We study non-local two-qubit operations from a geometric perspective. By applying Cartan decomposition to su(4), we find that the structure of gates is 3-Torus. derive invariants for local transformations, and connect these coordinates Since different points on 3-Torus may correspond same equivalence class, use Weyl group theory reduce symmetry. show classes are in one-to-one correspondence with tetrahedron except base. then properties perfect entanglers, is, can generate maximally entangled...

When visualized as an operation on the Bloch sphere, qubit $\ensuremath{\pi}/8$ gate corresponds to 1/8 of a complete rotation about vertical axis. This simple often plays important role in quantum information theory, typically situations for which Pauli and Clifford gates are insufficient. Most notably, if it supplements set gates, then universal computation can be achieved. The is simplest example from third level hierarchy (i.e., maps operations under conjugation). Here we derive explicit...

Enhancement of the production cold molecules via photoassociation is considered for ${\mathrm{Cs}}_{2}$ system. The employment chirped picosecond pulses proposed and studied theoretically. analysis based on ability to achieve impulsive excitation which given by ultracold initial conditions where nuclei are effectively stationary during interaction with a field. appropriate theoretical framework coordinate-dependent two-level Matching pulse parameters potentials results in full Rabi cycling...

Optimal control theory is a versatile tool that presents route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric local equivalence classes two-qubit operations derive an optimization algorithm determines best entangling gate given physical setting. demonstrate power this approach trapped polar molecules and neutral atoms.

Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal problem via numerical optimization depends crucially on choice functional. Here, we derive functional that targets full set two-qubit perfect entanglers, gates capable creating maximally-entangled state out some initial product state. The easily-computable local invariants and uniquely determines when gate evolves into entangler. Optimization with our...

The difficulty of an optimization task in quantum information science depends on the proper mathematical expression physical target. Here we demonstrate power functionals targeting arbitrary perfect two-qubit entangler, which allow generation a maximally entangled state from some initial product state. We show for two platforms current interest, i.e., nitrogen vacancy centers diamond and superconducting Josephson junctions, that entangler can be reached faster with higher fidelity than both...

We introduce AQCtensor , a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored the preparation of states generated time evolution many-body Hamiltonians. This has two clear advantages over previous algorithms that were designed map generic MPS circuit. First, we optimize all parameters parametric circuit at once using Approximate Quantum Compiling (AQC) - this be contrasted with other approaches based on locally...

The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of ${\mathrm{Li}}_{2}$ rovibrational eigenstates. function's character, either constant or balanced, evaluated by first imprinting the function, a phase-shaped femtosecond pulse, on superposition molecular states, and then projecting onto an ionic final state, second pulse at specific time delay.

We provide an analytic way to implement any arbitrary two-qubit unitary operation, given entangling gate together with local gates. This is shown explicit construction of a universal quantum circuit that exactly simulates operations in SU(4). Each block this closed form solution. also uniform upper bound the applications gates, and find half all controlled-unitary gates satisfy same as CNOT gate. These results allow for efficient implementation SU(4) required both computation simulation.

Optimal construction of quantum operations is a fundamental problem in the realization computation. We here introduce newly discovered gate, B, that can implement any arbitrary two-qubit operation with minimal number both two- and single-qubit gates. show this by giving an analytic circuit implements generic nonlocal from just two applications B gate. also demonstrate for highly scalable Josephson junction charge qubits, gate more easily quickly generated than CNOT physically feasible parameters.

We propose a way to manifestly reduce the entropy of finite system atoms arbitrarily small values. First, locations vacancies laser-cooled in deep optical lattice are measured. Then, distribution is efficiently compacted using combination site-specific atomic state flips and state-sensitive site translations. In final state, central region has exactly one atom per its vibrational ground state. This good initial for quantum computer. The process can be understood an experimentally viable...

We present a solution of Kitaev's spin model on the honeycomb lattice and related topologically ordered models. employ Jordan-Wigner type fermionization find that Hamiltonian takes BCS form, allowing system to be solved by Bogoliubov transformation. Our does not non-physical auxiliary degrees freedom eigenstates we obtain are completely explicit in terms variables. The ground-state is obtained as condensate fermion pairs over vacuum state which corresponds toric code with same vorticity....

