Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics

Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator $L$ is encoded into a quantum state $\psi$. Then, given access to $n$ copies of the state $\psi$, the task is to simulate the corresponding Markovian dynamics for time $t$. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses $n = O(t^2/\varepsilon)$ samples of $\psi$ to achieve the target dynamics, with an approximation error of $O(\varepsilon)$.Comment: 29 pages, 7 figures, published in the journal special issue dedicated to the memory of G\"oran Lindbla

Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent.Comment: 59 pages, 11 figures, submission to the second journal special issue dedicated to the memory of G\"oran Lindblad, sequel to arXiv:2307.1493

Surface Modifications to Construct Self-Healing Hydrophobic Surfaces For the Water Industry

Pipes and other plumbing fixtures often dissolve and leak materials into the water supply they are transporting leading to both aesthetic and health problems. Reducing corrosion, fouling, and wearing of components in the water industry can be done by developing a low cost, durable hydrophobic surface as current anti-corrosion coatings aren’t durable and often leak into water supply themselves contributing to the problem instead of solving it. A hydrophobic surface will increase the contact angles between the water and pipe material limiting the exchange of ions between the surfaces as well as reducing the frictional energy loss during water flow. This research focuses on demonstrating this phenomenon by examining the microstructure of the pipe material and establishing a relationship between the contact angles, corrosion rates, wear rates, and frictional energy loss that is done by water transport over long periods of time. A combination of techniques was used to adjust the microstructure of the material including oxidation, mechanical abrasion, polymeric coatings, and sol-gel coatings. Ideally, these techniques will work on in-situ surface modifications during conventional manufacturing and that the end product will have the ability to self-heal to prevent corrosion. To characterize the corrosion inhibition & self-healing effectiveness of the surface modifications were done by using scratch tests, electrochemical impedance spectroscopy (EIS), and scanning vibrating electrode technique (SVET). The results indicated that the surface if fouled contained salts of Mg, Na, and K spread out evenly on the surface along with chunks of compounds primarily containing Al, K, Si, and O. The coated surfaces helped decrease fouling, but there were some drawbacks as well; coatings showed low mechanical stability and bonding with the pipe material, was only able to self-heal in the presence of atmospheric oxygen, and wasn’t able to self-heal multiple times in the same location

Wideband and Low Power CMOS Analog Multiplier in Deep Submicron

In this paper CMOS Four Quadrant Analog Multiplier is designed. It is based on pair of common source amplifier, which acts as input transistor and two identical voltage controlled square root blocks which operate as nonlinear cancellation path. Simulated results using eldo spice in Mentor Graphics Tools for 350nm and 180nm CMOS technology. The main performances of the multiplier including bandwidth, power dissipation, and gain are improved