6,460 research outputs found
Scalable Neural Network Decoders for Higher Dimensional Quantum Codes
Machine learning has the potential to become an important tool in quantum
error correction as it allows the decoder to adapt to the error distribution of
a quantum chip. An additional motivation for using neural networks is the fact
that they can be evaluated by dedicated hardware which is very fast and
consumes little power. Machine learning has been previously applied to decode
the surface code. However, these approaches are not scalable as the training
has to be redone for every system size which becomes increasingly difficult. In
this work the existence of local decoders for higher dimensional codes leads us
to use a low-depth convolutional neural network to locally assign a likelihood
of error on each qubit. For noiseless syndrome measurements, numerical
simulations show that the decoder has a threshold of around when
applied to the 4D toric code. When the syndrome measurements are noisy, the
decoder performs better for larger code sizes when the error probability is
low. We also give theoretical and numerical analysis to show how a
convolutional neural network is different from the 1-nearest neighbor
algorithm, which is a baseline machine learning method
Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart
is the statement that the space of operators that commute with the tensor
powers of all unitaries is spanned by the permutations of the tensor factors.
In this work, we describe a similar duality theory for tensor powers of
Clifford unitaries. The Clifford group is a central object in many subfields of
quantum information, most prominently in the theory of fault-tolerance. The
duality theory has a simple and clean description in terms of finite
geometries. We demonstrate its effectiveness in several applications:
(1) We resolve an open problem in quantum property testing by showing that
"stabilizerness" is efficiently testable: There is a protocol that, given
access to six copies of an unknown state, can determine whether it is a
stabilizer state, or whether it is far away from the set of stabilizer states.
We give a related membership test for the Clifford group.
(2) We find that tensor powers of stabilizer states have an increased
symmetry group. We provide corresponding de Finetti theorems, showing that the
reductions of arbitrary states with this symmetry are well-approximated by
mixtures of stabilizer tensor powers (in some cases, exponentially well).
(3) We show that the distance of a pure state to the set of stabilizers can
be lower-bounded in terms of the sum-negativity of its Wigner function. This
gives a new quantitative meaning to the sum-negativity (and the related mana)
-- a measure relevant to fault-tolerant quantum computation. The result
constitutes a robust generalization of the discrete Hudson theorem.
(4) We show that complex projective designs of arbitrary order can be
obtained from a finite number (independent of the number of qudits) of Clifford
orbits. To prove this result, we give explicit formulas for arbitrary moments
of random stabilizer states.Comment: 60 pages, 2 figure
Cross-verification of independent quantum devices
Quantum computers are on the brink of surpassing the capabilities of even the
most powerful classical computers. This naturally raises the question of how
one can trust the results of a quantum computer when they cannot be compared to
classical simulation. Here we present a verification technique that exploits
the principles of measurement-based quantum computation to link quantum
circuits of different input size, depth, and structure. Our approach enables
consistency checks of quantum computations within a device, as well as between
independent devices. We showcase our protocol by applying it to five
state-of-the-art quantum processors, based on four distinct physical
architectures: nuclear magnetic resonance, superconducting circuits, trapped
ions, and photonics, with up to 6 qubits and 200 distinct circuits
Application of differential evolution to power system stabilizer design
Includes synopsis.Includes bibliographical references.In recent years, many Evolutionary Algorithms (EAs) such as Genetic Algorithms (GAs) have been proposed to optimally tune the parameters of the PSS. GAs are population based search methods inspired by the mechanism of evolution and natural genetic. Despite the fact that GAs are robust and have given promising results in many applications, they still have some drawbacks. Some of these drawbacks are related to the problem of genetic drift in GA which restricts the diversity in the population. ... To cope with the above mentioned drawbacks, many variants of GAs have been proposed often tailored to a particular problem. Recently, several simpler and yet effective heuristic algorithms such as Population Based Incremental Learning (PBIL) and Differential Evolution (DE), etc., have received increasing attention
An Adaptive Entanglement Distillation Scheme Using Quantum Low Density Parity Check Codes
Quantum low density parity check (QLDPC) codes are useful primitives for
quantum information processing because they can be encoded and decoded
efficiently. Besides, the error correcting capability of a few QLDPC codes
exceeds the quantum Gilbert-Varshamov bound. Here, we report a numerical
performance analysis of an adaptive entanglement distillation scheme using
QLDPC codes. In particular, we find that the expected yield of our adaptive
distillation scheme to combat depolarization errors exceed that of Leung and
Shor whenever the error probability is less than about 0.07 or greater than
about 0.28. This finding illustrates the effectiveness of using QLDPC codes in
entanglement distillation.Comment: 12 pages, 6 figure
A Heuristic Dynamic Programming Based Power System Stabilizer for a Turbogenerator in a Single Machine Power System
Power system stabilizers (PSS) are used to generate supplementary control signals for the excitation system in order to damp the low frequency power system oscillations. To overcome the drawbacks of conventional PSS (CPSS), numerous techniques have been proposed in the literature. Based on the analysis of existing techniques, a novel design of power system stabilizer (PSS) based on heuristic dynamic programming (HDP) is proposed in this paper. HDP combining the concepts of dynamic programming and reinforcement learning is used in the design of a nonlinear optimal power system stabilizer. The proposed HDP based PSS is evaluated against the conventional power system stabilizer and indirect adaptive neurocontrol based PSS under small and large disturbances in a single machine infinite bus power system setup. Results are presented to show the effectiveness of this new technique
Implementing and characterizing precise multi-qubit measurements
There are two general requirements to harness the computational power of
quantum mechanics: the ability to manipulate the evolution of an isolated
system and the ability to faithfully extract information from it. Quantum error
correction and simulation often make a more exacting demand: the ability to
perform non-destructive measurements of specific correlations within that
system. We realize such measurements by employing a protocol adapted from [S.
Nigg and S. M. Girvin, Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time
selection of arbitrary register-wide Pauli operators. Our implementation
consists of a simple circuit quantum electrodynamics (cQED) module of four
highly-coherent 3D transmon qubits, collectively coupled to a high-Q
superconducting microwave cavity. As a demonstration, we enact all seven
nontrivial subset-parity measurements on our three-qubit register. For each we
fully characterize the realized measurement by analyzing the detector
(observable operators) via quantum detector tomography and by analyzing the
quantum back-action via conditioned process tomography. No single quantity
completely encapsulates the performance of a measurement, and standard figures
of merit have not yet emerged. Accordingly, we consider several new fidelity
measures for both the detector and the complete measurement process. We measure
all of these quantities and report high fidelities, indicating that we are
measuring the desired quantities precisely and that the measurements are highly
non-demolition. We further show that both results are improved significantly by
an additional error-heralding measurement. The analyses presented here form a
useful basis for the future characterization and validation of quantum
measurements, anticipating the demands of emerging quantum technologies.Comment: 10 pages, 5 figures, plus supplemen
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