Work in Progress: Response Time Analysis of Real-Time Quantum Computing Systems

In scheduling algorithms based on the Rate Monotonic (RM) method which are widely used in development of real-time systems, tasks with shorter periods have higher priorities. In contrast, ones with longer periods are likely to suffer from increased response times and jitter due to their lower priorities. We propose an Execution Right Delegation (ERD) method based on RM where a high-priority server for particular (or important) task is introduced to shorten response time and jitter of the task. In the evaluation, it is confirmed that response times and jitter of a particular (important) task are reduced. We also show Response Time Analysis (RTA), which assures worst-case response time of the task. This paper shows the algorithm and RTA of ERD and evaluates it by comparing it to a Deadline Monotonic method. The evaluation by simulation shows that ERD can reduce the average worst-case response time by 13.45% at maximum compared to the Deadline Monotonic scheduling. In addition, we confirm that the RTA provides a worst-case response time close to the simulation results.

In recent years, the complexity of real-time embedded systems has increased dramatically. For those modern real-time systems, the limitations of original static Response Time Analysis (RTA) become more and more conspicuous. Most static analysis methods not only require much detailed system information, but also only target to some specific system model with non-realistic assumptions. As a result, those methods may produce overly pessimistic results, making them unsuitable to be applied on a complex industrial system. The best system model may be the system itself. Therefore, statistical RTA, which can produce probabilistic analysis results based on samples provided by real systems or simulators, may become more expedient. Statistical RTA usually requires more relaxed assumptions and less system information than static RTA. In this paper, we present an Extreme Value Theory (EVT) based method to compute Worst-Case Response Time (WCRT) targeting complex real-time systems. In the evaluation phase, we have applied this method to the calculation of worst-case transmission delays of messages over Controller Area Network (CAN), and some comparisons with static RTA are also provided. According to the experimental results, as the system complexity increases, our approach performs much more stable and less pessimistic.

A number of methods have been proposed for the response-time analysis (RTA) of controller area networks (CANs), which are the industry standard for in-vehicle network protocols. However, most of these methods are unsuitable for analyzing nonperiodically transmitted messages because they assume a constant transmission period for each message. Moreover, the calculated evaluation criteria are limited and comprise many over-pessimistic estimations, such as the worst-case response time (WCRT). To tackle these problems, this paper proposes an RTA method for CANs with randomly occurring messages, which replaces the constant transmission period with the average number of transmission instances per unit time. This approach finds the approximate probability distribution of the response time to any message in a CAN, providing a more general measure than the WCRT. To this end, a mathematical model based on M/G/1 queueing theory is developed. The model accurately emulates the behavior of nonperiodic CAN messages and enables RTA with minimal pessimistic estimations. When tested against the benchmarks, the proposed method accurately obtained response time distributions within several seconds to several tens of seconds.

Feasibility interval for the transactional event handlers of P-FRP

Entanglement and decoherence are two intimately related phenomena that lie at the heart of quantum information. The EPR-Bell states are the most basic quantum systems, which form the complete entangled basis of the two-particle Hilbert space, and which are important in many quantum computation schemes. The bit flip, phase flip, and bit-phase flip noise channels represent all the possible errors in quantum computation. Thus, the quantum decoherence characteristic of maximally and partially Bell entangled states under different noisy channels is studied using the concurrence. Our work is useful for linear-optical quantum computation and quantum communication schemes whose building blocks are entangled state.

Functional reactive programming (FRP) is a declarative programming paradigm where the basic notions are continuous, time-varying behaviors and discrete, event-based reactivity. FRP has been used successfully in many reactive programming domains such as animation, robotics, and graphical user interfaces. The success of FRP in these domains encourages us to consider its use in real-time applications, where it is crucial that the cost of running a program be bounded and known before run-time. But previous work on the semantics and implementation of FRP was not explicitly concerned about the issues of cost. In fact, the resource consumption of FRP programs in the current implementation is often hard to predict. As a first step towards addressing these concerns, this paper presents real-time FRP (RT-FRP), a statically-typed language where the time and space cost of each execution step for a given program is statically bounded. To take advantage of existing work on languages with bounded resources, we split RT-FRP into two parts: a reactive part that captures the essential ingredients of FRP programs, and a base language part that can be instantiated to any generic programming language that has been shown to be terminating and resource-bounded. This allows us to focus on the issues specific to RT-FRP, namely, two forms of recursion. After presenting the operational explanation of what can go wrong due to the presence of recursion, we show how the typed version of the language is terminating and resource-bounded. Most of our FRP programs are expressible directly in RT. The rest are expressible via a simple mechanism that integrates RT-FRP with the base language.

