Pauli String Partitioning Algorithm with the Ising Model for Simultaneous Measurements.

We propose an efficient algorithm for partitioning Pauli strings into subgroups, which can be simultaneously measured in a single quantum circuit. Our partitioning algorithm drastically reduces the total number of measurements in a variational quantum eigensolver for a quantum chemistry, one of the most promising applications of quantum computing. The algorithm is based on the Ising model optimization problem, which can be quickly solved using an Ising machine. We develop an algorithm that is applicable to problems with sizes larger than the maximum number of variables that an Ising machine can handle (nbit) through its iterative use. The algorithm has much better time complexity and solution optimality than other existing algorithms. We investigate the performance of the algorithm using the second-generation Digital Annealer, a high-performance Ising hardware, for up to 65535 Pauli strings using Hamiltonians of molecules and the full tomography of quantum states. We demonstrate a time complexity of O(N) for N ≤ nbit and O(N2) for N > nbit for the worst case, where N denotes the number of candidate Pauli strings and nbit = 8,192 in this study. The reduction factor, which is the number of Pauli strings divided by the number of obtained partitions, can be 200 at maximum.

Nanopattern transfer from high-density self-assembled nanosphere arrays on prepatterned substrates.

We have fabricated nanoimprint moulds with high-density well-defined nanopatterns by pattern transfer from self-assembled nanosphere arrays on prepatterned substrates. Silica nanospheres of 100 and 25 nm diameter were regularly arranged over large areas in a self-assembling manner by capillary force via a dip-coating technique on topographically patterned substrates having 220 nm pitch line/space patterns. The nanosphere arrays were used as etching masks, and nanodot arrays with the same arrangements were created on the silica substrate surfaces by reactive ion etching (RIE). By developing a combined pattern transfer process using Ru and SiO(x) mask layers and CF4 and O2 RIE, the aspect ratio between the height and diameter of the nanodots made from the 25 nm nanospheres is improved to about two. It is demonstrated that the nanopatterns of the moulds can be inversely transferred into polymer surfaces reproducibly by UV nanoimprint process.