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Operator Spreading in Random Unitary Circuits
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…
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Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, pointlike topological excitations, and subextensive…
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Local stabilizer codes in three dimensions without string logical operators
TLDR
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.
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Magic-state distillation with low overhead
TLDR
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.
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Quantum Entanglement Growth Under Random Unitary Dynamics
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…
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Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians
TLDR
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.
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A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
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.…
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Sample-Optimal Tomography of Quantum States
TLDR
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.
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Commuting Pauli Hamiltonians as Maps between Free Modules
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…
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Quantum self-correction in the 3D cubic code model.
TLDR
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.
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