Quantum circuit complexity of one-dimensional topological phases

Quantum circuit complexity of one-dimensional topological phases

Topological quantum states cannot be created from product states with local quantum circuits of constant depth and are in this sense more entangled than topologically trivial states, but how entangled are they? Here we quantify the entanglement in one-dimensional topological states by showing that local quantum circuits of linear depth are necessary to generate them from product states. We esta...

Interacting one-dimensional fermionic symmetry-protected topological phases.

In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, 0, Z2, or Z. For example, noninteracting one-dimensional fermionic superconducting phases with S(z) spin rotation and time-reversal symmetries are classified by Z. We show that with weak interactions, this classification reduces to Z4. Using g...

Topological phases and quantum computation

Topological quantum Lego Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall states

Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall states Some of the most beautiful discoveries of the last couple of years were made in the field of topological phases of matter. The simpler, non-interacting phases are included in the periodic table of topological insulators, and are distinguished by the appearance of the edge states protected by the bulk gap a...

Quantum Circuit Complexity

We propose a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomial-size quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines ...