arXiv subjects

Igor Zacharov

Publications and source records attributed to Igor Zacharov.

3 recordsLinked to original sources

arXiv2024

High order schemes for solving partial differential equations on a quantum computer

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for decomposing $d$-band diagonal matrices into Pauli strings that are grouped into mutually commuting sets. Using numerical simulations of the one-dimensional wave equation, we show that higher-order methods can reduce the number of qubits necessary for discretization, similar to the classical case, although they do not decrease the number of Trotter steps needed to preserve solution accuracy. This result has important consequences for the practical application of quantum algorithms based on Hamiltonian evolution.

quant-ph↗

arXiv2023

Tridiagonal matrix decomposition for Hamiltonian simulation on a quantum computer

The construction of quantum circuits to simulate Hamiltonian evolution is central to many quantum algorithms. State-of-the-art circuits are based on oracles whose implementation is often omitted, and the complexity of the algorithm is estimated by counting oracle queries. However, in practical applications, an oracle implementation contributes a large constant factor to the overall complexity of the algorithm. The key finding of this work is the efficient procedure for representation of a tridiagonal matrix in the Pauli basis, which allows one to construct a Hamiltonian evolution circuit without the use of oracles. The procedure represents a general tridiagonal matrix $2^n \times 2^n$ by systematically determining all Pauli strings present in the decomposition, dividing them into commuting subsets. The efficiency is in the number of commuting subsets $O(n)$. The method is demonstrated using the one-dimensional wave equation, verifying numerically that the gate complexity as function of the number of qubits is lower than the oracle based approach for $n < 15$ and requires half the number of qubits. This method is applicable to other Hamiltonians based on the tridiagonal matrices.

quant-ph↗

arXiv2019

'Zhores' -- Petaflops supercomputer for data-driven modeling, machine learning and artificial intelligence installed in Skolkovo Institute of Science and Technology

The Petaflops supercomputer "Zhores" recently launched in the "Center for Computational and Data-Intensive Science and Engineering" (CDISE) of Skolkovo Institute of Science and Technology (Skoltech) opens up new exciting opportunities for scientific discoveries in the institute especially in the areas of data-driven modeling, machine learning and artificial intelligence. This supercomputer utilizes the latest generation of Intel and NVidia processors to provide resources for the most compute intensive tasks of the Skoltech scientists working in digital pharma, predictive analytics, photonics, material science, image processing, plasma physics and many more. Currently it places 6th in the Russian and CIS TOP-50 (2018) supercomputer list. In this article we summarize the cluster properties and discuss the measured performance and usage modes of this scientific instrument in Skoltech.

cs.DC↗