![]() ![]() The Google’s Sycamore superconducting quantum processor with the architecture designed to be applied for this particular problem, introduces a multi-qubit entanglement, in Google’s device – 53-qubit entanglement. ![]() The exponentially growing computational difficulty in the verification of random binary distributions is a well recognized problem and it was the basis of the recent quantum supremacy result presented (2019) by Google and the UC Santa Barbara research team 24. In an ideal quantum case, the perfect randomness generated should be truly non-deterministic, without any correlations in terms of repeated patterns occurrences, as a consequence of the quantum measurement. This poses a main difficulty for practical testing of the randomness quality. But, for large random bits sequences computational complexity of classical algorithms for identifying correlations (finding repeated patterns) scales exponentially with the length of the patterns sought for (because the number of such patterns grows exponentially with their lengths). Hence the general problem can be viewed as finding the correlations (or all possible patterns) in the sequence, and on this ground, calculation of the frequential probabilities of given patterns occurrences, which finally allows to calculate the entropy. As the entropy of the source corresponds to random variable of possible generated bit configurations with frequential probabilities, the solution to problem of measuring this entropy can be implemented by searching all possible patterns occurrences in the bit string. Therefore measuring entropy of the bit string can be reduced to measuring entropy of the source at the cost of increasing length of the required bit string. Instead however if this bit string is long enough, it can be divided into parts that correspond to sampling of the source with shorter bit strings. It should be noted that in case of a single bit string there is no access to measuring of the entropy of the source (as this requires many generated bit strings). Different tools can be considered, including e.g., entropy accumulation theorem 23 or entropy monitoring 3. The measurement of the entropy of the random binary sequence (formally treated as a random variable of all the possible bit string configurations) is not an easy task computationally. Thus the problem of statistically analyzing the entropy of the source of randomness still remains an important aspect for any physical implementation with inevitable technical imperfections of quantum random generators (e.g. Eventually these issues can be reduced to statistical predictions, like in quantum component within continuous variables approaches or statistical proofs of Bell or Mermin type inequalities violation proving non-classical entanglement and thus quantumness of the protocol 12, 13 (but again statistically and imperfectly, which can be tackled with special protocols for error correction 14, 15, especially such as entanglement purification 14, 16– 21). 11, allow to separate a deterministic classical component from quantum one resulting in definable confidence levels of generated bit series (e.g. The other, like self-testing QRNG protocols, considered to be of the Device Independent approach-type, e.g., in ref. Some DI QRNG approaches are limited to specific generating techniques and setups (like e.g., continuous variables approaches) 4, 8– 10. Enhancement of the security level usually happens at a cost of lowering of the overall efficiency. Just similarly as for the quantum key distribution protocols, which are theoretically unconditionally secure, but in real implementations are always secure only up to some certain level, conditioned by physical implementation shortcomings. While some of the protocols extract quantum randomness and discard deterministic components 6, 7 arisen due to quantum processes implementation imperfections, the fidelity of such procedures is not ideal. The pureness of the quantum process, despite its theoretical non-deterministic fundamental unpredictability, still remains, however, the main problem in practical QRNG implementations, including the so-called Device Independent (DI) QRNGs 1– 5. Quantum random number generators (QRNGs) are aspiring to be a new standard of randomness generators, and not only in cryptography, but also in many other fields like AI, Monte Carlo like simulations, sampling, etc. ![]()
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