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International Journal of Scientific and Research Publications

Simulation and validation of qubits based on Phase estimation algorithm

T Elanchezhiyan, Dheerendra Singh Tomar

Published Jan 24, 2022• 0 citations
Publisher

Abstract

After the advent of Quantum Physics, new opportunities were created for research and development in the world of science and technology.Quantum computation is one such emerging technology which allows for notable speed-ups compared to conventional computational methods.Here a quantum bit simulator is presented.This simulator is an engineering work, and no deep understanding of quantum mechanics is required from the user.The well-known phase estimation algorithm is presented using this simulator.The qubit simulator will be a useful tool for the study of quantum computer circuits, quantum computing, and the development of new quantum algorithms

DOI
10.29322/ijsrp.12.01.2022.p12149

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After the advent of Quantum Physics, new opportunities were created for research and development in the world of science and technology.Quantum computation is one such emerging technology which allows for notable speed-ups compared to conventional computational methods.Here a quantum bit simulator is presented.This simulator is an engineering work, and no deep understanding of quantum mechanics is required from the user.The well-known phase estimation algorithm is presented using this simulator.The qubit simulator will be a useful tool for the study of quantum computer circuits, quantum computing, and the development of new quantum algorithms
A quantum computer simulator is presented. This simulator is an engineering work and no deep understanding of quantum mechanics is required from the user. The simulator is based on the circuit model of quantum computation in which quantum gates act on quantum registers which comprise a number of quantum bits (qubits). The inputs to the simulator are the initial states of the qubits that form a quantum register and the quantum gates applied at each computation step. The inputs are entered through a graphical user interface. The outputs of the simulator are the matrices that represent the quantum register state at each quantum computation step and graphical outputs that show the probability of measuring each one of the possible quantum register base states and the phase of each state at each computation step. The well-known Deutsch's algorithm and the quantum Fourier transform, which is the base of many quantum algorithms, are presented using this simulator. Furthermore, the generation and variation of entanglement during quantum computations can be calculated using this simulator. The quantum computer simulator is a useful tool for the study of quantum computer circuits, quantum computing, and the development of new quantum algorithms.
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.
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A significant new frontier in computing has been opened up by the emergence of the quantum computing paradigm in recent years. By utilising the special abilities of quantum bits, or qubits, to complete complicated calculations tenfold quicker than with traditional computers, quantum computing has the potential to completely transform the computing industry. As this nascent field advances, the need for accessible and versatile quantum computing tools becomes increasingly evident. This research highlights the evolving landscape of quantum computing tools, emphasizing their critical role in the development and application of quantum algorithms and technologies. These tools encompass a spectrum of software and hardware components that aid researchers, engineers, and developers in utilising quantum computing's potential.
Quantum computing is one of the emerging technologies with its immense capability, allowing us to solve computationally challenging problems more efficiently. Gaining a real quantum computer for running and testing algorithms is very costly. In order for developers and researchers to build and test algorithms, they can use simulators that can model the behaviour of a real quantum computer inside a classical computer. Simulating a quantum system on a classical machine is complex and requires a lot of processing power. This paper introduces some basic algorithms and methodologies we used to simulate an ideal multi-qubit simulator in classical terms
ABSTRACT Quantum Phase Estimation (QPE) is a cornerstone algorithm in quantum computing, with applications ranging from integer factorization to quantum chemistry simulations. However, the resource demands of standard QPE, which require a large number of coherent qubits and deep circuits, pose significant challenges for current Noisy Intermediate Scale Quantum (NISQ) devices. In this work, we introduce the Adaptive Windowed Quantum Phase Estimation (AWQPE) algorithm, a novel method designed to address the limitations of standard QPE. AWQPE utilizes small, independent blocks of control qubits to estimate multiple phase bits simultaneously within a “window,” thereby significantly reducing the number of coherent qubits required to achieve a desired precision. These independent blocks are amenable to parallelization and, when combined with a robust least‐significant‐bit (LSB) to most‐significant‐bit (MSB) ambiguity resolution mechanism, enhance the algorithm's accuracy while mitigating the risk of error propagation. Our numerical simulations demonstrate AWQPE's accuracy and improved robustness relative to standard QPE under representative noise models, showcasing a favorable balance between resource efficiency and computational speed. This makes AWQPE particularly well‐suited for near‐term quantum platforms.