Month: September 2022

QUANTUM AND BLACK HOLES. “It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration of time over which classical general relativity can describe the interior geometry of black holes. What is known is that these two questions are closely connected: the longer GR can describe black holes, the more limited are quantum computers.” (GR = general relativity). https://lnkd.in/dByfCJV View in LinkedIn

QUITE THE QUESTION. “Several years ago I asked Scott Aaronson a question: Can it be proved that the complexity of a universal quantum circuit, such as those that have been conjectured to describe black holes, grows at the fastest possible rate—linearly with time—until it saturates at the maximum complexity (exponential in the number of qubits)?” https://lnkd.in/dByfCJV View in LinkedIn

QUITE THE ANSWER. “The result was a theorem (mainly due to Aaronson) connecting the growth of complexity with certain plausible properties of complexity classes.” Originated from black hole quantum circuits. https://lnkd.in/dByfCJV View in LinkedIn

c(N). “Let us suppose that a universal quantum circuit, when run for exponential time failed to produce complexity greater than polynomial in the number of qubits. Consider some problem which is classically hard, i.e., it takes exponential time ∼ c(N) to solve it. It follows that there is a way to get to the answer in a polynomial number of steps running the computer as a quantum computer.” https://lnkd.in/dByfCJV View in LinkedIn

NON-COMPUTABILITY. “As we will see the argument also goes in the other direction: If the universal quantum computer produces greater than polynomial complexity in exponential time, then certain hard problems (PSPACE-complete) cannot be solved in polynomial time by a quantum computer.” https://lnkd.in/dByfCJV View in LinkedIn

ARTIFICIAL STABLE SILICON DOUBLE BOND. “While carbon–carbon double bonds are common in organic chemistry, at the heart of countless chemical transformations, silicon–silicon double bonds are much rarer. Despite silicon sitting just below carbon in the periodic table, silicon double bonds are much less stable than those involving carbon.” https://lnkd.in/dvvPbnC View in LinkedIn

The mechanical wonder is now an electrinic marvel. View in LinkedIn

POLYNOMIAL COMPLEXITY IN EXPONENTIAL TIME. “What does this have to do with black holes? We will see shortly.” https://lnkd.in/dByfCJV View in LinkedIn

ETERNAL FUTURE. “According to classical general relativity the volume of space behind the horizon of a black hole grows linearly (with time), into the eternal future.” (Time present and time past/Are both perhaps present in time future,/And time future contained in time past./If all time is eternally present/All time is unredeemable.” TSE Four Quartets). https://lnkd.in/dByfCJV View in LinkedIn

BEYOND TS ELIOT. “Conjecture: The complexity of certain quantum circuits grows linearly with the number of time-steps, until it reaches its maximum value, exponential in the number of qubits.” https://lnkd.in/dByfCJV View in LinkedIn