Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results… Expand

We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, pointlike topological excitations, and subextensive… Expand

It is proved that every stringlike logical operator of this code can be deformed to a disjoint union of short segments, each of which is in the stabilizer group, and introduced a notion of "logical string segments" to avoid difficulties in defining one-dimensional objects in discrete lattices.Expand

A new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation on all logical qubits are proposed and lead to a two-fold overhead reduction for distilling magic states with output accuracy compared with the best previously known protocol.Expand

Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of… Expand

This paper studies the problem of simulating the time evolution of a lattice Hamiltonian, and proves a matching lower bound on the gate count of such a simulation, showing that any quantum algorithm that can simulate a piecewise constant bounded local Hamiltonian in one dimension to constant error requires (nT) gates in the worst case.Expand

We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of fermion topological quantum order, building on a model presented by S.… Expand

This work gives a theoretical measurement scheme (POVM) that requires copies to achieve error, and proves that for independent (product) measurements, it can be implemented on a quantum computer in time polynomial.Expand

We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, a family of Hamiltonians that belong to the same phase of matter… Expand

Analytical and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code is reported and it is proved that its memory time is at least L(cβ), where L is the lattice size, β is the inverse temperature of the bath, and c>0 is a constant coefficient.Expand