QTM: computational package using MPI protocol for quantum trajectories method

The Quantum Trajectories Method (QTM) is one of {the} frequently used methods for studying open quantum systems. { The main idea of this method is {the} evolution of wave functions which {describe the system (as functions of time). Then,} so-called quantum jumps are applied at {a} randomly selected point in time. {The} obtained system state is called as a trajectory. After averaging many single trajectories{,} we obtain the approximation of the behavior of {a} quantum system.} {This fact also allows} us to use parallel computation methods. In the article{,} we discuss the QTM package which is supported by the MPI technology. Using MPI allowed {utilizing} the parallel computing for calculating the trajectories and averaging them -- as the effect of these actions{,} the time {taken by} calculations is shorter. In spite of using the C++ programming language, the presented solution is easy to utilize and does not need any advanced programming techniques. At the same time{,} it offers a higher performance than other packages realizing the QTM. It is especially important in the case of harder computational tasks{,} and the use of MPI allows {improving the} performance of particular problems which can be solved in the field of open quantum systems.Comment: 28 pages, 9 figure

Why Philosophers Should Care About Computational Complexity

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and beyond," MIT Press, 2012. Some minor clarifications and corrections; new references adde

Quantum Pseudorandom Scramblers

Quantum pseudorandom state generators (PRSGs) have stimulated exciting developments in recent years. A PRSG, on a fixed initial (e.g., all-zero) state, produces an output state that is computationally indistinguishable from a Haar random state. However, pseudorandomness of the output state is not guaranteed on other initial states. In fact, known PRSG constructions provably fail on some initial state. In this work, we propose and construct quantum Pseudorandom State Scramblers (PRSSs), which can produce a pseudorandom state on an arbitrary initial state. In the information-theoretical setting, we obtain a scrambler which maps an arbitrary initial state to a distribution of quantum states that is close to Haar random in total variation distance. As a result, our PRSS exhibits a dispersing property. Loosely, it can span an $\epsilon$-net of the state space. This significantly strengthens what standard PRSGs can induce, as they may only concentrate on a small region of the state space as long as the average output state approximates a Haar random state in total variation distance. Our PRSS construction develops a parallel extension of the famous Kac's walk, and we show that it mixes exponentially faster than the standard Kac's walk. This constitutes the core of our proof. We also describe a few applications of PRSSs. While our PRSS construction assumes a post-quantum one-way function, PRSSs are potentially a weaker primitive and can be separated from one-way functions in a relativized world similar to standard PRSGs

Integrated GHz silicon photonic interconnect with micrometer-scale modulators and detectors

We report an optical link on silicon using micrometer-scale ring-resonator enhanced silicon modulators and waveguide-integrated germanium photodetectors. We show 3 Gbps operation of the link with 0.5 V modulator voltage swing and 1.0 V detector bias. The total energy consumption for such a link is estimated to be ~120 fJ/bit. Such compact and low power monolithic link is an essential step towards large-scale on-chip optical interconnects for future microprocessors

GASPRNG: GPU accelerated scalable parallel random number generator library

AbstractGraphics processors represent a promising technology for accelerating computational science applications. Many computational science applications require fast and scalable random number generation with good statistical properties, so they use the Scalable Parallel Random Number Generators library (SPRNG). We present the GPU Accelerated SPRNG library (GASPRNG) to accelerate SPRNG in GPU-based high performance computing systems. GASPRNG includes code for a host CPU and CUDA code for execution on NVIDIA graphics processing units (GPUs) along with a programming interface to support various usage models for pseudorandom numbers and computational science applications executing on the CPU, GPU, or both. This paper describes the implementation approach used to produce high performance and also describes how to use the programming interface. The programming interface allows a user to be able to use GASPRNG the same way as SPRNG on traditional serial or parallel computers as well as to develop tightly coupled programs executing primarily on the GPU. We also describe how to install GASPRNG and use it. To help illustrate linking with GASPRNG, various demonstration codes are included for the different usage models. GASPRNG on a single GPU shows up to 280x speedup over SPRNG on a single CPU core and is able to scale for larger systems in the same manner as SPRNG. Because GASPRNG generates identical streams of pseudorandom numbers as SPRNG, users can be confident about the quality of GASPRNG for scalable computational science applications.Program summaryProgram title: GASPRNGCatalogue identifier: AEOI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: UTK license.No. of lines in distributed program, including test data, etc.: 167900No. of bytes in distributed program, including test data, etc.: 1422058Distribution format: tar.gzProgramming language: C and CUDA.Computer: Any PC or workstation with NVIDIA GPU (Tested on Fermi GTX480, Tesla C1060, Tesla M2070).Operating system: Linux with CUDA version 4.0 or later. Should also run on MacOS, Windows, or UNIX.Has the code been vectorized or parallelized?: Yes. Parallelized using MPI directives.RAM: 512 MB∼ 732 MB (main memory on host CPU, depending on the data type of random numbers.) / 512 MB (GPU global memory)Classification: 4.13, 6.5.Nature of problem:Many computational science applications are able to consume large numbers of random numbers. For example, Monte Carlo simulations are able to consume limitless random numbers for the computation as long as resources for the computing are supported. Moreover, parallel computational science applications require independent streams of random numbers to attain statistically significant results. The SPRNG library provides this capability, but at a significant computational cost. The GASPRNG library presented here accelerates the generators of independent streams of random numbers using graphical processing units (GPUs).Solution method:Multiple copies of random number generators in GPUs allow a computational science application to consume large numbers of random numbers from independent, parallel streams. GASPRNG is a random number generators library to allow a computational science application to employ multiple copies of random number generators to boost performance. Users can interface GASPRNG with software code executing on microprocessors and/or GPUs.Running time:The tests provided take a few minutes to run

Scalable probes of measurement-induced criticality

We uncover a local order parameter for measurement-induced phase transitions: the average entropy of a single reference qubit initially entangled with the system. Using this order parameter, we identify scalable probes of measurement-induced criticality (MIC) that are immediately applicable to advanced quantum computing platforms. We test our proposal on a 1+1 dimensional stabilizer circuit model that can be classically simulated in polynomial time. We introduce the concept of a "decoding light cone" to establish the local and efficiently measurable nature of this probe. We also estimate bulk and surface critical exponents for the transition. Developing scalable probes of MIC in more general models may be a useful application of noisy-intermediate scale quantum (NISQ) devices, as well as point to more efficient realizations of fault-tolerant quantum computation.Comment: 6 pages, 3 figures, v2 added Figure 2 and supplemen