Jiri Vala

Geometric theory of nonlocal two-qubit operations

We study nonlocal two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of nonlocal gates is a 3-torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-torus. Since different points on the 3-torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of nonlocal gates. We find that exactly half the nonlocal gates are perfect entanglers. We also investigate the nonlocal operations generated by a given Hamiltonian. We first study the gates that can be directly generated by a Hamiltonian. Then we explicitly construct a quantum circuit that contains at most three nonlocal gates generated by a two-body interaction Hamiltonian, together with at most four local gates generated by single-qubit terms. We prove that such a quantum circuit can simulate any arbitrary two-qubit gate exactly, and hence it provides an efficient implementation of universal quantum computation and simulation.

Experimental implementation of the Deutsch-Jozsa algorithm for three-qubit functions using pure coherent molecular superpositions

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

Does solvation cause symmetry breaking in the I3− ion in aqueous solution?

We seek to answer the question posed in the title by simulation of the tri-iodide ion in water, modeling the intermolecular interactions by classical potentials. The decrease in solvation free energy as a function of the dipole moment of the ion is calculated using an extended dynamics simulation method. This decrease is approximately quadratic in the ion dipole. Symmetry breaking occurs if this decrease is greater than the energy required to polarize the ion. We use ab initio calculations on an isolated ion to find the electronic and vibrational contributions to the polarizability, from which the polarization energy can be calculated. The solvated ion is found to be more stable when displaced along the asymmetric stretching coordinate, due to contributions of this deformation to the molecular dipole. As a test of the model’s reliability, it is used to derive solvation force autocorrelation functions from which time scales for vibrational energy and phase relaxation are estimated. The results are demonstr...

Exact two-qubit universal quantum circuit.

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

Minimum Construction of Two-Qubit Quantum Operations

Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. Realization of the B gate is illustrated with an example of charge-coupled superconducting qubits for which the B gate is seen to be generated in shorter time than the CNOT gate.

Ab initio and diatomics in molecule potentials for I2−, I2, I3−, and I3

The electronic structure of the I3− molecular anion and its photoproducts I2−, I2, and I3 were studied. Ab initio calculations were carried out using the multireference configuration interaction (MRCI) method for the valence electrons together with a relativistic effective core potential. The ab initio wave functions were also used to compute some spin–orbit coupling matrix elements, as well as approximate valence bond wave functions, used as guidelines in the construction of a 108-state diatomics in molecule (DIM) description of the electronic structure of I3−. In the DIM model, spin–orbit coupling was introduced as a sum of atomic operators. For I2− the ab initio and the DIM ground-state potentials show excellent agreement with the experimental results. The results for I2 are also in very good agreement with experimental data. For I3−, the MRCI calculations give a very good description of the spectroscopic constants and agree with the vertical excitation energies, provided spin–orbit coupling is included. The DIM description fails both quantitively by leading to erroneous spectroscopic constants, and qualitatively by not even reproducing the MRCI ordering of the excited-states. The failure of the DIM is attributed to the omission of ionic states. The overall qualitative picture of the excited-state potentials shows a maze of dense avoided crossings which means that all energetically allowed photoproducts will be present in the experiment. The ground electronic state of I3 was calculated to be a collinear and centrosymmetric 2Πu,3/2. The collinear state is stabilized by spin–orbit coupling relative to a bent configuration. Calculated vertical transition energies from the ground to low-lying excited states of the radical are in excellent agreement with the experimental data. The spin–orbit assignment of these states is provided.The electronic structure of the I3− molecular anion and its photoproducts I2−, I2, and I3 were studied. Ab initio calculations were carried out using the multireference configuration interaction (MRCI) method for the valence electrons together with a relativistic effective core potential. The ab initio wave functions were also used to compute some spin–orbit coupling matrix elements, as well as approximate valence bond wave functions, used as guidelines in the construction of a 108-state diatomics in molecule (DIM) description of the electronic structure of I3−. In the DIM model, spin–orbit coupling was introduced as a sum of atomic operators. For I2− the ab initio and the DIM ground-state potentials show excellent agreement with the experimental results. The results for I2 are also in very good agreement with experimental data. For I3−, the MRCI calculations give a very good description of the spectroscopic constants and agree with the vertical excitation energies, provided spin–orbit coupling is include...

Geminate recombination of I3− in cooled liquid and glassy ethanol

Abstract Geminate recombination following impulsive ultraviolet photolysis of cryogenically cooled triiodide in ethanol is followed with 100 fs time resolution. Caged fragments either recombine directly and vibrationally relax within picoseconds or produce a long-lived complex which decays in tens of picoseconds back to the I 3 − ground state. Cooling steadily enhances direct recombination at the expense of cage escape, which is essentially hindered at the lowest temperatures studied. Persistence of the slower recombination process, even in solid solutions, suggests it is due to recombination on a bound excited state of I 3 − . The identity of this long-lived intermediate, and possible mechanisms of its formation, are discussed.

Coherent Mechanism of Robust Population Inversion

A coherent mechanism of robust population inversion in atomic and molecular systems by a chirped field is presented. It is demonstrated that a field of sufficiently high chirp rate imposes a certain relative phase between a ground and excited state wavefunction of a two-level system. The value of the relative phase angle is thus restricted to be negative and close to 0 or - pi for positive and negative chirp, respectively. This explains the unidirectionality of the population transfer from the ground to the excited state.In a molecular system composed of a ground and excited potential energy surface the symmetry between the action of a pulse with a large positive and negative chirp is broken. The same framwork of the coherent mechanism can explain the symmetry breaking and the population inversion due to a positive chirped field.

Quantum error correction of a qubit loss in an addressable atomic system

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum nondemolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum nondemolition and projective measurements are implemented using a cavity quantum electrodynamics system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons.

Description of Kitaev’s honeycomb model with toric-code stabilizers

We present a solution of Kitaevs spin model on the honeycomb lattice and of related topologically ordered spin models. We employ a Jordan-Wigner-type fermionization and find that the Hamiltonian takes a BCS-type form, allowing the system to be solved by Bogoliubov transformation. Our fermionization does not employ nonphysical auxiliary degrees of freedom and the eigenstates we obtain are completely explicit in terms of the spin variables. The ground state is obtained as a BCS condensate of fermion pairs over a vacuum state which corresponds to the toric-code state with the same vorticity. We show in detail how to calculate all eigenstates and eigenvalues of the model on the torus. In particular, we find that the topological degeneracy on the torus descends directly from that of the toric-code, which now supplies four vacua for the fermions, one for each choice of periodic vs antiperiodic boundary conditions. The reduction of the degeneracy in the non-Abelian phase of the model is seen to be due to the vanishing of one of the corresponding candidate BCS ground states in that phase. This occurs in particular in the fully periodic vortex-free sector. The true ground state in this sector is exhibited and shown to be gapped away from the three partially antiperiodic ground states whenever the non-Abelian phase is gapped.