Related papers: A Trotter-Suzuki approximation for Lie groups with…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
Hamiltonian simulation represents an important module in a large class of quantum algorithms and simulations such as quantum machine learning, quantum linear algebra methods, and modeling for physics, material science and chemistry. One of…
Many relevant applications of group theoretical methods to physical problems are related, in some manner, to classification schemes by means of symmetry groups. In these schemes, irreducible representations of a Lie group have to be…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
Quantum error mitigation (QEM) has emerged as a powerful tool for the extraction of useful quantum information from quantum devices. Here, we introduce the Subspace Noise Tailoring (SNT) algorithm, which efficiently combines the cheap cost…
Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number…
In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central…
This is a continuation of a previous joint work with Robert Weston on the quantum group invariant XXZ spin-chain (math-ph/0703085). The previous results on quasi-Hermiticity of this integrable model are briefly reviewed and then connected…
We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…
In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
We study $\mathcal{O}$-operators and post-Lie products over the same Lie algebra compatible in a certain sense. We prove that the group product corresponding to the formal integration of the Lie algebra, which is adjacent to the sum of two…
We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators \eta_+, and \eta_+-pseudo-Hermitian operators acting in two-dimensional complex Euclidean space C^2. These operators…
In this work we propose a series-expansion thermal tensor network (SETTN) approach for efficient simulations of quantum lattice models. This continuous-time SETTN method is based on the numerically exact Taylor series expansion of…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…