Search

Quantum abstract detecting systems (QADS) provide a common framework to address detection problems in quantum computers. A particular QADS family, that of combinatorial QADS, has been proved to be useful for decision problems on eigenvalues or phase estimation methods. In this paper, we consider functional QADS, which not only have interesting theoretical properties (intrinsic detection ability, relation to the QFT), but also yield improved decision and phase estimation methods, as compared to combinatorial QADS. A first insight into the comparison with other phase estimation methods also shows promising results. [ABSTRACT FROM AUTHOR]

In 1985, Gabidulin introduced the rank metric in coding theory over finite fields, and used this kind of codes in a McEliece cryptosystem, six years later. In this paper, we consider rank metric codes over Galois rings. We propose a suitable metric for codes over such rings, and show its main properties. With this metric, we define Gabidulin codes over Galois rings, propose an efficient decoding algorithm for them, and hint their cryptographic application. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the quantum measurement detection algorithms (QMDA), whose objective is to detect whether unwanted measurements are being taken in a quantum circuit or not by applying the Zeno effect. A QMDA is a quantum circuit that includes three unitary matrices, one of them being applied numerous times consecutively, and whose initial state is fixed when no foreign measurements occur. One example is the Elitzur–Vaidman bomb tester, which is generalized by the QMDA definition, allowing the detection of measurements that are taken in an unknown basis and in circuits with an arbitrary number of qubits. We prove some key properties and limitations of these algorithms, as well as studying the performance of the Elitzur–Vaidman bomb tester and its possible improvements. Some extensions of the definition would lead to algorithms such as the counterfactual communication one. [ABSTRACT FROM AUTHOR]

The so-called Hamming distance measures the difference between two binary strings A and B. In simplified form, it measures the number of changes in A to get B. This type of distance is very useful in classical computing in applications such as error correction. It is also advantageous in quantum computing, being for example widely used in quantum machine learning. Since current quantum computers have limited resources, this type of distance is particularly attractive because it can be computed using fewer qubits and operations than other distances such as Euclidean or Manhattan distances. In this paper, two circuits for calculating Hamming distances using exclusively Clifford+T gates are presented. The aim of both circuits is to reduce the quantum cost and number of T gates needed to compute the Hamming distance. The T gate is more expensive than the other gates, so this reduction will have a significant impact on the total cost of the circuits. Furthermore, the proposed circuits are implemented using only Clifford+T gates. The circuits implemented exclusively with this group of gates are compatible with proven error detection and correction codes. [ABSTRACT FROM AUTHOR]

Current quantum computers have a limited number of resources and are heavily affected by internal and external noise. Therefore, small, noise-tolerant circuits are of great interest. With regard to circuit size, it is especially important to reduce the number of required qubits. Concerning to fault-tolerance, circuits entirely built with Clifford+T gates allow the use of error correction codes. However, the T-gate has an excessive cost, so circuits with a high number of T-gates should be avoided. This work focuses on optimising in such terms an operation that is widely used in larger circuits and algorithms: the calculation of the absolute-value of two's complement encoded integers. The proposed circuit halves the number of required T gates with respect to the best circuit currently available in the literature. Moreover, our circuit requires at least 2 qubits less than the other circuits for such an operation. [ABSTRACT FROM AUTHOR]

The algorithms that best demonstrate the potential of quantum computing are Shor's algorithm and Grover's algorithm. To this day, new evidence continues to emerge in the form of algorithms or ingenious applications that increase the field of application of this type of computing. However, given the limited number of qubits in current quantum computers, and also the noise problems they currently suffer from, implementing optimized circuits that allow us to take full advantage of the available resources, as well as detecting and correcting the errors caused by this noise, is a priority. In this work we present several leading zero detector circuits for quantum computers and simulators, optimized in terms of noise tolerance and number of qubits. These circuits are a fundamental part in major circuits that perform operations as important and basic in computation as addition and division. [ABSTRACT FROM AUTHOR]

Generating random numbers is important for many real-world applications, including cryptography, statistical sampling and Monte Carlo simulations. Quantum systems subject to a measurement produce random results via Born's rule, and thus it is natural to study the possibility of using such systems in order to generate high-quality random numbers. However, current quantum devices are subject to errors and noise, which can make the output bits deviate from the uniform distribution. In this work, we propose and analyse two protocols that can be used to increase the uniformity of the bits obtained when running a circuit with a Hadamard gate and a measurement in a noisy quantum computer. These protocols may be used prior to other standard processes, such as randomness amplification. We conduct experiments on both a quantum simulator and a real quantum computer, obtaining results that suggest that these protocols are useful to improve the probability of the generated bits passing statistical tests for uniformity. [ABSTRACT FROM AUTHOR]

In Goppa (1970), V. D. Goppa presents a new family of linear codes over finite fields. This family, now known as Goppa codes, has been studied for nearly 50 years, including efficient decoding algorithms (Patterson, 1975) and its applications in cryptography (McEliece, 1978). Moreover, in Andrade et al. (2005), de Andrade and Palazzo present a generalization of Goppa codes to finite rings. Motivated by cryptographic applications, in this article we focus on Goppa codes over Z ∕ 4 Z and study some of their properties. [ABSTRACT FROM AUTHOR]

The Quantum Approximate Optimization Algorithm (QAOA) was proposed as a way of finding good, approximate solutions to hard combinatorial optimization problems. QAOA uses a hybrid approach. A parametrized quantum state is repeatedly prepared and measured on a quantum computer to estimate its average energy. Then, a classical optimizer, running in a classical computer, uses such information to decide on the new parameters that are then provided to the quantum computer. This process is iterated until some convergence criteria are met. Theoretically, almost all classical minimizers can be used in the hybrid scheme. However, their behaviour can vary greatly in both the quality of the final solution and the time they take to find it. In this work, we study the performance of twelve different classical optimizers when used with QAOA to solve the maximum cut problem in graphs. We conduct a thorough set of tests on a quantum simulator both, with and without noise, and present results that show that some optimizers can be hundreds of times more efficient than others in some cases. [ABSTRACT FROM AUTHOR]