Related papers: Operator relationship between conventional coupled…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…
Associated to any acyclic cluster algebra is a corresponding triangulated category known as the cluster category. It is known that there is a one-to-one correspondence between cluster variables in the cluster algebra and exceptional…
We explore commutativity up to a factor, $AB=\lambda BA$, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor $\lambda$ are formulated and shown to depend on spectral properties of the operators…
The Fermi-Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum…
In this paper we investigate operators unitarily equivalent to truncated Toeplitz operators. We show that this class contains certain sums of tensor products of truncated Toeplitz operators. In particular, it contains arbitrary inflations…
Clustering is grouping of data by the proximity of some properties. We report on the possibility of increasing the efficiency of clustering of points in a plane using artificial quantum neural networks after the replacement of the two-level…
Quantum correlations, crucial for the advantage and advancement of quantum science and technology, arise from the impossibility of expressing a quantum state as a tensor product over a given set of parties. In this work, a generalized…
In the field of polaritonic chemistry, strong light-matter interactions are used to alter a chemical reaction inside an optical cavity. To explain and understand these processes, the development of reliable theoretical models is essential.…
We have developed a relativistic coupled-cluster theory to incorporate nuclear spin-dependent interaction Hamiltonians perturbatively. In this theory, the coupled-cluster operators in the electronic sector are defined as tensor operators of…
It is shown that the multiquark gauge-invariant operators can, in general, be decomposed into combinations of products of ordinary hadronic operators, exhibiting their cluster reducibility. The latter property inhibits the formation of…
Ambiguity in the contact between laboratory instruments and equations of quantum mechanics is formulated in terms of responses of the instruments to commands transmitted to them by a Classical digital Process-control Computer (CPC); in this…
One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
A dynamical formulation of coupled cluster theory is derived using a variational principle. By allowing time-dependent single-particle functions, a high degree of adaptivity is introduced, allowing complex systems to be simulated with high…
Preserving spin symmetry in variational quantum algorithms is essential for producing physically meaningful electronic wavefunctions. Implementing spin-adapted transformations on quantum hardware, however, is challenging because the…
Trotterization in quantum mechanics is an important theoretical concept in handling the exponential of noncommutative operators. In this communication, we give a mathematical formulation of the Trotter Product Formula, and apply it to basic…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
We consider the dynamics $t\mapsto\tau_t$ of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that…