Session D01: Quantum Computing and Statistical Mechanics

Quantum Monte Carlo simulations of a giant magnetic molecule with a S = 91 spin ground state

I will describe the basic idea of Monte Carlo simulations for statistical physics, and how these ideas can be applied to complex system of interacting quantum spins.  I will specifically discuss a recent application where we used Quantum Monte Carlo simulations to analyze a giant {Ni₂₁Gd₂₀} molecular cage with a remarkable S = 91 spin ground state.   

Parallelized Sequential Monte Carlo Sampling for Quantum State Tomography

This talk will look at the Bayesian inference algorithm Sequential Monte Carlo Sampling (SMC) as a way to efficiently sample from high-dimensional probability distributions found in quantum systems when performing Quantum State Tomography (QST). QST refers to any method that can characterize a quantum state given projections on that state. However, QST is notoriously challenging for all but the smallest quantum systems as the computational cost of simulating multiple qubits scales exponentially with the size of the Hilbert Space of the system. Although this is the main source of the computational power of quantum information processing, still, efficient QST algorithms are needed to help understand the nature of new quantum machines. Here, we use SMC to implement a parallelizable Bayesian tomography method. Our SMC algorithm combines established Bayesian tomography methods MCMC methods like preconditioned Crank-Nicholson Sampling, importance sampling, and particle filters to make an efficient and parallelizable method for QST. By finding a parallelizable Bayesian inference method, we can keep the statistical rigor of Bayesian methods, like natural error bars, and decrease some of the computational cost on each core that is notorious with Bayesian methods. Using SMC, we were able to demonstrate scaling of accuracy with increased core numbers, which was more evident with larger Hilbert Space systems, and we were able to get results obtained by non-parallel methods in a fraction of the time using this new QST method.   

Understanding Electron Transport Through Phosphorus Atoms Embedded in Silicon

Shriya Haravu 1, Maicol A. Ochoa 2

1Department of Physics, University of North Carolina at Chapel Hill, USA

 2 Institute for Research in Electronics and Applied Physics, University of Maryland College Park, USA

Electron transport through atoms can be described with Landauer theory which accounts for the quantum nature of the electron’s movement, assumes momentum is conserved within the atom, and incorporates Coulomb repulsion in a unique way. We model differential conductance through one and two phosphorus atoms embedded in silicon as a function of several parameters governing which atomic energy levels are open for transport, and discuss the validity of the Landauer model in representing electronic properties of these systems. Moreover, we observe how the differential conductance varies as a function of driving potentials and variables relating to the electronic structure of the P atoms, the silicon matrix, and the connections between them, thus realizing how each of these parameters affects transport and control. Control at this scale has applications in shrinking transistors, quantum computing, and semiconductor materials. Finally, in trying to reproduce experimental figures for single, double, and multiple impurities, we find the strengths and restrictions of the model.

    

Quantum Algorithm for Two-level Systems

Quantum computers are promisingly the world's future technology. In physics, we take interest in calculating the transition matrix elements. For instance, the rate of emission/absorption for a photon/neutrino in a physical process. In this work, we present a general algorithm to compute the transition rates in two-level systems using IBM Quantum. The transition probability is amplified by using an auxiliary qubit that can drive the system to resonance. Furthermore, the algorithm can prepare the excited state with 100% probability given the ground state of a system.   

RADIATIVE PROCESS ON A QUANTUM COMPUTER

We propose a method to compute radiative processes using a quantum computer. Transition between initial and final states during the capture process in a small box leads to Rabi oscillations. The amplitude and frequency of these oscillations are shown to be related to the transition matrix elements. This algorithm is demonstrated by calculating the E1 transition rate between ground and excited states of a particle in a harmonic oscillator potential using a quantum simulator.

    

Gate characterization by a rotational sweep procedure

Quantum process tomography (QPT) is a powerful tool to characterize quantum operations, but it requires considerable resources, making it impractical for more than two-qubit systems. This work proposes an alternative approach that requires significantly fewer resources for unitary process characterization with a built-in method for state preparation and measurement error mitigation. By measuring the quantum process as rotated through the X and Y axes on the Bloch sphere, we can acquire enough information to reconstruct the quantum process matrix χ and measure its fidelity. We test the algorithm's performance against standard QPT using simulated and physical experiments on several IBM quantum processors and compare the resulting process matrices. We demonstrate with numerical experiments that the method can improve gate fidelity via a noise reduction in the imaginary part of the process matrix, along with a stark decrease in the number of experiments needed to perform the characterization.