We seek to answer the question posed in title by simulation of tri-iodide ion water, modeling intermolecular interactions classical potentials. The decrease solvation free energy as a function dipole moment is calculated using an extended dynamics method. This approximately quadratic dipole. Symmetry breaking occurs if this greater than required polarize ion. use ab initio calculations on isolated find electronic and vibrational contributions polarizability, from which polarization can be...

From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct universal quantum circuit. A new analytic construction procedure is presented and shown be either optimal or close optimal. This result can extended improve efficiency circuit from any entangling gate. Specifically, both Controlled-NOT Double-CNOT gates, develop simple ways circuits with three applications, which least possible.

We report on ultracold atomic collision experiments utilizing frequency-chirped laser light. A rapid chirp below the resonance results in adiabatic excitation to an attractive molecular potential over a wide range of internuclear separation. This leads transient inelastic rate which is large compared that obtained with fixed-frequency excitation. The combination high efficiency and temporal control demonstrates benefit applying techniques coherent domain.

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive perturbative low-energy effective Hamiltonian that is valid all orders expansion and for possible toroidal configurations. Using this form we demonstrate at what order system's degeneracy lifted by finite size effects note thermodynamic limit it robust orders. Further, themselves correspond creation, propagation, annihilation fermions....

We study a model for itinerant, strongly interacting fermions where judicious tuning of the interactions leads to supersymmetric Hamiltonian. On triangular lattice this is known exhibit property called superfrustration, which characterized by an extensive ground state entropy. Using combination numerical and analytical methods we various ladder geometries obtained imposing doubly periodic boundary conditions on lattice. compare our results bounds degeneracy in literature. For all systems...

We derive expressions for the invariant length element and measure simple compact Lie group SU(4) in a coordinate system particularly suitable treating entanglement quantum information processing. Using this metric, we compute volume of space two-qubit perfect entanglers. find that corresponds to more than 84% total gates. This same metric is also used determine effective target sizes selected gates will present any quantum-control procedure designed implement them.

Coherent control of I3- ground state dynamics in ethanol and acetonitrile solutions is demonstrated. The method based on impulsive excitation creating a dynamic hole employing sub 30 fsec tunable UV laser pulses. target was to increase the ratio second first harmonic spectral modulations symmetric stretching vibrational coherences. Methods demonstrated achieve this include altering pulse intensity when pulses are tuned maximum absorption peak, double separated by half cycle, tuning pumping...

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The is first detected using non-demolition measurement and then transformed into standard by inserting new atom the vacated lattice site. logical qubit, encoded here four physical qubits Grassl-Beth-Pellizzari code, reconstructed via sequence of one projective measurement, two single-qubit gates, three controlled-NOT operations. No ancillary are required. Both...

We show that networks of superconducting topological nanowires can realize the physics exactly solvable Kitaev spin models on trivalent lattices. This connection arises from low-energy theory both systems being described by a tight-binding model Majorana modes. In description provides convenient representation to solve model, whereas in an array Josephson junctions it localized physical modes tunneling between wire ends. explicitly three wires---a setup relevant quantum computing with...

We study a supersymmetric model for strongly interacting lattice fermions in the presence of staggering parameter. The is introduced as tunable parameter manifestly Hamiltonian. obtain analytic expressions ground states limit small and large on class doubly decorated lattices. On this type there are two states, each with different density. In one we find these to be simple Wigner crystal valence bond solid (VBS) state. other types quantum liquids. As special case, investigate liquid state...

The Pauli groups are ubiquitous in quantum information theory because of their usefulness describing states and operations readily understood symmetry properties. In addition, the most well-understood error correcting codes -- stabilizer built using operators. eigenstates these operators display a structure (e.g., mutual orthogonality relationships) that has made them useful examples multi-qubit non-locality contextuality. Here, we apply graph-theoretical contextuality formalism Cabello,...

Exactly solvable lattice models for spins and non-interacting fermions provide fascinating examples of topological phases, some them exhibiting the localized Majorana that feature in proposals quantum computing. The Chern invariant ν is an important characterization such phases. Here we look at square–octagon variant Kitaev's honeycomb model. It maps to spinful paired enjoys a rich phase diagram featuring distinct Abelian non-Abelian phases with = 0,±1,±2,±3 ±4. ±1 ±3 all support modes are...