arXiv subjects

Andrew T. Sornborger

Publications and source records attributed to Andrew T. Sornborger.

42 records · Page 3Linked to original sources

arXiv2012

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.

quant-ph↗

arXiv2010

Quantum Simulation of Molecular Collisions with Superconducting Qubits

We introduce a protocol for the fast simulation of $n$-dimensional quantum systems on $n$-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of $H_{\rm s}(t)$, an arbitrary, real, time-dependent $n\times n$ dimensional Hamiltonian that is simulated in the $n$-dimensional `single excitation' subspace of the quantum computer. A time-dependent energy/time rescaling minimizes the simulation time on hardware having a fixed coherence time. We demonstrate how three tunably coupled phase qubits simulate a three-channel molecular collision using this protocol, then study the simulation's fidelity as a function of total simulation time.

quant-ph↗

arXiv2006

Quantum computing with superconductors I: Architectures

Josephson junctions have demonstrated enormous potential as qubits for scalable quantum computing architectures. Here we discuss the current approaches for making multi-qubit circuits and performing quantum information processing with them.

quant-ph↗

arXiv2004

Superconducting Phase Qubit Coupled to a Nanomechanical Resonator: Beyond the Rotating-Wave Approximation

We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems. Here we present a simple theoretical technique, using a basis of dressed states, to perturbatively account for the leading-order corrections to the RWA. By comparison with exact numerical results, we demonstrate that the method is accurate for moderately strong coupling, and provides a useful theoretical tool for describing fast quantum information processing. The method applies to any quantum two-level system linearly coupled to a harmonic oscillator or single-mode boson field.

quant-ph↗

arXiv1997

High-Resolution Analysis of Cold and Hot Dark Matter in Cosmic String Wakes

We study the accretion of cold and hot dark matter onto a cosmic string wake using a high-resolution numerical simulation. We verify previous analytical calculations predicting the radius of bound matter around wakes and inflow velocities of the dark matter, as well as assumptions about the self-similarity of the solution. In cold wakes, we show that self-similarity is approached quickly after a `binding' transition. Hot wakes approach self-similarity rapidly once the free streaming `pressure' falls below a critical value and accretion begins. We also analytically calculate the size of the overdensity in wakes with cold dark matter and compare the results to simulations. We remark that the results derived may be used in testing gravitational numerical codes in the non-linear regime.

astro-ph↗

arXiv1993

A Semi-Analytical Analysis of Texture Collapse

This study presents a simplified approach to studying the dynamics of global texture collapse. We derive equations of motion for a spherically symmetric field configuration using a two parameter ansatz. Then we analyse the effective potential for the resulting theory to understand possible trajectories of the field configuration in the parameter space of the ansatz. Numerical results are given for critical winding and collapse time in spatially flat non-expanding, and flat expanding universes. In addition, the open non-expanding and open-expanding cases are studied.

astro-ph↗