Real-time systems usually consist of a set of periodic and sporadic tasks. Periodic tasks can be divided into two classes: synchronous and asynchronous. The first type does not define the task first release, contrary to the second. Hence, synchronous periodic tasks are assumed to be released at the worst instant: the critical instant. The schedulability test is reduced to check a single execution of the task under analysis. The integration of sporadic tasks is also straightforward: they are treated as a periodic task with maximum arrival frequency. On the other hand, asynchronous periodic tasks require a test for each release in the hyper period and the integration of sporadic tasks is not trivial: the worst release instant is unknown a priori. However, they do not assume that the tasks are released at the worst instant.This paper presents a new schedulability analysis method based on the Response Time Analysis (RTA) to determine the worst response time of both asynchronous periodic and sporadic tasks, scheduled by a fixed-priority preemptive algorithm with general deadlines. It also presents another method that enables the introduction of a user configurable degree of pessimism, reducing the hyper period dependency.

Local Friendliness (LF) inequalities follow from seemingly reasonable assumptions about reality: (i) ``absoluteness of observed events'' (e.g., every observed event happens for all observers) and (ii) ``local agency'' (e.g., free choices can be made uncorrelated with other events outside their future light cone). Extended Wigner's Friend Scenario (EWFS) thought experiments show that textbook quantum mechanics violates these inequalities. Thus, experimental evidence of these violations would make these two assumptions incompatible. In [Nature Physics 16, 1199 (2020)], the authors experimentally implemented an EWFS, using a photonic qubit to play the role of each of the ``friends'' and measured violations of LF. One may question whether a photonic qubit is a physical system that counts as an ``observer'' and thereby question whether the experiment's outcome is significant. Intending to measure increasingly meaningful violations, we propose using a statistical measure called the ``branch factor'' to quantify the ``observerness'' of the system. We then encode the EWFS as a quantum circuit such that the components of the circuit that define the friend are quantum systems of increasing branch factor. We run this circuit on quantum simulators and hardware devices, observing LF violations as the system sizes scale. As errors in quantum computers reduce the significance of the violations, better quantum computers can produce better violations. Our results extend the state of the art in proof-of-concept experimental violations from branch factor 0.0 to branch factor 16.0. This is an initial result in an experimental program for measuring LF violations at increasingly meaningful branch factors using increasingly more powerful quantum processors and networks. We introduce this program as a fundamental science application for near-term and developing quantum technology.

Quantum computers are susceptible to errors. While quantum computers can be guarded against errors using error correction codes, near-term quantum computers will not have sufficient number of qubits to implement error correction and must perform their computation in the presence of errors. Qubit measurement is typically the most error-prone operation on a quantum computer, with measurement errors ranging from 8% to 30% reported on current machines. This goal of this paper is to mitigate measurement errors by exploiting the state-dependent bias of measurement errors. Experiments on the IBM-Q5 and IBM-Q14 machines show variation in measurement errors depending on the state being measured. For example, measuring an all-zero state on IBM-Q5 has a fidelity of 84%; however, the fidelity drops to 62% while measuring the all-one state. To improve measurement fidelity, we propose Invert-and-Measure, which transforms the system from a vulnerable state to a stronger state and then performs the measurement in the stronger state. We propose two designs for Invert-and-Measure. First, Static Invert-and-Measure (SIM), which executes two instances of the program, one with standard measurements and the other with inverted measurements and combines the results. Second, Adaptive Invert and Measure (AIM), which learns the relative bias of different states using runtime profiling and produces specialized inversions to increase the likelihood of obtaining the correct answer. Our evaluations, using IBM-Q5 and IBM-Q14, show that SIM improves the application reliability by up to 2X, and AIM by up to 3X.

