AI News, Artificial intelligence techniques reconstruct mysteries of quantum systems

Artificial intelligence techniques reconstruct mysteries of quantum systems

For the first time, physicists have demonstrated that machine learning can reconstruct a quantum system based on relatively few experimental measurements.

This method will allow scientists to thoroughly probe systems of particles exponentially faster than conventional, brute-force techniques.

'We have shown that machine intelligence can capture the essence of a quantum system in a compact way,' says study co-author Giuseppe Carleo, an associate research scientist at the Center for Computational Quantum Physics at the Flatiron Institute in New York City.

Each electron, for instance, can have either an upward or downward spin, similar to Schrödinger's cat being either dead or alive in the famous thought experiment.

Through quantum entanglement, independent particles become intertwined and can no longer be treated as purely separate entities even when physically separated.

In turn, this ability can help scientists validate that a quantum computer is correctly set up and that any quantum software would run as intended, the researchers suggest.

Center for Computational Quantum Physics co-director Andrew Millis notes that the ideas provide an important new approach to the center's ongoing development of novel methods for understanding the behavior of interacting quantum systems, and connect with work on other quantum physics-inspired machine learning approaches.

Besides applications to fundamental research, Carleo says that the lessons the team learned as they blended machine learning with ideas from quantum physics could improve general-purpose applications of artificial intelligence as well.

Artificial Intelligence Techniques Reconstruct Mysteries of Quantum Systems

The same techniques used to train self-driving cars and chess-playing computers are now helping physicists explore the complexities of the quantum world.

“We have shown that machine intelligence can capture the essence of a quantum system in a compact way,” says study co-author Giuseppe Carleo, an associate research scientist at the Center for Computational Quantum Physics at the Flatiron Institute in New York City.

“AlphaGo was really impressive,” he says, “so we started asking ourselves how we could use those ideas in quantum physics.” Systems of particles such as electrons can exist in lots of different configurations, each with a particular probability of occurring.

Through quantum entanglement, independent particles become intertwined and can no longer be treated as purely separate entities even when physically separated.

In turn, this ability can help scientists validate that a quantum computer is correctly set up and that any quantum software would run as intended, the researchers suggest.

Center for Computational Quantum Physics co-director Andrew Millis notes that the ideas provide an important new approach to the center’s ongoing development of novel methods for understanding the behavior of interacting quantum systems, and connect with work on other quantum physics–inspired machine learning approaches.

Besides applications to fundamental research, Carleo says that the lessons the team learned as they blended machine learning with ideas from quantum physics could improve general-purpose applications of artificial intelligence as well.

New quantum method generates really random numbers

The new NIST method generates digital bits (1s and 0s) with photons, or particles of light, using data generated in an improved version of a landmark 2015 NIST physics experiment.

In the new work, researchers process the spooky output to certify and quantify the randomness available in the data and generate a string of much more random bits.

That's because they are generated by software formulas or physical devices whose supposedly random output could be undermined by factors such as predictable sources of noise.

Running statistical tests can help,but no statistical test on the output alone can absolutely guarantee that the output was unpredictable, especially if an adversary has tampered with the device.

The new quantum-based method is part of an ongoing effort to enhance NIST's public randomness beacon, which broadcasts random bits for applications such as secure multiparty computation.

Quantum mechanics provides a superior source of randomness because measurements of some quantum particles (those in a 'superposition' of both 0 and 1 at the same time) have fundamentally unpredictable results.

In NIST's experiment, that proof comes from observing the spooky quantum correlations between pairs of distant photons while closing the 'loopholes' that might otherwise allow non-random bits to appear to be random.

The timing of the measurements ensures that the correlations cannot be explained by classical processes such as pre-existing conditions or exchanges of information at, or slower than,the speed of light.

Statistical tests of the correlations demonstrate that quantum mechanics is at work,and these data allow the researchers to quantify the amount of randomness present in the long string of bits.

To obtain a short, uniform string with concentrated randomness such that each bit has a 50/50 chance of being 0 or 1, a second step called 'extraction' is performed.

The full process requires the input of two independent strings of random bits to select measurement settings for the Bell tests and to 'seed' the software to help extract the randomness from the original data.

Monte Carlo method

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean-Vlasov processes, kinetic models of gases).

Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk in business and, in math, evaluation of multidimensional definite integrals with complicated boundary conditions.

In application to space and oil exploration problems, Monte Carlo–based predictions of failure, cost overruns and schedule overruns are routinely better than human intuition or alternative 'soft' methods.[2]

These flows of probability distributions can always be interpreted as the distributions of the random states of a Markov process whose transition probabilities depend on the distributions of the current random states (see McKean-Vlasov processes, nonlinear filtering equation).[8][9]

In other instances we are given a flow of probability distributions with an increasing level of sampling complexity (path spaces models with an increasing time horizon, Boltzmann-Gibbs measures associated with decreasing temperature parameters, and many others).

A natural way to simulate these sophisticated nonlinear Markov processes is to sample a large number of copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures.

When the size of the system tends to infinity, these random empirical measures converge to the deterministic distribution of the random states of the nonlinear Markov chain, so that the statistical interaction between particles vanishes.

Uses of Monte Carlo methods require large amounts of random numbers, and it was their use that spurred the development of pseudorandom number generators, which were far quicker to use than the tables of random numbers that had been previously used for statistical sampling.

