23 research outputs found
Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
Over the past few years, topological insulators have taken center stage in
solid state physics. The desire to tune the topological invariants of the bulk
and thus control the number of edge states has steered theorists and
experimentalists towards periodically driving parameters of these systems. In
such periodically driven setups, by varying the drive sequence the effective
(Floquet) Hamiltonian can be engineered to be topological: then, the principle
of bulk--boundary correspondence guarantees the existence of robust edge
states. It has also been realized, however, that periodically driven systems
can host edge states not predicted by the Floquet Hamiltonian. The exploration
of such edge states, and the corresponding topological phases unique to
periodically driven systems, has only recently begun. We contribute to this
goal by identifying the bulk topological invariants of periodically driven
one-dimensional lattice Hamiltonians with chiral symmetry. We find simple
closed expressions for these invariants, as winding numbers of blocks of the
unitary operator corresponding to a part of the time evolution, and ways to
tune these invariants using sublattice shifts. We illustrate our ideas on the
periodically driven Su-Schrieffer-Heeger model, which we map to a discrete time
quantum walk, allowing theoretical results about either of these systems to be
applied to the other. Our work helps interpret the results of recent
simulations where a large number of Floquet Majorana fermions in periodically
driven superconductors have been found, and of recent experiments on discrete
time quantum walks
Scattering theory of topological phases in discrete-time quantum walks
One-dimensional discrete-time quantum walks show a rich spectrum of
topological phases that have so far been exclusively analysed in momentum
space. In this work we introduce an alternative approach to topology which is
based on the scattering matrix of a quantum walk, adapting concepts from
time-independent systems. For gapped quantum walks, topological invariants at
quasienergies 0 and {\pi} probe directly the existence of protected boundary
states, while quantum walks with a non-trivial quasienergy winding have a
discrete number of perfectly transmistting unidirectional modes. Our
classification provides a unified framework that includes all known types of
topology in one dimensional discrete-time quantum walks and is very well suited
for the analysis of finite size and disorder effects. We provide a simple
scheme to directly measure the topological invariants in an optical quantum
walk experiment.Comment: 12 pages. v2: minor correction
Density-matrix simulation of small surface codes under current and projected experimental noise
We present a full density-matrix simulation of the quantum memory and
computing performance of the distance-3 logical qubit Surface-17, following a
recently proposed quantum circuit and using experimental error parameters for
transmon qubits in a planar circuit QED architecture. We use this simulation to
optimize components of the QEC scheme (e.g., trading off stabilizer measurement
infidelity for reduced cycle time) and to investigate the benefits of feedback
harnessing the fundamental asymmetry of relaxation-dominated error in the
constituent transmons. A lower-order approximate calculation extends these
predictions to the distance- Surface-49. These results clearly indicate
error rates below the fault-tolerance threshold of surface code, and the
potential for Surface-17 to perform beyond the break-even point of quantum
memory. At state-of-the-art qubit relaxation times and readout speeds,
Surface-49 could surpass the break-even point of computation.Comment: 10 pages + 8 pages appendix, 12 figure
Andreev-Bragg reflection from an Amperian superconductor
We show how an electrical measurement can detect the pairing of electrons on
the same side of the Fermi surface (Amperian pairing), recently proposed by
Patrick Lee for the pseudogap phase of high- cuprate superconductors.
Bragg scattering from the pair-density wave introduces odd multiples of
momentum shifts when an electron incident from a normal metal is
Andreev-reflected as a hole. These Andreev-Bragg reflections can be detected in
a three-terminal device, containing a ballistic Y-junction between normal leads
and the superconductor. The cross-conductance has the
opposite sign for Amperian pairing than it has either in the normal state or
for the usual BCS pairing.Comment: 5 pages, 6 figures; v2 includes study of disorder and interface
barrie
Adaptive weight estimator for quantum error correction
Quantum error correction of a surface code or repetition code requires the
pairwise matching of error events in a space-time graph of qubit measurements,
such that the total weight of the matching is minimized. The input weights
follow from a physical model of the error processes that affect the qubits.
This approach becomes problematic if the system has sources of error that
change over time. Here we show how the weights can be determined from the
measured data in the absence of an error model. The resulting adaptive decoder
performs well in a time-dependent environment, provided that the characteristic
time scale of the variations is greater than , with the duration of one error-correction cycle and
the typical error probability per qubit in one cycle.Comment: 5 pages, 4 figure
General method for extracting the quantum efficiency of dispersive qubit readout in circuit QED
We present and demonstrate a general three-step method for extracting the
quantum efficiency of dispersive qubit readout in circuit QED. We use active
depletion of post-measurement photons and optimal integration weight functions
on two quadratures to maximize the signal-to-noise ratio of the
non-steady-state homodyne measurement. We derive analytically and demonstrate
experimentally that the method robustly extracts the quantum efficiency for
arbitrary readout conditions in the linear regime. We use the proven method to
optimally bias a Josephson traveling-wave parametric amplifier and to quantify
different noise contributions in the readout amplification chain.Comment: 10 pages, 6 figure
Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements
Protecting quantum information from errors is essential for large-scale
quantum computation. Quantum error correction (QEC) encodes information in
entangled states of many qubits, and performs parity measurements to identify
errors without destroying the encoded information. However, traditional QEC
cannot handle leakage from the qubit computational space. Leakage affects
leading experimental platforms, based on trapped ions and superconducting
circuits, which use effective qubits within many-level physical systems. We
investigate how two-transmon entangled states evolve under repeated parity
measurements, and demonstrate the use of hidden Markov models to detect leakage
using only the record of parity measurement outcomes required for QEC. We show
the stabilization of Bell states over up to 26 parity measurements by
mitigating leakage using postselection, and correcting qubit errors using
Pauli-frame transformations. Our leakage identification method is
computationally efficient and thus compatible with real-time leakage tracking
and correction in larger quantum processors.Comment: 22 pages, 15 figure