Bit by Bit: Gravity Through the Lens of Quantum Information

This dissertation reviews several recent advances at the intersection of quantum information and holography. In holography, properties of quantum systems admit a gravitational interpretation via the AdS/CFT correspondence. For holographic states, boundary entanglement entropy is dual to bulk geodesic areas, known as Ryu-Takayanagi surfaces. Furthermore, the viability to possess a holographic dual at all is constrained by entanglement structure. Accordingly, entanglement enables a coarse classification of states in a Hilbert space. Similarly, state transformation under operator groups also provides a classification on the Hilbert space. Stabilizer states, for example, are invariant under large sets of operations and consequently can be simulated on a classical computer. Cayley graphs offer a useful representation for a group of operators, where vertices represent group elements and edges represent generators. The orbit of a state under action of the group can also be represented as a "reachability graph", a quotient of the group Cayley graph. Reachability graphs can be dressed to encode entanglement information, making them a useful tool for studying entanglement dynamics. Quotienting a reachability graph by group elements that fix a state computable, e.g. entanglement entropy, builds a "contracted graph". Contracted graphs explicitly bound state parameter evolution in quantum circuits. In this thesis, an upper bound on entanglement entropy evolution in Clifford circuits is presented. Another important property of quantum systems is magic, which quantifies the difficulty of simulating a quantum state. Magic and entanglement play complementary roles when describing emergent phenomena in AdS/CFT. This work describes the interplay of entanglement and magic, offering holographic consequences for magic as cosmic brane back-reaction.