Despite having most of the necessary data, such as the average distance a neutron would travel in a substance before it collided with an atomic nucleus, and how much energy the neutron was likely to give off following a collision, the Los Alamos physicists were unable to solve the problem using conventional, deterministic mathematical methods.

Using lists of 'truly random' random numbers was extremely slow, but von Neumann developed a way to calculate pseudorandom numbers, using the middle-square method.

In the 1950s they were used at Los Alamos for early work relating to the development of the hydrogen bomb, and became popularized in the fields of physics, physical chemistry, and operations research.

The authors named their algorithm 'the bootstrap filter', and demonstrated that compared to other filtering methods, their bootstrap algorithm does not require any assumption about that state-space or the noise of the system.

From 1950 to 1996, all the publications on Sequential Monte Carlo methodologies including the pruning and resample Monte Carlo methods introduced in computational physics and molecular chemistry, present natural and heuristic-like algorithms applied to different situations without a single proof of their consistency, nor a discussion on the bias of the estimates and on genealogical and ancestral tree based algorithms.

distinguishes between a simulation, a Monte Carlo method, and a Monte Carlo simulation: a simulation is a fictitious representation of reality, a Monte Carlo method is a technique that can be used to solve a mathematical or statistical problem, and a Monte Carlo simulation uses repeated sampling to obtain the statistical properties of some phenomenon (or behavior).

Low-discrepancy sequences are often used instead of random sampling from a space as they ensure even coverage and normally have a faster order of convergence than Monte Carlo simulations using random or pseudorandom sequences.

In an effort to assess the impact of random number quality on Monte Carlo simulation outcomes, astrophysical researchers tested cryptographically-secure pseudorandom numbers generated via Intel's RdRand instruction set, as compared to those derived from algorithms, like the Mersenne Twister, in Monte Carlo simulations of radio flares from brown dwarfs.

For example, a comparison of a spreadsheet cost construction model run using traditional “what if” scenarios, and then running the comparison again with Monte Carlo simulation and triangular probability distributions shows that the Monte Carlo analysis has a narrower range than the “what if” analysis.[example needed]

This is because the “what if” analysis gives equal weight to all scenarios (see quantifying uncertainty in corporate finance), while the Monte Carlo method hardly samples in the very low probability regions.

Monte Carlo methods are very important in computational physics, physical chemistry, and related applied fields, and have diverse applications from complicated quantum chromodynamics calculations to designing heat shields and aerodynamic forms as well as in modeling radiation transport for radiation dosimetry calculations.[53][54][55]

In statistical physics Monte Carlo molecular modeling is an alternative to computational molecular dynamics, and Monte Carlo methods are used to compute statistical field theories of simple particle and polymer systems.[28][56]

In cases where it is not feasible to conduct a physical experiment, thought experiments can be conducted (for instance: breaking bonds, introducing impurities at specific sites, changing the local/global structure, or introducing external fields).

Repeated sampling of any given pixel will eventually cause the average of the samples to converge on the correct solution of the rendering equation, making it one of the most physically accurate 3D graphics rendering methods in existence.

The Monte Carlo approach is based on a specified number of randomly drawn permutations (exchanging a minor loss in precision if a permutation is drawn twice – or more frequently—for the efficiency of not having to track which permutations have already been selected).

Monte Carlo methods are also efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in global illumination computations that produce photo-realistic images of virtual 3D models, with applications in video games, architecture, design, computer generated films, and cinematic special effects.[80]

Monte Carlo simulation allows the business risk analyst to incorporate the total effects of uncertainty in variables like sales volume, commodity and labour prices, interest and exchange rates, as well as the effect of distinct risk events like the cancellation of a contract or the change of a tax law.

Monte Carlo approach was used for evaluating the potential value of a proposed program to help female petitioners in Wisconsin be successful in their applications for harassment and domestic abuse restraining orders.

In general, the Monte Carlo methods are used in mathematics to solve various problems by generating suitable random numbers (see also Random number generation) and observing that fraction of the numbers that obeys some property or properties.

As long as the function in question is reasonably well-behaved, it can be estimated by randomly selecting points in 100-dimensional space, and taking some kind of average of the function values at these points.

To do this precisely one would have to already know the integral, but one can approximate the integral by an integral of a similar function or use adaptive routines such as stratified sampling, recursive stratified sampling, adaptive umbrella sampling[88][89]

Many problems can be phrased in this way: for example, a computer chess program could be seen as trying to find the set of, say, 10 moves that produces the best evaluation function at the end.

That is, all the facts (distances between each destination point) needed to determine the optimal path to follow are known with certainty and the goal is to run through the possible travel choices to come up with the one with the lowest total distance.

As a result, to determine our optimal path we would want to use simulation - optimization to first understand the range of potential times it could take to go from one point to another (represented by a probability distribution in this case rather than a specific distance) and then optimize our travel decisions to identify the best path to follow taking that uncertainty into account.

in the general case, the theory linking data with model parameters is nonlinear, the posterior probability in the model space may not be easy to describe (it may be multimodal, some moments may not be defined, etc.).

But it is possible to pseudorandomly generate a large collection of models according to the posterior probability distribution and to analyze and display the models in such a way that information on the relative likelihoods of model properties is conveyed to the spectator.

The best-known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possibly highly nonlinear) inverse problems with complex a priori information and data with an arbitrary noise distribution.[92][93]

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