applications. The performance of the proposed method was evaluated using several key metrics: an accuracy of 94.8%, a Root Mean Squared Error (RMSE) of 0.208, and a Mean Absolute Error (MAE) of 0.406. These metrics collectively underscore the robustness and reliability of the proposed quantum algorithms, highlighting their potential to significantly enhance computational efficiency and accuracy across various domains. This study delves into the development of quantum algorithms, exploring their theoretical foundations, practical implementations, and the challenges faced in their realization. By leveraging the principles of quantum mechanics, these algorithms hold the promise of not only solving existing problems more efficiently but also unlocking new computational paradigms previously deemed unattainable. Through a comprehensive analysis, this research aims to elucidate the current state of quantum algorithm research, highlight the advancements made, and identify the pathways forward in this rapidly evolving field.