37,336 research outputs found
Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification
Stochastic spectral methods are efficient techniques for uncertainty
quantification. Recently they have shown excellent performance in the
statistical analysis of integrated circuits. In stochastic spectral methods,
one needs to determine a set of orthonormal polynomials and a proper numerical
quadrature rule. The former are used as the basis functions in a generalized
polynomial chaos expansion. The latter is used to compute the integrals
involved in stochastic spectral methods. Obtaining such information requires
knowing the density function of the random input {\it a-priori}. However,
individual system components are often described by surrogate models rather
than density functions. In order to apply stochastic spectral methods in
hierarchical uncertainty quantification, we first propose to construct
physically consistent closed-form density functions by two monotone
interpolation schemes. Then, by exploiting the special forms of the obtained
density functions, we determine the generalized polynomial-chaos basis
functions and the Gauss quadrature rules that are required by a stochastic
spectral simulator. The effectiveness of our proposed algorithm is verified by
both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201
Digital zero noise extrapolation for quantum error mitigation
Zero-noise extrapolation (ZNE) is an increasingly popular technique for
mitigating errors in noisy quantum computations without using additional
quantum resources. We review the fundamentals of ZNE and propose several
improvements to noise scaling and extrapolation, the two key components in the
technique. We introduce unitary folding and parameterized noise scaling. These
are digital noise scaling frameworks, i.e. one can apply them using only
gate-level access common to most quantum instruction sets. We also study
different extrapolation methods, including a new adaptive protocol that uses a
statistical inference framework. Benchmarks of our techniques show error
reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE
effectiveness at larger qubit numbers than have been tested previously. In
addition to presenting new results, this work is a self-contained introduction
to the practical use of ZNE by quantum programmers.Comment: 11 pages, 7 figure
Zero-noise extrapolation for quantum-gate error mitigation with identity insertions
Quantum-gate errors are a significant challenge for achieving precision measurements on noisy intermediate-scale quantum (NISQ) computers. This paper focuses on zero-noise extrapolation (ZNE), a technique that can be implemented on existing hardware, studying it in detail and proposing modifications to existing approaches. In particular, we consider identity insertion methods for amplifying noise because they are hardware agnostic. We build a mathematical formalism for studying existing ZNE techniques and show how higher order polynomial extrapolations can be used to systematically reduce depolarizing errors. Furthermore, we introduce a method for amplifying noise that uses far fewer gates than traditional methods. This approach is compared with existing methods for simulated quantum circuits. Comparable or smaller errors are possible with fewer gates, which illustrates the potential for empowering an entirely new class of moderate-depth circuits on near term hardware
Metastability-Containing Circuits
In digital circuits, metastability can cause deteriorated signals that
neither are logical 0 or logical 1, breaking the abstraction of Boolean logic.
Unfortunately, any way of reading a signal from an unsynchronized clock domain
or performing an analog-to-digital conversion incurs the risk of a metastable
upset; no digital circuit can deterministically avoid, resolve, or detect
metastability (Marino, 1981). Synchronizers, the only traditional
countermeasure, exponentially decrease the odds of maintained metastability
over time. Trading synchronization delay for an increased probability to
resolve metastability to logical 0 or 1, they do not guarantee success.
We propose a fundamentally different approach: It is possible to contain
metastability by fine-grained logical masking so that it cannot infect the
entire circuit. This technique guarantees a limited degree of metastability
in---and uncertainty about---the output.
At the heart of our approach lies a time- and value-discrete model for
metastability in synchronous clocked digital circuits. Metastability is
propagated in a worst-case fashion, allowing to derive deterministic
guarantees, without and unlike synchronizers. The proposed model permits
positive results and passes the test of reproducing Marino's impossibility
results. We fully classify which functions can be computed by circuits with
standard registers. Regarding masking registers, we show that they become
computationally strictly more powerful with each clock cycle, resulting in a
non-trivial hierarchy of computable functions
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