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We propose a branch-and-bound algorithm for minimizing a bilinear functional
of the form \[ f(X,Y) = \mathrm{tr}((X\otimes
Y)Q)+\mathrm{tr}(AX)+\mathrm{tr}(BY) , \] of pairs of Hermitian matrices
$(X,Y)$ restricted by joint semidefinite programming constraints. The
functional is parametrized by self-adjoint matrices $Q$, $A$ and $B$. This
problem generalizes that of a bilinear program, where $X$ and $Y$ belong to
polyhedra. The algorithm converges to a global optimum and yields upper and

Certain quantum operations can be built more efficiently through a procedure
known as Repeat-Until-Success. Differently from other non-deterministic quantum
operations, this procedure provides a classical flag which certifies the
success or failure of the procedure and, in the latter case, a recovery step
allows the restoration of the quantum state to its original condition. The
procedure can then be repeated until success is achieved. After success is
certified, the RUS procedure can be equated to a coherent gate. However, this

We compare recently proposed methods to compute the ground state energies of
the Hamiltonian for the water molecule on a quantum computer. The methods
include the phase estimation algorithm based on Trotter decomposition, the
phase estimation algorithm based on the direct implementation of the
Hamiltonian, direct measurement based on the implementation of the Hamiltonian
and the variational quantum eigensolver. After deriving the Hamiltonian using
STO-3G basis, we first explain how each method works and then compare the

We propose a scheme for the quantum simulation of sub-Ohmic spin--boson
models by color centers in free-standing hexagonal boron nitride (h-BN)
membranes. The electronic spin of a color center that couples to the membrane
vibrational spectrum constitute the physical model. The spin-motion coupling is
provided by an external magnetic field gradient. In this study, we show that a
class of spectral densities can be attained by engineering geometry and
boundary conditions of the h-BN resonator. We then put our focus on two extreme