Low Rank Density Matrix Evolution for Noisy Quantum Circuits

Abstract

In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full matrix. We implement this algorithm in an in-house simulator, and show that the low rank algorithm speeds up simulations by more than two orders of magnitude over an existing implementation of full rank simulator, and with negligible error in the target noise and final observables. Finally, we demonstrate the utility of the low rank method as applied to representative problems of interest by using the algorithm to speed-up noisy simulations of Grover's search algorithm and quantum chemistry solvers.

Positivity Preserving Density Matrix Minimization for Fermi-Dirac States at Finite Temperatures

“…This approach may lay the ground for a new generation of DMM methods. A possible future direction is to utilize the fact that a low-temperature Fermi-Dirac density matrix is of a low rank, hence it is possible to further accelerate calculations by utilizing low-rank corner space techniques recently developed for solving master equations for large open quantum systems [28][29][30][31][32].…”

Continuous-time dynamics and error scaling of noisy highly entangling quantum circuits

“…However, their number is not known in general [43] and, in the case of weak dissipation, the method can quickly become equivalent to a full integration of the master equation as a greater amount of trajectories are needed to reach convergence. In recent years, there has been a growing interest in the idea that for a certain class of low-entropy systems, a limited number of states, belonging to a so-called "corner" subspace, can efficiently and faithfully represent the density matrix [44][45][46][47]. Since quantum processors are conceived to be weakly dissipative and with low entropy, they belong to this class.…”