Slováci testujú neprelomiteľný spôsob šifrovania, idú spojiť Bratislavu a Viedeň. Pri súčasnej vedomosti o tom, ako vyzerá fyzika a svet, nie je kvantovú šifru možné zlomiť, hovorí o prevratnej technológii profesor Vladimír Bužek, jeden z najcitovanejších slovenských fyzikov ... || pdf ||

Probabilistic storage and retrieval (PSR) of unitary quantum dynamics is possible with exponentially small failure probability with respect to the number of systems used as a quantum memory [M. Sedlák, A. Bisio, and M. Ziman, Phys. Rev. Lett. 122, 170502 (2019)]. Here we study improvements due to a priori knowledge about the unitary transformation to be stored. In particular, we study N→1 PSR of qubit phase gates, i.e., qubit rotations around the Z axis with an unknown angle, and show that if we access the gate only N times the optimal probability of perfect retrieving of its single use is N/(N+1). We propose a quantum circuit realization for the optimal protocol and show that a programmable phase gate [G. Vidal, L. Masanes, and J. I. Cirac, Phys. Rev. Lett. 88, 047905 (2002)] can be turned into a (2k−1)→1 optimal PSR of phase gates and requires only k controlled-not gates, while having exponentially small failure probability in k.

Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems. However, in many interesting situations, QMC methods are faced with a sign problem, causing the severe limitation of an exponential increase in the runtime of the QMC algorithm. In this work, we develop a systematic, generally applicable, and practically feasible methodology for easing the sign problem by efficiently computable basis changes and use it to rigorously assess the sign problem. Our framework introduces measures of non-stoquasticity that—as we demonstrate analytically and numerically—at the same time provide a practically relevant and efficiently computable figure of merit for the severity of the sign problem. Complementing this pragmatic mindset, we prove that easing the sign problem in terms of those measures is generally an NP-complete task for nearest-neighbor Hamiltonians and simple basis choices by a reduction to the MAXCUT-problem.