Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.01759

Optimal fidelity in implementing Grover's search algorithm on open quantum system

Nilanjana Chanda, Rangeet Bhattacharyya

Published Mar 3, 2023• 0 citations
arXivHTMLPDF

Abstract

We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

DOI
10.48550/arxiv.2303.01759

Related papers

Optimal Clock Speed of Single-Qubit Operations

Nilanjana Chanda, Rangeet Bhattacharyya

Efficient implementation of quantum algorithms requires single- or multi-qubit gates with high fidelity. We use a recently reported thermal fluctuation-regulated quantum master equation to estimate the fidelity of single-qubit gates on open quantum systems. We show that the fidelity is a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves non-monotonically with the drive-amplitude. The calculated fidelity is found to have a maximum corresponding to an optimum value of the drive-amplitude. Therefore, the highest fidelity of the single-qubit operations on open quantum systems would require an optimal clock speed. The arguments are also extended to multi-qubit systems.

•Aug 1, 2019•0 citations

Optimal clock speed of qubit gate operations on open quantum systems

Nilanjana Chanda, Rangeet Bhattacharyya

Efficient implementation of quantum algorithms requires single- or multiple-qubit gates with high fidelity. Here we report that the fidelity of gate operations on open quantum systems has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To demonstrate this, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The fidelity is found to be a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves nonmonotonically with the drive amplitude. The existence of an optimum drive amplitude implies that the qubit gate operations on open quantum systems would have an optimal clock speed. We demonstrate the universality of the results for the gate operations on single- and multiple-qubit gates.

arXiv:1908.00443•Physical Review A•Apr 22, 2020•11 citations

Quantum Noise and Information in Quantum Search Algorithm

Demosthenes Ellinas

External influences in the form of quantum noise on Grover’s search algorithm are investigated. The study shows that the algorithm can be robust under such external dissipation. The effect of noise is described by a completely positive trace preserving map, acting on an unsorted N‐dimensional database made of projective density matrices. To evaluate the efficiency of the algorithm two figures of merit are used, the radial fidelity giving the projection between the Bloch vectors of target and final density operators, and the cosine of angular fidelity between the same vectors. Explicitly we prove that the resulting search positive map depends on x, the strength of the coupling to the environment, and that there are infinitely many x values, named good x’s and bad x’s, for which search is successful after O(N) queries, or fails, respectively . Next we study the information theoretic aspects of the dissipative quantum search algorithm. To this end we view the initial state as a pure qubit signal entering through a cascade of quantum channels, each channel described by a completely positive map, and corresponds to the iterations of the algorithm. This map is identical to the dissipative search map of the algorithm for which the parameter x now characterizes the influence of the noisy channel exercised upon the incoming quantum signal. The process of searching is understood as transmission of the initial signal/item through the composite channel made by O(N) elementary channels. The quality of this transmission corresponds to the fidelity of targeting the wanted item in the quantum database, and is studied in terms of the majorization/quantum entropy of the input‐output density matrix, and by the entropy exchanged between the qubit signal/item and an external environment.

AIP conference proceedings•Jan 1, 2004•1 citation

Multi-Qubit Dynamical Quantum Search Algorithm with Dissipation

Ali H. Homid, Mahmoud Abdel‐Aty, A.‐S. F. Obada

We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in implementing the current algorithm.

arXiv:1509.04858•Sep 16, 2015•0 citations

DOI: 10.1140/epjd/e2006-00046-x THE EUROPEAN PHYSICAL JOURNAL D

Abstract. Using the methods of quantum trajectories we study effects of dissipative decoherence on the accuracy of the Grover quantum search algorithm. The dependence on the number of qubits and dissipation rate are determined and tested numerically with up to 16 qubits. As a result, our numerical and analytical studies give the universal law for decay of fidelity and probability of searched state which are induced by dissipative decoherence effects. This law is in agreement with the results obtained previously for quantum chaos algorithms. PACS. 03.67.Lx Quantum Computation – 03.65.Yz Decoherence; open systems; quantum statistical meth-ods – 24.10.Cn Many-body theory QICS. 11.40.+s Search – 13.10.+n Effects of noise and imperfections – 11.50.+m Quantum maps, quantum chaos Nowadays the quantum computing attracts a great inter-est of the scientific community [1]. The main reason of that is due to the fact that certain quantum algorithms allow to perform computations much faster than the usual classical algorithms. The famous example is the Shor algo-

•Jan 1, 2005•0 citations

Coherence Fraction in Grover Search Algorithm

Si-Qi Zhou, Hai Jin, Jin-Min Liang +3 more

The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain the quantum advantage achieved by the Grover search algorithm. By introducing a generalized Grover search algorithm, we demonstrate that the success probability depends not only on the querying number of oracles but also on the coherence fraction, which quantifies the fidelity between an arbitrary initial quantum state and the equal superposition state. Additionally, we explore the role of the coherence fraction in the quantum minimization algorithm, which offers a framework for solving complex problems in quantum machine learning. These findings offer insights into the origins of quantum advantage and open pathways for the development of new quantum algorithms.

quant-pharXiv:2511.06835•Physical Review A•Nov 11, 2025•6 citations
We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.
Efficient implementation of quantum algorithms requires single- or multi-qubit gates with high fidelity. We use a recently reported thermal fluctuation-regulated quantum master equation to estimate the fidelity of single-qubit gates on open quantum systems. We show that the fidelity is a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves non-monotonically with the drive-amplitude. The calculated fidelity is found to have a maximum corresponding to an optimum value of the drive-amplitude. Therefore, the highest fidelity of the single-qubit operations on open quantum systems would require an optimal clock speed. The arguments are also extended to multi-qubit systems.
Efficient implementation of quantum algorithms requires single- or multiple-qubit gates with high fidelity. Here we report that the fidelity of gate operations on open quantum systems has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To demonstrate this, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The fidelity is found to be a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves nonmonotonically with the drive amplitude. The existence of an optimum drive amplitude implies that the qubit gate operations on open quantum systems would have an optimal clock speed. We demonstrate the universality of the results for the gate operations on single- and multiple-qubit gates.
External influences in the form of quantum noise on Grover’s search algorithm are investigated. The study shows that the algorithm can be robust under such external dissipation. The effect of noise is described by a completely positive trace preserving map, acting on an unsorted N‐dimensional database made of projective density matrices. To evaluate the efficiency of the algorithm two figures of merit are used, the radial fidelity giving the projection between the Bloch vectors of target and final density operators, and the cosine of angular fidelity between the same vectors. Explicitly we prove that the resulting search positive map depends on x, the strength of the coupling to the environment, and that there are infinitely many x values, named good x’s and bad x’s, for which search is successful after O(N) queries, or fails, respectively . Next we study the information theoretic aspects of the dissipative quantum search algorithm. To this end we view the initial state as a pure qubit signal entering through a cascade of quantum channels, each channel described by a completely positive map, and corresponds to the iterations of the algorithm. This map is identical to the dissipative search map of the algorithm for which the parameter x now characterizes the influence of the noisy channel exercised upon the incoming quantum signal. The process of searching is understood as transmission of the initial signal/item through the composite channel made by O(N) elementary channels. The quality of this transmission corresponds to the fidelity of targeting the wanted item in the quantum database, and is studied in terms of the majorization/quantum entropy of the input‐output density matrix, and by the entropy exchanged between the qubit signal/item and an external environment.
We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in implementing the current algorithm.
Abstract. Using the methods of quantum trajectories we study effects of dissipative decoherence on the accuracy of the Grover quantum search algorithm. The dependence on the number of qubits and dissipation rate are determined and tested numerically with up to 16 qubits. As a result, our numerical and analytical studies give the universal law for decay of fidelity and probability of searched state which are induced by dissipative decoherence effects. This law is in agreement with the results obtained previously for quantum chaos algorithms. PACS. 03.67.Lx Quantum Computation – 03.65.Yz Decoherence; open systems; quantum statistical meth-ods – 24.10.Cn Many-body theory QICS. 11.40.+s Search – 13.10.+n Effects of noise and imperfections – 11.50.+m Quantum maps, quantum chaos Nowadays the quantum computing attracts a great inter-est of the scientific community [1]. The main reason of that is due to the fact that certain quantum algorithms allow to perform computations much faster than the usual classical algorithms. The famous example is the Shor algo-
The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain the quantum advantage achieved by the Grover search algorithm. By introducing a generalized Grover search algorithm, we demonstrate that the success probability depends not only on the querying number of oracles but also on the coherence fraction, which quantifies the fidelity between an arbitrary initial quantum state and the equal superposition state. Additionally, we explore the role of the coherence fraction in the quantum minimization algorithm, which offers a framework for solving complex problems in quantum machine learning. These findings offer insights into the origins of quantum advantage and open pathways for the development of new quantum algorithms.