There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at this https URL. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.

/pdf/supplementary-information-for-quantum-supremacy-using-a-3tkhfafpzk.pdf

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

In this article, we present a small, complete, and efficient SAT-solver in the style of conflict-driven learning, as exemplified by Chaff. We aim to give sufficient details about implementation to enable the reader to construct his or her own solver in a very short time.This will allow users of SAT-solvers to make domain specific extensions or adaptions of current state-of-the-art SAT-techniques, to meet the needs of a particular application area. The presented solver is designed with this in mind, and includes among other things a mechanism for adding arbitrary boolean constraints. It also supports solving a series of related SAT-problems efficiently by an incremental SAT-interface.

/pdf/an-extensible-sat-solver-4r6o94uank.pdf

An Extensible SAT-solver

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

/pdf/quantum-supremacy-using-a-programmable-superconducting-5182kq634u.pdf

Quantum supremacy using a programmable superconducting processor

The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

to more compact problem encodings and faster probIemsolving. Work on PB constraints has been extended to With impressive progress in Boolean Satisfiability (SAT) Boolean optimization through 0-1 Integer Linear Programsolving and several extensions to pseudo-Boolean (PB) con- ming (ILP). This may be attractive in formal verification straints, many applications that use SAT, such as highdebugging. For example, for a circuit containing a binary to checking? sarisjiability of certain conditions. However, counter, it may be useful to find counter-examples or bugs at there is also frequently a need to express a preference for the smallest value of the counter (since it presumably takes certain solutions. Extending SAT-solving to Boolean opti- fewer cycles to reach such a state). We can design an objecmization aIlows the use of objective functions to describe a tive function that encourages counter-examples with smaller desirable solution. Although recent work in 0- I Integer Lin- integers in the binary counter, with weights in the objective ear Programming (ILP) offers extensions that can optimize a function reflecting preferences for certain bits ~ the lower the linear objective function, this is often achieved by solving a series of SAT or ILP decision problems. Our work articulates weights, the lower the preference. Thus, by assigning negative coefficients to all bits in the counter value, we can bias some pitfalls of this approach. An objective function may the search toward smaller values of the counter. Such an obcomplicate the use of any symmetry that might be present in jective function, arithmetic-min, behaves in much the same the given constraints, even when the constraints are unsatisfi- way as the MinLex SBPs discussed in the Appendix. able and the objective function is irrelevant. We propok sevperformance formal verification techniques still restricted because Some counter-examples are much more for

Dynamic S ymmetry-Breaking €or Improved Boolean Optimization

Checking Equivalence of States and Circuits

Many groups in academia and industry are now extending their tools to handle super-sized designs. In addition to scalable algorithms, this requires software infrastructure and development policies to ensure and verify the robustness and scalability of implementations. Specific issues include programming for and executing programs in 32-bit and 64-bit memory models, modular tool infrastructure, diagnostic visualization of super-sized designs, and the use of simulation clusters for thorough evaluation of CAD tools.

CAD Tool Development for Multi-Million Gate Designs

Testing circuit vulnerability to probabilistic faults, like single-event upsets (SEUs), requires a reformulation of test-generation methods. Unlike in traditional testing, a probabilistic fault can be detected by different test vectors with different probabilities, i.e., they have different sensitivities to probabilistic faults. We develop an efficient PTM-based algorithm to compute test-vector sensitivity. We also propose several test generation and compaction methods for probabilistic faults, with the goals of estimating and bounding fault detection probabilities. These methods use integer linear programming (ILP) to optimize test sets. The results show that our methods can generate tests quickly and require only half as many (repeated) vectors as testing with random patterns.

Testing Logic Circuits for Probabilistic Faults

Today, Machine Learning (ML) applications can have access to tens of thousands of features. With such feature sets, efficiently browsing and curating subsets of most relevant features is a challenge. In this paper, we present a novel approach to visualize up to several thousands of features in a single image. The image not only shows information on individual features, but also expresses feature interactions via the relative positioning of features.

Igor L. Markov

Papers

Dynamic S ymmetry-Breaking €or Improved Boolean Optimization

Checking Equivalence of States and Circuits

CAD Tool Development for Multi-Million Gate Designs

Testing Logic Circuits for Probabilistic Faults

Picasso: Model-free Feature Visualization.