Method for construction of operators in Fock space

M. Durga Prasad

Ameur Dhahri, Franco Fagnola, D Poletti +1 more

We construct Gaussian quantum Markov semigroups on the representation of the Weyl algebra in the tensor product of the Fock space and its conjugate Fock space by the minimal semigroup method. We prove the explicit formula for the action on Weyl operators and study some properties.

Egon Marx

V. V. Kuryshkin

Leszek Z. Stolarczyk, Hendrik J. Monkhorst

A detailed and systematic presentation of algebraic and diagrammatic techniques introduced in paper I [L. Z. Stolarczyk and H. J. Monkhorst, Phys. Rev. A 32, 725 (1985)] is given. Performing a similarity transformation of an operator in Fock space, e.g., a Hamiltonian in the generalized coupled-cluster method (see paper I), leads to lengthy algebraic formulas for the linear parameters (amplitudes) of the transformed operator. These formulas can be expressed in a compact form by means of the so-called reduced diagrams. Precise rules are given for constructing such diagrams (related to the so-called directed graphs of the graph theory) and the algebraic expressions corresponding to them. In particular, rules for generating a connected-diagram expansion of the amplitudes of the transformed operator are formulated. Several examples illustrating the use of this diagrammatic-algebraic approach are considered.

Kazuyuki Fujii

We construct an exchange gate with small elementary gates on the space of qudits, which consist of three controlled shift gates and three 'reverse' gates. This is a natural extension of the qubit case. We also consider a similar situation in Fock space, but in this case we find some differences. However, we can construct the exchange gate by making use of a generalized coherent operator based on the Lie algebra su (2), which is a well-known method in quantum optics. We also make a brief comment on 'imperfect clones'.