Related papers: The Quantum Paldus Transform: Efficient Circuits w…
To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical…
The "quantum duality principle" states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing…
The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually…
Experimental realization of a universal set of quantum logic gates with high-fidelity is critical to quantum information processing, which is always challenging by inevitable interaction between the quantum system and environment. Geometric…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
We discover a deep connection between parity-time (PT) symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with…
Quantum Selected Configuration Interaction (QSCI) and an extended protocol known as Sample-based Quantum Diagonalization (SQD) have emerged as promising algorithms to solve the electronic Schr\"odinger equation with noisy quantum computers.…
This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schr\"odinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
Conservation of symmetries plays a crucial role in both classical and quantum simulations of many-body systems, enabling the tracking of states with specific symmetry properties and leading to substantial reductions in the number of…
We propose an effective field theory (EFT) of fractional quantum Hall systems near the filling fraction $\nu=5/2$ that flows to pertinent IR candidate phases, including non-abelian Pfaffian, anti-Pfaffian, and particle-hole Pfaffian states…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. We achieve the promotion…
The Schr\"odinger Hamiltonian of a spin zero particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a…