© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Scientific and technical journal of information technologies mechanics and optics

Modeling of integrated optical quantum search algorithm

E.O. Samsonov, Fedor Dmitrievich Kiselev, Sergey A. Chivilikhin, V. I. Egorov, Danylo Kirichenko, Yu.A. Adam, R.A. Kabiev, Artur V. Gleim

Published Jun 3, 2019• 0 citations

Abstract

Subject of Research. The paper presents a quantum search algorithm model, suitable for integration into a linear optical chip. Error impact caused by two-qubit operator implementation and directional coupler manufacture imperfection on the algorithm output is studied. Method. Analytical calculation of the algorithm scheme was performed to assess error impact caused by two-qubit operator optical implementation. Numerical simulation of the algorithm was executed for taking into account distortions caused by directional coupler imperfections. The simulation was completed using Qutip library on Python programming language. Main Results. Two well-known implementations of the algorithm scheme main component, a two-qubit CZ gate, are compared in order to select the most optimal chip architecture. It was shown that one of two-qubit gate implementations introduces an error critical for the algorithm work. Another implementation based on projection measurements does not introduce an error, but has a lower efﬁciency. We have performed simulation of the proposed scheme, taking into account the imperfections of its components in the framework of unitary dynamics. We have shown that the algorithm error probability does not exceed 0.011. Two-qubit Grover’s algorithm оptical implementation with regard to directional coupler imperfections has a low error rate, but it is limited by the low two-qubit operator efﬁciency. Practical Relevance. The study carried out can be useful for the physical implementation of the algorithm. Creation of an integrated optical scheme that implements Grover’s algorithm will make it possible to build a quantum router for the optimal route search in quantum networks with complex topology.

DOI: 10.17586/2226-1494-2019-19-3-394-401

Related papers

Modeling two-qubit Grover’s algorithm implementation in a linear optical chip

E.O. Samsonov, Fedor Dmitrievich Kiselev, Y Shmelev +5 more

Abstract This paper introduces a model of Grover’s algorithm suitable for implementation in a linear photonic chip. We compare two known realizations of its main components, two-qubit CZ gates, in order to define optimal chip architecture. The algorithm operation is simulated considering directional coupler imperfection influence on the scheme parameters. We also determined tolerance boundaries for distortions of the coupler dimensions.

Physica Scripta•Dec 23, 2019•7 citations

Modeling two-qubit Grovers algorithm implementation in a linear optical chip

E.O. Samsonov, Fedor Dmitrievich Kiselev

We introduce a model of Grovers algorithm suitable for implementation in a linear photonic chip. We compared two known realizations of two-qubit CZ gates and determined tolerance boundaries for distortions of the coupler dimensions.

Quantum Information and Measurement (QIM)•Jan 1, 2019•0 citations

Recursive multiport schemes for implementing quantum algorithms with photonic integrated circuits

Gelo Noel M. Tabia

We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on $2d$ modes using a pair of circuits for the same operation on $d$ modes. The circuits operate on path-encoded qudits and realize $d$-dimensional unitary transformations on these states using linear optical networks with $O\left({d}^{2}\right)$ optical elements. To evaluate the schemes against realistic errors, we ran simulations of proof-of-principle experiments using a simple fabrication model of silicon-based photonic integrated devices that employ directional couplers and thermo-optic modulators for beam splitters and phase shifters, respectively. We find that high-fidelity performance is achievable with our multiport circuits for 2-qubit and 3-qubit quantum Fourier transforms, and for quantum search on four-item and eight-item databases.

arXiv:1509.04246•Physical Review A•Jan 14, 2016•13 citations

Implementation of an efficient linear-optical quantum router

Karol Bartkiewicz, Antonín Černoch, Karel Lemr

For several decades, scientists have been aware of significant benefits allowing quantum information processing technologies to surpass their classical counterparts. Recent technological development allows these benefits to be tested experimentally and in some cases also implemented in practical devices. So far the majority of experimental quantum networks was limited to peer-to-peer communications between two parties. Practical implementation of quantum communications networks, however, needs to address the problem of scalability to serve large numbers of users. Similarly to classical computer networks, their quantum counterparts would require routing protocols to direct the signal from its source to destination. Devices implementing these routing protocols are called quantum routers and have recently been subject of an intense research. In this paper, we report on experimental implementation of a linear-optical quantum router. Our device allows single-photon polarization-encoded qubits to be routed coherently into two spatial output modes depending on the state of two identical control qubits. The polarization qubit state of the routed photon is maintained during the routing operation. The success probability of our scheme can be increased up to 25% making it the most efficient linear-optical quantum router developed to this date.

arXiv:1802.05741•Scientific Reports•Sep 3, 2018•17 citations

Modeling of linear optical controlled-z quantum gate with dimensional errors of passive components

Fedor Dmitrievich Kiselev, E.Y. Samsonov, Artur V. Gleim

Linear optical quantum computing can be realized using photonic integrate circuits (PICs).It is advantageous in comparison to other physical implementations of quantum computing due to simplicity of qubit encoding using photons and low decoherence times.Passive components like beamsplitters and phaseshifters are key elements for such PICs.In this article, we present modeling of linear optical controlled-Z gate with imperfections of beamsplitters and phaseshifters taken into account.Results showed that errors occur which cannot be detected by projection measurements and post-selection proposed by Knill, Laflamme and Milburn.We studied how these errors and success probability changes with the increase of dimensional errors using Monte-Carlo simulation.The obtained results can be used for design and calibration stages of chip manufacturing.

Nanosystems Physics Chemistry Mathematics•Dec 28, 2019•2 citations

Simulating a Quantum Computer : Grover's Search Algorithm with Error Correction

Martin Sjöborg, Hanna Linn

Classical simulations of quantum computers give us an insight into various things such as what quantum algorithms can achieve, whether it is possible to verify that they function as postulated, the difficulties that have to be overcome before quantum computers can be realized, as well as how we can handle these difficulties. We build a Python library to simulate a quantum computer that can perform all quantum algorithms by defining an universal gate set, from which all quantum gates – and thereby all circuits – can be constructed. We implement two algorithms that both highlight two important aspects of quantum computing: Grover’s quantum search algorithm, which demonstrates the efficiency of quantum algorithms and their superiority over their classical counterparts by searching an unsorted list quadratically faster; and an error correcting code, the Shor code, which highlights the cost of correcting the possible errors in a quantum computer.We test the rigidity of Grover’s algorithm by introducing errors without correction, and find that the algorithm shows resilience to smaller 1-qubit Pauli errors, but looses its efficiency under larger errors and thus the need for Pauli error correction arise.

•Jan 1, 2018•0 citations

Subject of Research. The paper presents a quantum search algorithm model, suitable for integration into a linear optical chip. Error impact caused by two-qubit operator implementation and directional coupler manufacture imperfection on the algorithm output is studied. Method. Analytical calculation of the algorithm scheme was performed to assess error impact caused by two-qubit operator optical implementation. Numerical simulation of the algorithm was executed for taking into account distortions caused by directional coupler imperfections. The simulation was completed using Qutip library on Python programming language. Main Results. Two well-known implementations of the algorithm scheme main component, a two-qubit CZ gate, are compared in order to select the most optimal chip architecture. It was shown that one of two-qubit gate implementations introduces an error critical for the algorithm work. Another implementation based on projection measurements does not introduce an error, but has a lower efﬁciency. We have performed simulation of the proposed scheme, taking into account the imperfections of its components in the framework of unitary dynamics. We have shown that the algorithm error probability does not exceed 0.011. Two-qubit Grover’s algorithm оptical implementation with regard to directional coupler imperfections has a low error rate, but it is limited by the low two-qubit operator efﬁciency. Practical Relevance. The study carried out can be useful for the physical implementation of the algorithm. Creation of an integrated optical scheme that implements Grover’s algorithm will make it possible to build a quantum router for the optimal route search in quantum networks with complex topology.

We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on

2d

modes using a pair of circuits for the same operation on

d

modes. The circuits operate on path-encoded qudits and realize

d

-dimensional unitary transformations on these states using linear optical networks with

O\left({d}^{2}\right)

optical elements. To evaluate the schemes against realistic errors, we ran simulations of proof-of-principle experiments using a simple fabrication model of silicon-based photonic integrated devices that employ directional couplers and thermo-optic modulators for beam splitters and phase shifters, respectively. We find that high-fidelity performance is achievable with our multiport circuits for 2-qubit and 3-qubit quantum Fourier transforms, and for quantum search on four-item and eight-item databases.

For several decades, scientists have been aware of significant benefits allowing quantum information processing technologies to surpass their classical counterparts. Recent technological development allows these benefits to be tested experimentally and in some cases also implemented in practical devices. So far the majority of experimental quantum networks was limited to peer-to-peer communications between two parties. Practical implementation of quantum communications networks, however, needs to address the problem of scalability to serve large numbers of users. Similarly to classical computer networks, their quantum counterparts would require routing protocols to direct the signal from its source to destination. Devices implementing these routing protocols are called quantum routers and have recently been subject of an intense research. In this paper, we report on experimental implementation of a linear-optical quantum router. Our device allows single-photon polarization-encoded qubits to be routed coherently into two spatial output modes depending on the state of two identical control qubits. The polarization qubit state of the routed photon is maintained during the routing operation. The success probability of our scheme can be increased up to 25% making it the most efficient linear-optical quantum router developed to this date.

Linear optical quantum computing can be realized using photonic integrate circuits (PICs).It is advantageous in comparison to other physical implementations of quantum computing due to simplicity of qubit encoding using photons and low decoherence times.Passive components like beamsplitters and phaseshifters are key elements for such PICs.In this article, we present modeling of linear optical controlled-Z gate with imperfections of beamsplitters and phaseshifters taken into account.Results showed that errors occur which cannot be detected by projection measurements and post-selection proposed by Knill, Laflamme and Milburn.We studied how these errors and success probability changes with the increase of dimensional errors using Monte-Carlo simulation.The obtained results can be used for design and calibration stages of chip manufacturing.

Classical simulations of quantum computers give us an insight into various things such as what quantum algorithms can achieve, whether it is possible to verify that they function as postulated, the difficulties that have to be overcome before quantum computers can be realized, as well as how we can handle these difficulties. We build a Python library to simulate a quantum computer that can perform all quantum algorithms by defining an universal gate set, from which all quantum gates – and thereby all circuits – can be constructed. We implement two algorithms that both highlight two important aspects of quantum computing: Grover’s quantum search algorithm, which demonstrates the efficiency of quantum algorithms and their superiority over their classical counterparts by searching an unsorted list quadratically faster; and an error correcting code, the Shor code, which highlights the cost of correcting the possible errors in a quantum computer.We test the rigidity of Grover’s algorithm by introducing errors without correction, and find that the algorithm shows resilience to smaller 1-qubit Pauli errors, but looses its efficiency under larger errors and thus the need for Pauli error correction arise.