Gauss sum factorization with cold atoms

Exploration of nonlinear optical enhancement in acceptor-π-donor indacenodithiophene based derivatives via structural variations: a DFT approach

Herein, a series of indacenodithiophene-based derivatives (TNPD1-TNPD6) were designed having D-π-A architecture via end capped acceptor modulation of a reference molecule (TNPR) to investigate nonlinear optical (NLO) behavior. Quantum chemical calculations were accomplished to examine electronic, structural and optical properties utilizing a density functional theory (DFT) approach at M06 functional with 6-311G(d,p) basis set. For this, natural bond orbitals (NBOs), density of states (DOS), frontier molecular orbitals (FMOs), transition density matrix (TDM) and non-linear optical (NLO) analyses were performed for TNPR and TNPD1-TNPD6. The structural modifications revealed a significant electronic contribution in tuning the HOMOs and LUMOs of the derivatives with lowered energy gaps and wider absorption spectra. FMOs findings revealed that compound TNPD5 was found with the lowest energy gap (1.692 eV) and with the highest softness (0.591 eV-1) among the derivatives. Furthermore, a UV-Vis study also disclosed that maximum absorption (λmax = 852.242 nm) was exhibited by TNPD5 in chloroform solvent. All the derivatives exhibited significant NLO results; in particular, TNPD5 showed the highest first hyper-polarizability (βtot = 4.653 × 10-27 esu) and second hyper-polarizability (γtot = 9.472 × 10-32 esu). These DFT findings revealed that the end-capped substituents play a key role in enhancing the NLO response of these push-pull chromophores and the studied derivatives can be utilized as efficient NLO materials.

ICARUS-Q: Integrated control and readout unit for scalable quantum processors

We present a control and measurement setup for superconducting qubits based on the Xilinx 16-channel radio-frequency system-on-chip (RFSoC) device. The proposed setup consists of four parts: multiple RFSoC boards, a setup to synchronize every digital to analog converter (DAC) and analog to digital converter (ADC) channel across multiple boards, a low-noise direct current supply for tuning the qubit frequency, and cloud access for remotely performing experiments. We also designed the setup to be free of physical mixers. The RFSoC boards directly generate microwave pulses using sixteen DAC channels up to the third Nyquist zone, which are directly sampled by its eight ADC channels between the fifth and the ninth zones.

Prime number decomposition using the Talbot effect

We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to analyze the properties of prime numbers as well as to decompose composite numbers into their prime factors. We employ the well-established connection between the Talbot effect and Gauss sums to implement prime number decompositions with a novel approach, making use of the longitudinal intensity profile of the Talbot carpet. The new algorithm is experimentally verified and the limits of the approach are discussed.

An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition Problem

Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to develop other types of quantum algorithms that widen the range of possible applications. Here we propose an efficient and exact quantum algorithm for finding the square-free part of a large integer - a problem for which no efficient classical algorithm exists. The algorithm relies on properties of Gauss sums and uses the quantum Fourier transform. We give an explicit quantum network for the algorithm. Our algorithm introduces new concepts and methods that have not been used in quantum information processing so far and may be applicable to a wider class of problems.

Enhanced factoring with a bose-einstein condensate

We present a novel method to realize analog sum computation with a Bose-Einstein condensate in an optical lattice potential subject to controlled phase jumps. We use the method to implement the Gauss sum algorithm for factoring numbers. By exploiting higher order quantum momentum states, we are able to improve the algorithm's accuracy beyond the limits of the usual classical implementation.

Factorization of numbers with the temporal Talbot effect: optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.