Online dispatching and parallel processing algorithms for saving money in systems with heterogeneous, single-buffered, speed-scalable processors

A generalization of the results of Rasetti and Zanardi concerning avoiding\nerrors in quantum computers by using states preserved by evolution is\npresented. The concept of dynamical symmetry is generalized from the level of\nclassical Lie algebras and groups to the level of dynamical symmetry based on\nquantum Lie algebras and quantum groups (in the sense of Woronowicz). A natural\nconnection is proved between states preserved by representations of a quantum\ngroup and states preserved by evolution with dynamical symmetry of the\nappropriate universal enveloping algebra. Illustrative examples are discussed.\n

Quantum Refrigerator Keeps Qubits CoolPhysicists have demonstrated a quantum machine that could reduce errors in quantum computers by ensuring that the qubits they use remain in their initial state before a calculation starts.

Quantum computers are growing at a rapid pace. Trends show that the current decade could be the one in which quantum computers deliver commercial value. Today's quantum computers are overwhelmed by errors. To unlock their massive potential, a significant reduction in errors is required. Several qubit technologies are under research, e.g. superconducting, neutral atoms, trapped ions, photons and silicon. For useful quantum computing on these qubit technologies, Quantum Error Correction (QEC) turns unreliable physical qubits into useful logical qubits. QEC requires solving a real-time, large data volume decoding problem that determines the effect of physical noise on the computation carried out on logical qubits. The nature of the decoding problem depends on the qubit technology, choice of QEC code and mode of quantum computation. These are actively researched subjects in the quantum computing world. Hardware-based decoders that use Field Programmable Gate Array (FPGA) or Application Specific Integrated Circuits (ASIC) technologies are the most promising solutions in terms of speed and scalability. However, the design methodology for these solutions typically suffers from long lead times and a lack of flexibility. We propose GridGenQ, a hardware design utility that automates part of the FPGA/ASIC design methodology for distributed QEC decoders. We show that with our novel solution, development time for such distributed hardware decoders can be reduced from several weeks to few minutes. This allows for fast prototyping of distributed decoder architectures to meet the requirements posed by a dynamic QEC landscape.

Traditional methods rely on Static Timing Analysis techniques to compute the Worst Case Response Time for tasks in real-time systems. Multi-Core real-time systems are faced up with concurrent task executions, semaphore accesses, and task migrations where it may be difficult to obtain the worst case upper bound. A new three staged probabilistic estimation concept is presented. Worst Case Response Times are estimated for tasksets which consist of tasks with multiple time bases. The concept involves data generation with sample classification and sample size equalization, model fit and Worst Case Response Time estimation on the basis of extreme value distribution models. A Generalized Pareto Distribution model fit method which includes threshold detection and parameter estimation is also presented. Sample classification in combination with the new Generalized Pareto Distribution model fit method allows to estimate Worst Case Response Times with low pessimism ranges compared to estimation methods that uses the Generalized Pareto or the Gumbel max distribution without sample classification.

In a real-time system with both hard deadline periodic tasks and soft deadline aperiodic tasks, hard deadline tasks must be guaranteed to meet their deadlines and soft deadline tasks are serviced in a best-effort manner. To schedule soft deadline aperiodic tasks in dynamic priority systems, one can assign a virtual deadline like the TBS algorithm or use capacity servers like the DPE algorithm. Both approaches have their own advantages, and we cannot say which one is better in terms of response time. In some cases, TBS provides shorter response time than DPE server. In other cases, the reverse may happen. In this paper, we propose a combined approach to improve the response time of soft deadline aperiodic tasks. The proposed method combines the deadline assignment and the capacity server approach. When there is enough capacity available for aperiodic tasks, the aperiodic tasks are served by capacity servers. Otherwise, our method assigns a deadline and schedule aperiodic task together with periodic tasks by EDF algorithm. In the worst case, the proposed method provides response time no later than TBS. Experimental results show that the proposed approach improves the responsiveness of soft deadline aperiodic tasks.