Related papers: Closed-Form Expressions for Unitaries of Spin-Adap…
Among recent proposals for next-generation, non-charge-based logic is the notion that a single electron can be trapped and its spin can be manipulated through the application of gate potentials. In this paper, we present numerical…
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow…
We discuss the quantum-circuit realization of the state of a nucleon in the scope of simple symmetry groups. Explicit algorithms are presented for the preparation of the state of a neutron or a proton as resulting from the composition of…
We review recent studies on spin decoherence of electrons and holes in quasi-two-dimensional quantum dots, as well as electron-spin relaxation in nanowire quantum dots. The spins of confined electrons and holes are considered major…
We consider quantum spin chains with a hidden free fermionic structure, distinct from the Jordan-Wigner transformation and its generalizations. We express selected local operators with the hidden fermions. This way we can exactly solve the…
We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…
We develop a systematic framework for the spin adaptation of the cumulants of p-particle reduced density matrices (RDMs), with explicit constructions for p = 1 to 3. These spin-adapted cumulants enable rigorous treatment of both S_z and S^2…
Encoding a dimension in the internal degree of freedom of an atom provides an interesting tool for quantum simulation, facilitating the realization of artificial gauge fields. We propose an extension of the synthetic dimension toolbox,…
One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
Spin properties of two interacting electrons in a quantum dot (QD) embedded in a nanowire with controlled aspect ratio and longitudinal magnetic fields are investigated by using a configuration interaction (CI) method and exact…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
We obtain an exact solution for the spectral function for one-dimensional Bose-Bose and Fermi- Fermi mixtures with strong repulsive interactions, valid in arbitrary confining potentials and at all frequency scales. For the case of harmonic…
We introduce the notion of combinatorial gauge symmetry -- a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states) -- that preserve the commutation and anti-commutation…
In recent decades the field of quantum computation has seen remarkable development. While much progress has been made toward the realization of a fully digital, scalable, and fault tolerant quantum computer, there are still many essential…
We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis when the phase contributed by each path is described by a quadratic form over…
We show that spin-orbit coupling in a quantum dot molecule allows for coherent manipulation of two electron spin states using Raman transitions. Such two-electron spin states defined by the singlet and triplet states of two exchange coupled…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
The permutation symmetry is a fundamental attribute of the collective wavefunction of indistinguishable particles. It makes a difference for the behavior of collective systems having different quantum statistics but existing in the same…
An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy…