Linear decomposition of approximate multi-controlled single qubit gates

We provide a method for compiling approximate multi-controlled single qubit gates into quantum circuits without ancilla qubits. The total number of elementary gates to decompose an n-qubit multi-controlled gate is proportional to 32n, and the previous best approximate approach without auxiliary qubits requires 32nk elementary operations, where k is a function that depends on the error threshold. The proposed decomposition depends on an optimization technique that minimizes the CNOT gate count for multi-target and multi-controlled CNOT and SU(2) gates. Computational experiments show the reduction in the number of CNOT gates to apply multi-controlled U(2) gates. As multi-controlled single-qubit gates serve as fundamental components of quantum algorithms, the proposed decomposition offers a comprehensive solution that can significantly decrease the count of elementary operations employed in quantum computing applications

Linear-depth quantum circuits for multi-qubit controlled gates

Quantum circuit depth minimization is critical for practical applications of circuit-based quantum computation. In this work, we present a systematic procedure to decompose multi-qubit-controlled unitary gate, which is essential in many quantum algorithms, to controlled-NOT and single-qubit gates with which quantum circuit depth only increases linearly with the number of control qubits. Our algorithm does not require any ancillary qubits and achieves a quadratic reduction of the circuit depth against known methods. We demonstrate the advantage of our algorithm with proof-of-principle experiments implemented on the IBM quantum cloud platform

2- Universidade Federal Rural de Pernambuco

Abstract. Computability of weightless neural networks is the major topic of this paper. In previous works it has been shown that, one can simulate a Turing machine with a weightless neural network (WNN) with an infinite tape. And it has also been shown that one can simulate probabilistic automata with a WNN with two queues. In this paper, we will show that is possible to simulate a probabilistic automata with a single layer WNN with no auxiliary data structures.

Compact quantum kernel-based binary classifier

Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications of these quantum machine learning methods, an important issue is to minimize the size of quantum circuits. We present the simplest quantum circuit for constructing a kernel-based binary classifier. This is achieved by generalizing the interference circuit to encode data labels in the relative phases of the quantum state and by introducing compact amplitude encoding, which encodes two training data vectors into one quantum register. When compared to the simplest known quantum binary classifier, the number of qubits is reduced by two and the number of steps is reduced linearly with respect to the number of training data. The two-qubit measurement with post-selection required in the previous method is simplified to single-qubit measurement. Furthermore, the final quantum state has a smaller amount of entanglement than that of the previous method, which advocates the cost-effectiveness of our method. Our design also provides a straightforward way to handle an imbalanced data set, which is often encountered in many machine learning problems.Comment: 10 pages, 2 figure