Quantum Gates, Quantum Circuit and Quantum Computation

2008 ◽  
pp. 65-97
Keyword(s):  
Quantum Computation ◽  
Quantum Circuit ◽  
Quantum Gates

scholarly journals Optical-photon quantum computing

2018 ◽  
Author(s):  
Eugenio Piasini
Keyword(s):  
Quantum Computation ◽  
Optical Fibers ◽  
Canonical Quantization ◽  
Quantum Circuit ◽  
Phase Shifters ◽  
Quantum Gates ◽  
Quantum Bit ◽  
Optical Photon ◽  
Quantum Phenomena ◽  
Physical Tools

Optical photons present many interesting aspects in the context of the research for suitable physical representations of quantum bits. Photons are chargeless particles, and do not interact strongly with each other, or even with most matter. They can be guided along long distances with low loss in optical fibers, delayed efficiently using phase shifters, and combined easily using beamsplitters. Photons exhibit typical quantum phenomena, such as the interference produced in two-slit experiments. Furthermore, in principle, photons can be made interact with each other if carefully handled. There are many practical problems with this approach; nevertheless it presents, beyond what has already been noted, an appealing conceptual simplicity.The purpose of this work is to present - at least, in its fundamental principles - a set of optical photon quantum gates that is universal for quantum computation. To do so, we begin by gathering the necessary mathematical and physical tools. We discuss canonical quantization for the electromagnetic field, and we formalize in an abstract context the characteristic properties of every realization of the Fock canonical commutation relationships (CCR). We analize the class of the spaces where it is possible to give such a realization, and that naturally lend themselves to host the physical model of our interest. Once acquired these bases, we turn ourselves to a particular optic system, the Mach-Zehnder interferometer, and we study the general properties of this system and of its essential constituents. At this point we choose a particular encoding of quantum bit and we look at the optical devices just discussed as elements of a quantum circuit. We then discuss the fundamental ideas that may guide the implementation of some important quantum gates: Hadamard gate, $\pi/8$ gate and controlled-NOT. We conclude by showing that these three quantum gates form a universal set of gates for quantum computation.

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

scholarly journals Generation of elementary gates and Bell’s states using controlled adiabatic evolutions

2019 ◽  
Vol 17 (03) ◽  
pp. 1950020
Author(s):  
Abderrahim Benmachiche ◽  
Ali Sellami ◽  
Sherzod Turaev ◽  
Derradji Bahloul ◽  
Azeddine Messikh ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Open Systems ◽  
Circuit Model ◽  
Quantum Gates ◽  
Single Quantum ◽  
New Model ◽  
Adiabatic Quantum Computation ◽  
Usual Quantum

Fundamental quantum gates can be implemented effectively using adiabatic quantum computation or circuit model. Recently, Hen combined the two approaches to introduce a new model called controlled adiabatic evolutions [I. Hen, Phys. Rev. A, 91(2) (2015) 022309]. This model was specifically designed to implement one and two-qubit controlled gates. Later, Santos extended Hen’s work to implement [Formula: see text]-qubit controlled gates [A. C. Santos and M. S. Sarandy, Sci. Rep., 5 (2015) 15775]. In this paper, we discuss the implementation of each of the usual quantum gates, as well as demonstrate the possibility of preparing Bell’s states using the controlled adiabatic evolutions approach. We conclude by presenting the fidelity results of implementing single quantum gates and Bell’s states in open systems.

scholarly journals Measuring the Tangle of Three-Qubit States

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 436 ◽  
Author(s):  
Adrián Pérez-Salinas ◽  
Diego García-Martín ◽  
Carlos Bravo-Prieto ◽  
José Latorre
Keyword(s):  
Direct Measurement ◽  
Canonical Form ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Tripartite Entanglement ◽  
Single Qubit ◽  
Optimal Values ◽  
Random States ◽  
Qubit States ◽  
Computational Basis

We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal values for the parameters are learned in a variational fashion. Once this transformation is achieved, direct measurement of outcome probabilities in the computational basis provides an estimate of the tangle, which quantifies genuine tripartite entanglement. We perform simulations on a set of random states under different noise conditions to asses the validity of the method.

scholarly journals Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States

Micromachines ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1111
Author(s):  
Meng Li ◽  
Qian Zhang ◽  
Yang Chen ◽  
Xifeng Ren ◽  
Qihuang Gong ◽  
...  
Keyword(s):  
Femtosecond Laser ◽  
Quantum Computation ◽  
Logic Gates ◽  
Quantum Circuit ◽  
Bell States ◽  
Direct Writing ◽  
Laser Direct Writing ◽  
Quantum Logic Gates ◽  
Complex Circuits ◽  
Computation Algorithms

Integrated photonic quantum chip provides a promising platform to perform quantum computation, quantum simulation, quantum metrology and quantum communication. Femtosecond laser direct writing (FLDW) is a potential technique to fabricate various integrated photonic quantum chips in glass. Several quantum logic gates fabricated by FLDW have been reported, such as polarization and path encoded quantum controlled-NOT (CNOT) gates. By combining several single qubit gates and two qubit gates, the quantum circuit can realize different functions, such as generating quantum entangled states and performing quantum computation algorithms. Here we demonstrate the FLDW of integrated photonic quantum chips composed of one Hadamard gate and one CNOT gate for generating all four path-encoded Bell states. The experimental results show that the average fidelity of the reconstructed truth table reaches as high as 98.8 ± 0.3%. Our work is of great importance to be widely applied in many quantum circuits, therefore this technique would offer great potential to fabricate more complex circuits to realize more advanced functions.

Experimental demonstration of optimized quantum process tomography on the IBM quantum experience

2020 ◽  
pp. 2040004
Author(s):  
Akshay Gaikwad ◽  
Krishna Shende ◽  
Kavita Dorai
Keyword(s):  
Quantum Circuit ◽  
Quantum Gates ◽  
Experimental Demonstration ◽  
Superconducting Qubit ◽  
Quantum Process ◽  
Single Qubit ◽  
Quantum Process Tomography ◽  
Process Tomography ◽  
Quantum Processor ◽  
Least Squares Optimization

We experimentally performed complete and optimized quantum process tomography of quantum gates implemented on superconducting qubit-based IBM QX2 quantum processor via two constrained convex optimization (CCO) techniques: least squares optimization and compressed sensing optimization. We studied the performance of these methods by comparing the experimental complexity involved and the experimental fidelities obtained. We experimentally characterized several two-qubit quantum gates: identity gate, a controlled-NOT gate, and a SWAP gate. The general quantum circuit is efficient in the sense that the data needed to perform CCO-based process tomography can be directly acquired by measuring only a single qubit. The quantum circuit can be extended to higher dimensions and is also valid for other experimental platforms.

scholarly journals An Algorithm of Quantum Restricted Boltzmann Machine Network Based on Quantum Gates and Its Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Peilin Zhang ◽  
Sheng Li ◽  
Yu Zhou
Keyword(s):  
Quantum Computer ◽  
Quantum Circuit ◽  
Classification Performance ◽  
Generative Model ◽  
Restricted Boltzmann Machine ◽  
Quantum Gates ◽  
Boltzmann Machine ◽  
Discriminative Models

We present an algorithm of quantum restricted Boltzmann machine network based on quantum gates. The algorithm is used to initialize the procedure that adjusts the qubit and weights. After adjusting, the network forms an unsupervised generative model that gives better classification performance than other discriminative models. In addition, we show how the algorithm can be constructed with quantum circuit for quantum computer.

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