Quantum Gates, Quantum Circuit and Quantum Computa- tion

2008 ◽  
pp. 81-114
Keyword(s):  
Quantum Circuit ◽  
Quantum Gates

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.

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.

scholarly journals Quantum Implementation of Powell’s Conjugate Direction Method

2019 ◽  
Vol 23 (4) ◽  
pp. 726-734
Author(s):  
Kehan Chen ◽  
Fei Yan ◽  
Kaoru Hirota ◽  
Jianping Zhao ◽  
◽  
...  
Keyword(s):  
Search Algorithm ◽  
Quantum Circuit ◽  
Data Fitting ◽  
Quadratic Equation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Circuit Implementation ◽  
One Dimensional ◽  
Conjugate Direction ◽  
Conjugate Direction Method

A quantum circuit implementation of Powell’s conjugate direction method (“Powell’s method”) is proposed based on quantum basic transformations in this study. Powell’s method intends to find the minimum of a function, including a sequence of parameters, by changing one parameter at a time. The quantum circuits that implement Powell’s method are logically built by combining quantum computing units and basic quantum gates. The main contributions of this study are the quantum realization of a quadratic equation, the proposal of a quantum one-dimensional search algorithm, the quantum implementation of updating the searching direction array (SDA), and the quantum judgment of stopping the Powell’s iteration. A simulation demonstrates the execution of Powell’s method, and future applications, such as data fitting and image registration, are discussed.

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.

Analyzing Heuristic-based Randomized Search Strategies for the Quantum Circuit Compilation Problem

2020 ◽  
Vol 174 (3-4) ◽  
pp. 259-281
Author(s):  
Angelo Oddi ◽  
Riccardo Rasconi
Keyword(s):  
Quantum Computing ◽  
Nearest Neighbor ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Ranking Functions ◽  
Solution Quality ◽  
Circuit Realization ◽  
Definition Of

In this work we investigate the performance of greedy randomised search (GRS) techniques to the problem of compiling quantum circuits to emerging quantum hardware. Quantum computing (QC) represents the next big step towards power consumption minimisation and CPU speed boost in the future of computing machines. Quantum computing uses quantum gates that manipulate multi-valued bits (qubits). A quantum circuit is composed of a number of qubits and a series of quantum gates that operate on those qubits, and whose execution realises a specific quantum algorithm. Current quantum computing technologies limit the qubit interaction distance allowing the execution of gates between adjacent qubits only. This has opened the way to the exploration of possible techniques aimed at guaranteeing nearest-neighbor (NN) compliance in any quantum circuit through the addition of a number of so-called swap gates between adjacent qubits. In addition, technological limitations (decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized. One core contribution of the paper is the definition of two lexicographic ranking functions for quantum gate selection, using two keys: one key acts as a global closure metric to minimise the solution makespan; the second one is a local metric, which favours the mutual approach of the closest qstates pairs. We present a GRS procedure that synthesises NN-compliant quantum circuits realizations, starting from a set of benchmark instances of different size belonging to the Quantum Approximate Optimization Algorithm (QAOA) class tailored for the MaxCut problem. We propose a comparison between the presented meta-heuristics and the approaches used in the recent literature against the same benchmarks, both from the CPU efficiency and from the solution quality standpoint. In particular, we compare our approach against a reference benchmark initially proposed and subsequently expanded in [1] by considering: (i) variable qubit state initialisation and (ii) crosstalk constraints that further restrict parallel gate execution.

A Quantum Model of Computation

2006 ◽  
Author(s):  
Phillip Kaye ◽  
Raymond Laflamme ◽  
Michele Mosca
Keyword(s):  
Quantum Circuit ◽  
Circuit Model ◽  
Circuit Diagram ◽  
Qubit State ◽  
Quantum Gates ◽  
Quantum Model ◽  
Reversible Circuit ◽  
Logical Qubits ◽  
General Measurement ◽  
Computational Basis

In Section 1.3, we introduced the circuit model of (classical) computation. We restricted attention to reversible circuits since they can simulate any non-reversible circuit with modest overhead. This model can be generalized to a model of quantum circuits. In the quantum circuit model, we have logical qubits carried along ‘wires’, and quantum gates that act on the qubits. A quantum gate acting on n qubits has the input qubits carried to it by n wires, and n other wires carry the output qubits away from the gate. A quantum circuit is often illustrated schematically by a circuit diagram as shown in Figure 4.1. The wires are shown as horizontal lines, and we imagine the qubits propagating along the wires from left to right in time. The gates are shown as rectangular blocks. For convenience, we will restrict attention to unitary quantum gates (which are also reversible). Recall from Section 3.5.3 that non-unitary (non-reversible) quantum operations can be simulated by unitary (reversible) quantum gates if we allow the possibility of adding an ancilla and of discarding some output qubits. A circuit diagram describing a superoperator being implemented using a unitary operator is illustrated in Figure 4.2. In the example of Figure 4.1, the 4-qubit state |ψi⟩= |0⟩⊗ |0⟩⊗ |0⟩⊗ |0⟩ enters the circuit at the left (recall we often write this state as |ψi⟩ = |0⟩|0⟩|0⟩|0⟩ or |ψi⟩ = |0000⟩.) These qubits are processed by the gates U1, U2, U3, and U4. At the output of the circuit we have the collective (possibly entangled) 4-qubit state |ψf⟩. A measurement is then made of the resulting state. The measurement will often be a simple qubit-by-qubit measurement in the computational basis, but in some cases may be a more general measurement of the joint state. A measurement of a single qubit in the computational basis is denoted on a circuit diagram by a small triangle, as shown in Figure 4.1 (there are other symbols used in the literature, but we adopt this one). The triangle symbol will be modified for cases in which there is a need to indicate different types of measurements.R50

scholarly journals Towards optimization of quantum circuits

Open Physics ◽  
2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Michal Sedlák ◽  
Martin Plesch
Keyword(s):  
Quantum Information ◽  
Quantum Information Processing ◽  
Quantum Circuit ◽  
Quantum Gate ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Unitary Operation ◽  
Short Sequence ◽  
Toffoli Gates ◽  
Universal Procedure

AbstractAny unitary operation in quantum information processing can be implemented via a sequence of simpler steps — quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates — efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.

scholarly journals Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers

2022 ◽  
Vol 12 (2) ◽  
pp. 759
Author(s):  
Anna M. Krol ◽  
Aritra Sarkar ◽  
Imran Ashraf ◽  
Zaid Al-Ars ◽  
Koen Bertels
Keyword(s):  
Quantum Algorithms ◽  
Optimization Method ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Underlying Structure ◽  
Quantum Computers ◽  
Unitary Matrices ◽  
Quantum Operations ◽  
Test Part ◽  
Input Gate

Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.

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