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Register a new userThe influence of quantum noise on the Grover algorithm and quantum Fourier transform: quantum operations theory approach
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Added by
Yurii Ivanovich Bogdanov
Publication date
2017
fields
Physics
and research's language is
English
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The method of noisy multiqubit quantum circuits modeling is proposed. The analytical formulas for the dependence of quantum algorithms accuracy on qubits count and noise level are obtained for Grover algorithm and quantum Fourier transform. It is shown that the proposed approach is very much in line with results obtained by Monte Carlo statistical modeling method. The developed theory makes it possible to predict the influence of quantum noise on the accuracy of the forward-looking multiqubit quantum systems under development.
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Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.
In the Grover-type quantum search process a search operator is iteratively applied, say, k times, on the initial database state. We present an additive decomposition scheme such that the iteration process is expressed, in the computational space, as a linear combination of k operators, each of which consists of a single Grover-search followed by an overall phase-rotation. The value of k and the rotation phase are the same as those determined in the framework of the search with certainty. We further show that the final state can be expressed in terms of a single oracle operator of the Grover-search and phase-rotation factors. We discuss how the additive form can be utilized so that it effectively reduces the computational load of the iterative search, and we propose an effective shortcut gate that realizes the same outcome as the iterative search.
The Quantum Fourier Transformation ($QFT$) is a key building block for a whole wealth of quantum algorithms. Despite its proven efficiency, only a few proof-of-principle demonstrations have been reported. Here we utilize $QFT$ to enhance the performance of a quantum sensor. We implement the $QFT$ algorithm in a hybrid quantum register consisting of a nitrogen-vacancy (NV) center electron spin and three nuclear spins. The $QFT$ runs on the nuclear spins and serves to process the sensor - NV electron spin signal. We demonstrate $QFT$ for quantum (spins) and classical signals (radio frequency (RF) ) with near Heisenberg limited precision scaling. We further show the application of $QFT$ for demultiplexing the nuclear magnetic resonance (NMR) signal of two distinct target nuclear spins. Our results mark the application of a complex quantum algorithm in sensing which is of particular interest for high dynamic range quantum sensing and nanoscale NMR spectroscopy experiments.
We investigate the role of quantum coherence depletion (QCD) in Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure ($mathcal{C}_r$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the $l_1$ norm of coherence measure ($mathcal{C}_{l_1}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of database, no matter using $mathcal{C}_r$ or $mathcal{C}_{l_1}$. In generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichnys inequality are not violated.
It is called blind quantum computation(BQC) that a client who has limited quantum technologies can delegate her quantum computing to a server who has fully-advanced quantum computers. But the privacy of the clients quantum inputs, algorithms and outputs is still a challenge. To realize a secure BQC, we mainly study how to hide quantum fourier transform (QFT) performed on Bell states. In this paper, three cases are considered as follows. For the first case, we design primary BQC protocols of QFT performed on qubits 12 of belonging to ${|phi^pmrangle_{12},$ $|psi^pmrangle_{12}}$ with relevant circuits. To strengthen security, we construct enhanced BQC protocols of QFT performed on qubits 13 of any two Bell states $|xirangle_{12}otimes|thetarangle_{34}$ with relevant quantum circuits. Featured the property of stronger security, we give generalized BQC protocols of QFT performed on qubits 13 and 24 of any two Bell states with relevant quantum circuits respectively. At last, we analyze and prove the blindness and correctness.
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