Related papers: QSym$^2$: A Quantum Symbolic Symmetry Analysis Pro…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
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…
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…
A point group is a set of spatial symmetry operations in molecular systems and is an indispensable tool for analyzing molecular orbitals and spectroscopy experiments in chemistry. Several quantum algorithms to exploit this symmetry have…
A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
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…
Quantum computer provides new opportunities for quantum chemistry. In this article, we present a versatile, extensible, and efficient software package, named Q$^2$Chemistry, for developing quantum algorithms and quantum inspired classical…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
We develop a method to deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. Symmetries, such as point-group symmetries in molecules, are apparent in the…
In solid state systems, group representation theory is powerful in characterizing the behavior of quasiparticles, notably the energy degeneracy. While conventional group theory is effective in answering yes-or-no questions related to…
Quantifying how much a quantum state breaks a symmetry is essential for characterizing phases, nonequilibrium dynamics, and open-system behavior. Quantum resource theory provides a rigorous operational framework to define and characterize…
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…
Quasisymmetry (QS) provides a novel route to understand and control near-degeneracies, Berry curvature, optical selection rules, and symmetry-protected phenomena in quantum materials. Here we give physical interpretations of the emergence…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
Quantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of…
Quantum chemistry calculations on a quantum computer frequently suffer from symmetry breaking: the situation when a state of assumed spin and number of electrons is contaminated with contributions of undesired symmetry. The situation may…
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle…