Browsing by Subject "qubit"

The framework of quantum field theory (QFT) underlies our modern understanding of both particle physics and condensed matter physics. Despite its importance, precise quantitative calculations in strongly-coupled theories in QFTs have generally only been possible through non-perturbative lattice Monte Carlo (MC) methods. Traditionally, such lattice MC methods proceed by starting from a lattice regularization of the continuum QFT of interest, which has the same (possibly infinite dimensional) local Hilbert space at each lattice site as the continuum QFT. In this thesis, we explore an alternative regularization where the local Hilbert space is also replaced by a smaller finite dimensional Hilbert space. Motivated by the appeal of such models for near-term quantum computers, we dub this approach qubit regularization. Using this approach, in this thesis, we present three main results. First, we develop a qubit-regularization for the O(N) nonlinear sigma model (NLSM) in D $\geq$ 3 spacetime dimensions. We show using numerical lattice calculations that the O(N ) qubit model lies in the correct universality class for N = 2, 4, 6, 8, and reproduces the universal physics of the O(N) Wilson-Fisher (WF) fixed point in D = 3 spacetime dimensions by computing some well-known critical exponents. Next, we explore sectors of large global charges of the O(N) WF conformal field theory (CFT) using the O(N) qubit model. This allows us to test the predictions of a recently proposed large-charge effective field theory (EFT) and extract the two leading low-energy constants (LECs) in the EFT. Performing computations for N = 2, 4, 6, 8, we are also able to quantitatively test predictions of a recent large-N analysis in the large-charge sectors. Finally, we show that our qubit approach can also be used to study the few-body physics of non-relativistic particles. In particular, we consider a system of two species of mass-imbalanced fermions in $1 + 1$ dimensions. We compute the ground state energies for a range of mass-imbalances and interaction strengths, and uncover some problems with recent results obtained from the Complex Langevin (CL) method for the same system.

The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times, high qubit readout fidelity, and universal logic gates. While these essential properties have been demonstrated, the ability to scale a trapped ion quantum system has not yet been shown. The challenge of scaling the system calls for methods to realize high-fidelity logic gates in scalable trap structures. Surface electrode ion traps, that are microfabricated from a silicon substrate, provide a scalable platform for trapping ion qubits only if high-fidelity operations are achievable in these structures. Here, we present a system for trapping and manipulating ions in a scalable surface trap. Trapping times exceeding 20 minutes without laser cooling, and heating rates as low as 0.8 quanta/ms indicate stable trapping conditions in these microtraps. Coherence times of more than one second verify adequate qubit and control field stability. We demonstrate low-error single-qubit gates performed using stimulated Raman transitions driven by lasers that are tightly focused on the ion qubit. Digital feedback loops are implemented to control the driving field's amplitude and frequency. Gate errors are measured using a randomized benchmarking protocol for single qubit gates, where residual amplitude error in the control beam is compensated using various pulse sequence techniques. Using pulse compensation, we demonstrate single qubit gates with an average error per randomized Clifford group gate of $3.6(3)\times10^{-4}$, which is below the fault-tolerant threshold for some error-correction schemes.