Related papers: Revealing symmetries in quantum computing for many…
Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer. We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian,…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
Simulating molecules is believed to be one of the early-stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence, therefore optimizing resources to execute quantum algorithms is…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
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…
Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body…
Characterizing quantum many-body systems is a fundamental problem across physics, chemistry, and materials science. While significant progress has been made, many existing Hamiltonian learning protocols demand digital quantum control over…
We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum…
Strong repelling interactions between a few fermions or bosons confined in two-dimensional circular traps lead to particle localization and formation of quantum Wigner molecules (QWMs) possessing definite point-group space symmetries. These…
We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
Using a global rotation by theta about the z-axis in the spin sector of the Jordan-Wigner transformation rotates Pauli matrices X and Y in the x-y-plane, while it adds a global complex phase to fermionic quantum states that have a fixed…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Model calculations of nuclear properties are peformed using quantum computing algorithms on simulated and real quantum computers. The models are a realistic calculation of deuteron binding based on effective field theory, and a simplified…
Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries…
We aim to explore a more efficient way to simulate few-body dynamics on quantum computers. Instead of mapping the second quantization of the system Hamiltonian to qubit Pauli gates representation via the Jordan-Wigner transform, we propose…
A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a…