Related papers: Stabilizer entropy of quantum tetrahedra
The entanglement entropy (EE) can measure the entanglement between a spatial subregion and its complement, which provides key information about quantum states. Here, rather than focusing on specific regions, we study how the entanglement…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
The formal structure of quantum electrodynamics consists of various elements. These include the Schroedinger equation which evolves the system forward in time, the vacuum state which is assumed to be the state with a free field energy of…
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare…
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…
A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is…
We construct a macroscopic semiclassical state state for a quantum tetrahedron. The expectation values of the geometrical operators representing the volume, areas and dihedral angles are peaked around assigned classical values, with…
The gauge principle is a cornerstone of particle-physics model building. Nevertheless, many constructions leave certain global $U(1)$ redundancies ungauged. In this work, we take the gauge principle to its logical extreme by promoting all…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
A universal finite system-size scaling analysis of the entanglement entropy is presented for highly degenerate ground states arising from spontaneous symmetry breaking with type-B Goldstone modes in exactly solvable one-dimensional quantum…
The emergence of randomness from unitary quantum dynamics is a central problem across diverse disciplines, ranging from the foundations of statistical mechanics to quantum algorithms and quantum computation. Physical systems are invariably…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…
Quantum engineering requires controllable artificial systems with quantum coherence exceeding the device size and operation time. This can be achieved with geometrically confined low-dimensional electronic structures embedded within…
A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching…
A perturbative formulation of quantum electrodynamics is given in terms of geometrical invariants of the energy-momentum space, whose geometry is taken to be one of a constant curvature. The construction is relevant for different classes of…
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground…