Massively Parallel Quantum Computer Simulations: Towards Realistic Systems

Koen De Raedt, Kristel F. L. Michielsen, Hans A. De Raedt +6 more

Doan Binh Trieu

The theoretical concepts of quantum computation in the idealized and undisturbed case are well understood. However, in practice, all quantum computation devices do suffer from decoherence effects as well as from operational imprecisions.\nThis work assesses the power of error-prone quantum computation devices using largescale\nnumerical simulations on parallel supercomputers. We present the Juelich Massively Parallel Ideal Quantum Computer Simulator (JUMPIQCS), that simulates a generic quantum computer on gate level. It comprises an error model for decoherence and operational errors. The robustness of various algorithms in the presence of noise has been analyzed.\nThe simulation results show that for large system sizes and long computations it is imperative to actively correct errors by means of quantum error correction. We implemented the 5-, 7-, and 9-qubit quantum error correction codes. Our simulations confirm that using error-prone correction circuits with non-fault-tolerant quantum error correction will always fail, because more errors are introduced than being corrected. Fault-tolerant methods can\novercome this problem, provided that the single qubit error rate is below a certain threshold.\nWe incorporated fault-tolerant quantum error correction techniques into JUMPIQCS using\nSteane’s 7-qubit code and determined this threshold numerically. Using the depolarizing\nchannel as the source of decoherence, we find a threshold error rate of (5.2 ± 0.2) · 10−6.\nFor Gaussian distributed operational over-rotations the threshold lies at a standard deviation of 0.0431±0.0002. We can conclude that quantum error correction is especially well suited for the correction of operational imprecisions and systematic over-rotations.\nFor realistic simulations of specific quantum computation devices we need to extend the generic model to dynamic simulations, i.e. time-dependent Hamiltonian simulations of realistic hardware models. We focus on today’s most advanced technology, i.e. ion trap quantum computation. We developed the Dynamic Quantum Computer Simulator for Ion Traps (DyQCSI). Starting from a microscopic Hamiltonian, it does not rely on approximations that are usually necessary for an analytical approach. We show that the effects due to these\napproximations are significant. We present several ways for the visualization of the state of the system during its time evolution and demonstrated the benefit of the simulation approach for parameter optimizations.

M. Baumgärtel, Khaldoon Ghanem, Amin Kiani +4 more

We discuss the efficient implementation of general impurity solvers for dynamical mean-field theory. We show that both Lanczos and quantum Monte Carlo in different flavors (Hirsch-Fye, continuous-time hybridization- and interaction-expansion) exhibit excellent scaling on massively parallel supercomputers. We apply these algorithms to simulate realistic model Hamiltonians including the full Coulomb vertex, crystal-field splitting, and spin-orbit interaction. We discuss how to remove the sign problem in the presence of non-diagonal crystal-field and hybridization matrices. We show how to extract the physically observable quantities from imaginary time data, in particular correlation functions and susceptibilities. Finally, we present benchmarks and applications for representative correlated systems.

LEVI, Benjamin, Bertrand Georgeot

Naoki Yoshioka, Nobuyasu Ito

Abstract A new parallelization method for state-vector simulations of quantum circuits in massively parallel supercomputers is proposed. It removes the requirements about the number of MPI processes and the size of data array of state vector in the commonly used parallelization method, and therefore it enables to use memory in the supercomputers as much as possible. It is demonstrated by using the supercomputer Fugaku that simulations implementing our method work well up to 40 qubits.

Tzvetan S. Metodi, Arvin I. Faruque, Frederic T. Chong