6 research outputs found
Symmetry-resolved entanglement of 2D symmetry-protected topological states
Symmetry-resolved entanglement is a useful tool for characterizing
symmetry-protected topological states. In two dimensions, their entanglement
spectra are described by conformal field theories but the symmetry resolution
is largely unexplored. However, addressing this problem numerically requires
system sizes beyond the reach of exact diagonalization. Here, we develop tensor
network methods that can access much larger systems and determine universal and
nonuniversal features in their entanglement. Specifically, we construct
one-dimensional matrix product operators that encapsulate all the entanglement
data of two-dimensional symmetry-protected topological states. We first
demonstrate our approach for the Levin-Gu model. Next, we use the cohomology
formalism to deform the phase away from the fine-tuned point and track the
evolution of its entanglement features and their symmetry resolution. The
entanglement spectra are always described by the same conformal field theory.
However, the levels undergo a spectral flow in accordance with an insertion of
a many-body Aharonov-Bohm flux.Comment: 16 pages, 12 figure
Redundant String Symmetry-Based Error Correction: Experiments on Quantum Devices
Computational power in measurement-based quantum computing (MBQC) stems from
symmetry protected topological (SPT) order of the entangled resource state. But
resource states are prone to preparation errors. We introduce a quantum error
correction (QEC) approach using redundant non-local symmetry of the resource
state. We demonstrate it within a teleportation protocol based on extending the
symmetry of one-dimensional cluster states
to other graph states. Qubit ZZ-crosstalk errors, which are prominent in
quantum devices, degrade the teleportation fidelity of the usual cluster state.
However, as we demonstrate experimentally, once we grow graph states with
redundant symmetry, perfect teleportation fidelity is restored. We identify the
underlying redundant-SPT order as error-protected degeneracies in the
entanglement spectrum
Multipartite entanglement and quantum error identification in -dimensional cluster states
An entangled state is said to be -uniform if the reduced density matrix of
any qubits is maximally mixed. This formal definition is known to be
intimately linked to pure quantum error correction codes (QECCs), which allow
not only to correct errors, but also to identify their precise nature and
location. Here, we show how to create -uniform states using local gates or
interactions and elucidate several QECC applications. We first point out that
-dimensional cluster states, i.e. the ground states of frustration-free
local cluster Hamiltonians, are -uniform with . We discuss finite size
limitations of -uniformity and how to achieve larger values using
quasi- dimensional cluster states. We demonstrate experimentally on a
superconducting quantum computer that the 1D cluster state allows to detect and
identify 1-qubit errors, distinguishing, , and errors. Finally, we
show that -uniformity allows to formulate pure QECCs with a finite logical
space
Navigating the noise-depth tradeoff in adiabatic quantum circuits
Adiabatic quantum algorithms solve computational problems by slowly evolving
a trivial state to the desired solution. On an ideal quantum computer, the
solution quality improves monotonically with increasing circuit depth. By
contrast, increasing the depth in current noisy computers introduces more noise
and eventually deteriorates any computational advantage. What is the optimal
circuit depth that provides the best solution? Here, we address this question
by investigating an adiabatic circuit that interpolates between the
paramagnetic and ferromagnetic ground states of the one-dimensional quantum
Ising model. We characterize the quality of the final output by the density of
defects , as a function of the circuit depth and noise strength
. We find that is well-described by the simple form
, where the ideal case is controlled by the Kibble-Zurek mechanism, and the noise
contribution scales as . It follows that the
optimal number of steps minimizing the number of defects goes as
. We implement this algorithm on a noisy superconducting
quantum processor and find that the dependence of the density of defects on the
circuit depth follows the predicted non-monotonous behavior and agrees well
with noisy simulations. Our work allows one to efficiently benchmark quantum
devices and extract their effective noise strength