Simulating chemistry efficiently on fault-tolerant quantum computers

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposed chemical simulation algorithms computationally fast on fault-tolerant quantum computers in the circuit model. Fault tolerance constrains the choice of available gates, so that arbitrary gates required for a simulation algorithm must be constructed from sequences of fundamental operations. We examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm [C.M. Dawson and M.A. Nielsen, \emph{Quantum Inf. Comput.}, \textbf{6}:81, 2006]. For a given approximation error $\epsilon$, arbitrary single-qubit gates can be produced fault-tolerantly and using a limited set of gates in time which is $O(\log \epsilon)$ or $O(\log \log \epsilon)$; with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for Lithium hydride.Comment: 33 pages, 18 figure

Design, Verification, Test and In-Field Implications of Approximate Computing Systems

Today, the concept of approximation in computing is becoming more and more a “hot topic” to investigate how computing systems can be more energy efficient, faster, and less complex. Intuitively, instead of performing exact computations and, consequently, requiring a high amount of resources, Approximate Computing aims at selectively relaxing the specifications, trading accuracy off for efficiency. While Approximate Computing gives several promises when looking at systems’ performance, energy efficiency and complexity, it poses significant challenges regarding the design, the verification, the test and the in-field reliability of Approximate Computing systems. This tutorial paper covers these aspects leveraging the experience of the authors in the field to present state-of-the-art solutions to apply during the different development phases of an Approximate Computing system

Stochastic Theater: Stochastic Datapath Generation Framework for Fault-Tolerant IoT Sensors

Stochastic Computing has emerged as a competitive computing paradigm that produces fast and simple implementations of arithmetic operations, while offering high levels of parallelism, and graceful degradation of the results when in the presence of errors. IoT devices are often operate under limited power and area constraints and subjected to harsh environments, for which, traditional computing paradigms struggle to provide high availability and fault-tolerance. Stochastic Computing is based on the computation of pseudo-random sequences of bits, hence requiring only a single bit per signal, rather than a data-bus. Notwithstanding, we haven’t witnessed its inclusion in custom computing systems. In this direction, this work presents Stochastic Theater, a framework to specify, simulate, and test Stochastic Datapaths to perform computations using stochastic bitstreams targeting IoT systems. In virtue of the granularity of the bitstreams, the bit-level specification of circuits, high-performance characteristics and reconfigurable capabilities, FPGAs were adopted to implement and test such systems. The proposed framework creates Stochastic Machines from a set of user defined arithmetic expressions, and then tests them with the corresponding input values and specific fault injection patterns. Besides the support to create autonomous Stochastic Computing systems, the presented framework also provides generation of stochastic units, being able to produce estimates on performance, resources and power. A demonstration is presented targeting KLT, typical method for data compression in IoT applications