A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to the distribu
tion of fragments. The resulting power law directly leads to Benfords law for the first digits of the parts.
We present a theoretical analysis of different methods to synthesize entangled states of two superconducting resonators. These methods use experimentally demonstrated interactions of resonators with artificial atoms, and offer efficient routes to gen
erate nonclassical states. We analyze the theoretical structure of these algorithms and their average performance for arbitrary states and for deterministically preparing NOON states. Using a new state synthesis algorithm, we show that NOON states can be prepared in a time linear in the desired photon number and without any state-selective interactions.
An all-resonant method is proposed to control the quantum state of superconducting resonators. This approach uses a tunable artificial atom linearly coupled to resonators, and allows for efficient routes to Fock state synthesis, qudit logic operation
s, and synthesis of NOON states. This resonant approach is theoretically analyzed, and found to perform signficantly better than existing proposals using the same technology.
Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We numerically st
udy the effect of static disorder on a quantum walk on the glued trees graph. For small disorder, we find that the dominant effect is a type of quantum decay, and not quantum localization. For intermediate disorder, there is a crossover to diffusive transport, while a localization transition is observed at large disorder, in agreement with Anderson localization on the Cayley tree.
We study the routing of quantum information in parallel on multi-dimensional networks of tunable qubits and oscillators. These theoretical models are inspired by recent experiments in superconducting circuits using Josephson junctions and resonators.
We show that perfect parallel state transfer is possible for certain networks of harmonic oscillator modes. We further extend this to the distribution of entanglement between every pair of nodes in the network, finding that the routing efficiency of hypercube networks is both optimal and robust in the presence of dissipation and finite bandwidth.
We present a method to synthesize an arbitrary quantum state of two superconducting resonators. This state-synthesis algorithm utilizes a coherent interaction of each resonator with a tunable artificial atom to create entangled quantum superpositions
of photon number (Fock) states in the resonators. We theoretically analyze this approach, showing that it can efficiently synthesize NOON states, with large photon numbers, using existing technology.
We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atom
s in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the ``tilt). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity.
