Post in Quantum Computing group on Facebook on 13th March, 2019
<Well I had a eureka moment last night just like Archimedes (and this by the way is why AI will never surpass human intelligence; they can't sleep and dream; machines have no unconscious mind) I had a dream about these strange triangle shapes that were differentiating each other up to 10 times. Woke up and couldn't make head nor tail of it. Got to thinking about it and realized they were <BRA KET> Dirac formalism and they were performing QM matrix calculations on themselves. I realized that a quantum computer performs complex QM linear algebra and matrix math to solve Schrodinger's multi-particle time dependent wave equation at the speed of light. We gotta do away with all thought of binary numbers. Think solitons with geometric phase that represent Heisenberg Dirac Pauli matrices that are manipulated by holonomic quantum gates that may or may not use Boolean algebra to do complex calculus - differentiation integrals Fourier transforms etc. But wait - there's more. A quantum computer can also solve Einstein's time dependent field equations using 4x4 matrices that represent space-time vectors and Christoffel symbols. Eventually quantum computers will be able to simulate the universe. So the bottom line is forget about all this binary qubit stuff. Think linear algebra and matrix math and in the short term start thinking how you could make a quantum computer that will perform all the basic operations of MATLAB at the speed of light.>
This link by Francesco Rizzo is astounding. The future of computing will be using matrices to solve complex differential equations like Schrodinger's equation in just one step! Can you imagine if this is being done at the speed of light in a quantum computer. Here is the full abstract: "Conventional digital computers can execute advanced operations by a sequence of elementary Boolean functions of 2 or more bits. As a result, complicated tasks such as solving a linear system or solving a differential equation require a large number of computing steps and an extensive use of memory units to store individual bits. To accelerate the execution of such advanced tasks, in-memory computing with resistive memories provides a promising avenue, thanks to analog data storage and physical computation in the memory. Here, we show that a cross-point array of resistive memory devices can directly solve a system of linear equations, or find the matrix eigenvectors. These operations are completed in just one single step, thanks to the physical computing with Ohm’s and Kirchhoff’s laws, and thanks to the negative feedback connection in the cross-point circuit. Algebraic problems are demonstrated in hardware and applied to classical computing tasks, such as ranking webpages and solving the Schrödinger equation in one step."
Post in Quantum Computing on Facebook on 17th March, 2019
This paper Solving matrix equations in one step with cross-point resistive arrays involves memristors which basically uses the memory in electric current. Years ago Roger Penrose found quantum effects in microtubules. I posted a few days ago a paper about biophotons and microtubules "Our theoretical analysis indicates that the interaction of biophotons and microtubules causes transitions/fluctuations of microtubules between coherent and incoherent states." I have also come across theory that these microtubules act as optic fiber that enables light signals to pass to the various sections of the brain that gives the brain phenomenal parallel processing capacity. Electrical signals are too slow for signals to pass to widely separated parts of the brain for parallel processing. This paper about solving matrix equations in one step also involves parallel processing. What I would like to propose is that these 'quantum effects' that Penrose found and these "transitions/fluctuations of microtubules between coherent and incoherent states" actually are a form of memristor for light similar to the memristors in electric current. Here is relevant sentence from an abstract of paper <To facilitate cytoplasmic remodeling and timely responses to cell signaling events, microtubules depolymerize and repolymerize rapidly at their ends.>