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Current Applied Science and Technology

Understand Noise on Universal Quantum Adder Circuit

Wiphoo Methachawalit, Prabhas Chongstitvatana

Published Dec 14, 2023• 0 citations
Publisher

Abstract

Quantum Fourier Transform (QFT) is an essential algorithm for quantum computers. There are many uses of QFT in the application of quantum computing. In this work, we proposed a generalized adder circuit that was fundamental for QFT. We designed and ran the experiments with the proposed adder circuit on an IBM quantum computer facility. We observed that the number of qubits was one factor in the error rate. We found that our proposed two-qubits adder circuit running on the IBM quantum computer had an error rate of around 25%. The complexity of the adder circuit includes qubit connectivity, physical devices, and error from noise due to the environment. We demonstrated the constraints of the proposed adder circuit.

DOI
10.55003/cast.2023.255872

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Quantum Fourier Transform (QFT) is an essential algorithm for quantum computers. There are many uses of QFT in the application of quantum computing. In this work, we proposed a generalized adder circuit that was fundamental for QFT. We designed and ran the experiments with the proposed adder circuit on an IBM quantum computer facility. We observed that the number of qubits was one factor in the error rate. We found that our proposed two-qubits adder circuit running on the IBM quantum computer had an error rate of around 25%. The complexity of the adder circuit includes qubit connectivity, physical devices, and error from noise due to the environment. We demonstrated the constraints of the proposed adder circuit.
This paper reports the experiments on IBM quantum devices. We design an adder circuit based on Thomas G. Draper proposal. This circuit is a part of a general circuit to build Shor prime number factorization algorithm. We perform the experiments on three IBM quantum devices. The result of the experiment shows that on IBM Essex device, the best possible adder for one qubits has 100% accuracy. However, the results for two qubits adder circuit are much worse. The details analysis of the accuracy of three IBM devices are reported.
This paper reports the results of an investigation into the performance of quantum addition operations carried out by two quantum adders. These algorithms were run on IBM quantum computers and simulated with a noise model on Qiskit. Following this experimentation, we studied the rates of errors and the differences between the two adders. This study illuminated the benefits and drawbacks of the adders as well as the capabilities of a noise simulation consisting of coupling and basis gates noise to emulate real hardware. Our work provides additional data to inform the development of more efficient addition algorithms aimed at helping minimize error rates.
Quantum computers are able to efficiently solve certain problems that are very computationally demanding or even intractable on classical computers. With recent advances in quantum computing hardware, we are entering an exciting era where it is becoming possible to execute ‘useful’ quantum algorithms. However, quantum computers will continue to be noisy for the foreseeable future. In this paper, quantum adder circuits are used to evaluate three simple error mitigation methods: (1) error correction through the use of replicated circuits and a voter circuit, (2) error detection by encoding, which involves expanding the qubit space and partitioning it into orthogonal subspaces consisting of correct and incorrect code words, and (3) error mitigation by reducing circuit depth at the expense of increasing the number of qubits. These three mitigation methods are what we dub replication, encoding, and simplification, respectively. We find simplification to be most effective for implementing the simple quantum adders on the IBM Quantum Experience, while replication increases the gate count and the error count on current quantum devices. The encoding methods used in this study proved to be not effective for even the simple adder circuits that were implemented, suggesting the need to study and evaluate more sophisticated error correcting schemes.
The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor's algorithm, weighted sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM's superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands' superposed integer states. We analyze performance, and identify the most effective approximation depths for quantum add and quantum multiply within the given context. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. We analyze performance trends in our results and speculate on possible future development within this computational paradigm.
This article demonstrates a quantum calculator by experimentally simulating and performing basic arithmetic operations, namely addition, subtraction, multiplication, division on real quantum devices using the IBM Quantum Experience (IBM QE) platform. Two addition algorithms are considered, the classical version, using the Toffoli gate, and using the quantum Fourier transform (QFT). In particular summation with QFT saves memory and time. The task of the work is to build a quantum circuit that performs arithmetic operations between the binary representation of two integers. We then propose a quantum algorithm for converting decimal to binary. This method also allows for massive parallelization during its execution. The addition, subtraction, multiplication, and division functions based on QFT have been improved with some changes. The proposed operations are compared with the closest quantum arithmetic operations. Therefore, we can implement a practical quantum calculator by performing operations on a real quantum computer. The circuits are defined as a kind of quantum adder using a quantum Fourier transform, implemented in Qiskit and demonstrated on one or two copies.
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The complexity of the algorithm is O(log⁡2(M)/d)\mathcal{O}( \log^2(M)/d )O(log2(M)/d) for an array with M=(2n)dM=(2^n)^dM=(2n)d elements (n∈N)(n \in \mathbb{N})(n∈N) equally separated along ddd dimensions. Relevant properties for application are discussed. An example on current hardware is depicted by a 6 qubit 2D-QFT with an IBM quantum computer.