Related papers: A Trotter-Suzuki approximation for Lie groups with…
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via…
Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
This letter continues the program aimed at analysis of the scalar product of states in the Chern-Simons theory. It treats the elliptic case with group SU(2). The formal scalar product is expressed as a multiple finite dimensional integral…
The encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut--Susskind limit. In the electric basis, Hilbert space…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural…
This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…
This work applies a reduced basis method to study the continuum physics of a finite quantum system -- either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schr\"{o}dinger…
Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement,…
We provide formulas for computing the discriminant of noncommutative algebras over central subalgebras in the case of Ore extensions and skew group extensions. The formulas follow from a more general result regarding the discriminants of…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
We study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible…
It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus…
The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of fermionic Gaussian circuits and Ising…
Universal quantum simulation may provide insights into those many-body systems that cannot be described classically, and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary…