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Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the 2 n -cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only O (n 2 + n t) two-qubit gates compared to the O (n 2 t) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers. [ABSTRACT FROM AUTHOR]

Physical limitations of quantum hardware often necessitate nearest-neighbor (NN) architecture. When synthesizing quantum circuits using the basic gate library, which consists of CNOT and single-qubit gates, CNOT gates are required to convert a quantum circuit into one suitable for an NN architecture. In the basic gate library, CNOT gates are considered the primary cost of quantum circuits due to their higher error rates and longer execution times compared to single-qubit gates. In this paper, we propose a new linear NN (LNN) circuit design for quantum Fourier transform (QFT), one of the most versatile subroutines in quantum algorithms. Our LNN QFT circuit has only about 40% of the number of CNOT gates compared to previously known LNN QFT circuits. Subsequently, we input both our QFT circuits and conventional QFT circuits into the Qiskit transpiler to construct QFTs on IBM quantum computers, which necessitate NN architectures. Consequently, our QFT circuits demonstrate a substantial advantage over conventional QFT circuits in terms of the number of CNOT gates. This outcome implies that the proposed LNN QFT circuit design could serve as a novel foundation for developing QFT circuits implemented in quantum hardware that demands NN architecture. [ABSTRACT FROM AUTHOR]

Drive cycles in vehicle systems are important determinants for energy consumption, emissions, and safety. Estimating the frequency of the drive cycle quickly is important for control applications related to fuel efficiency, emission reduction and improving safety. Quantum computing has established the computational efficiency that can be gained. A drive cycle frequency estimation algorithm based on the quantum Fourier transform is exponentially faster than the classical Fourier transform. The algorithm is applied on real world data set. We evaluate the method using a quantum computing simulator, demonstrating remarkable consistency with the results from the classical Fourier transform. Current quantum computers are noisy, a simple method is proposed to mitigate the impact of the noise. The method is evaluated on a 15 qubit IBM-q quantum computer. The proposed method for a noisy quantum computer is still faster than the classical Fourier transform. [ABSTRACT FROM AUTHOR]

The present study aimed to analyze the simulation data of two different quantum algorithms: Deutsch Algorithm and the Quantum Fourier Transform. In order to execute this, has been used the Qiskit framework to implement the afore mentioned algotihms. Such simulations took place on local machine (classic computer) and on the quantum chips of International Business Machines (IBM) via cloud. On the local machine the results obtained are those predicted by the theory. In IBM prototypes, small error fluctuations have been observed. However, the expected states were obtained with high probability. Our results show that the quantum computers are robust to the studied algorithms, been this an intuitive way to teach the concepts of quantum information and computation to students in the professional (techinical) level of graduation. [ABSTRACT FROM AUTHOR]

Diamond quantum processors consisting of a nitrogen-vacancy centre and surrounding nuclear spins have been the key to significant advancements in room-temperature quantum computing, quantum sensing and microscopy. The optimisation of these processors is crucial for the development of large-scale diamond quantum computers and the next generation of enhanced quantum sensors and microscopes. Here, we present a full model of multi-qubit diamond quantum processors and develop a semi-analytical method for designing gate pulses. This method optimises gate speed and fidelity in the presence of random control errors and is readily compatible with feedback optimisation routines. We theoretically demonstrate infidelities approaching ∼10−5 for single-qubit gates and established evidence that this can also be achieved for a two-qubit CZ gate. Consequently, our method reduces the effects of control errors below the errors introduced by hyperfine field misalignment and the unavoidable decoherence that is intrinsic to the processors. Having developed this optimal control, we simulated the performance of a diamond quantum processor by computing quantum Fourier transforms. We find that the simulated diamond quantum processor is able to achieve fast operations with low error probability. [ABSTRACT FROM AUTHOR]

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver. [ABSTRACT FROM AUTHOR]

Quantum computers promise to be able to solve tasks beyond the reach of standard computational platforms. Among the others, photonic quantum walks prove to be great candidates for their implementation, since single photon sources, passive linear optics and photo-detectors are sufficient for universal quantum computation. To this aim, a device performing the quantum Fourier transform represents a fundamental building block for quantum algorithms, whose applications are not limited to the field of quantum computation. Recently, an algorithm has been developed to efficiently realize a quantum Fourier transform of an input photonic state by using a quantum walk on elementary linear-optical components. Here we provide a simple operative description of the algorithm, introducing a whole class of quantum transformations achievable through a generalization of this procedure. We finally discuss how femtosecond laser writing technology well represents an efficient and scalable platform for the implementation of this class of photonic quantum walks. [ABSTRACT FROM AUTHOR]

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40Ca+ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm. [ABSTRACT FROM AUTHOR]

The maximum clique in an undirected graph is the largest subset of a set of graph's vertices where each pair of elements in the subset is connected. The problem of finding maximum clique in an arbitrary graph is NP-Hard problem with many applications in practice and it is very important to try to develop a new and a potentially faster algorithms that solve it. In this paper I would like to propose a new algorithm for quantum computers that finds the maximum clique in an arbitrary undirected graph which is based on a version of Grover's quantum algorithm for finding an element in an unsorted list in which there can be an unknown number of solutions. Anew algorithm has 0(∣V∣ √2∣V∣) worst case time complexity and 0(∣V∣ √2∣V∣) best case time complexity. Algorithm's, quantum alogrithm, maximum clique. [ABSTRACT FROM AUTHOR]

Abstract: We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The Quantum Fourier Transform is one of the most important quantum subroutines known at present, used in most algorithms that have exponential speed-up compared to the classical ones. We briefly review Fast Fourier Transform and then make explicit all the steps that led to the quantum formulation of the algorithm, generalizing Coppersmith’s work. [Copyright &y& Elsevier]

We consider quantum learning machines-quantum computers that modify themselves in order to improve their performance in some way-that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k = 2m and mϵℕ. The reason for this speed-up is that the classical machine requires memory of size log k = m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k. [ABSTRACT FROM AUTHOR]

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed to be able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these toe problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, for example the number of digits of the integer to be factored. [ABSTRACT FROM AUTHOR]