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.

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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.

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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.

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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」

Dedication. List of Figures. List of Tables. Preface. Part I Background and Prior Art. 1. INTRODUCTION. 1.1 Design Trends and Challenges. 1.2 State of the Art. 1.3 Our Approach. 1.4 Key Innovations and Book Outline. 2. CURRENT LANDSCAPE IN DESIGN AND VERIFICATION. 2.1 Front-End Design. 2.2 Back-End Logic Design. 2.3 Back-End Physical Design. 2.4 Post-Silicon Debugging. 3. FINDING BUGS AND REPAIRING CIRCUITS. 3.1 Simulation-Based Verification. 3.2 Formal Verification. 3.3 Design for Debugging and Post-Silicon Metal Fix. Part II FogClearMethodologies and Theoretical Advances in Error Repair. 4. CIRCUIT DESIGN AND VERIFICATION METHODOLOGIES. 4.1 Front-End Design. 4.2 Back-End Logic Design. 4.3 Back-End Physical Design. 4.4 Post-Silicon Debugging. 5. COUNTEREXAMPLE-GUIDED ERROR-REPAIR FRAMEWORK. 5.1 Background. 5.2 Error-Correction Framework for Combinational Circuits. 6. SIGNATURE-BASED RESYNTHESIS TECHNIQUES. 6.1 Pairs of Bits to be Distinguished (PBDs). 6.2 Resynthesis Using Distinguishing-Power Search. 6.3 Resynthesis Using Goal-Directed Search. 7. SYMMETRY-BASED REWIRING. 7.1 Background. 7.2 Exhaustive Search for Functional Symmetries. 7.3 Post-Placement Rewiring. 7.4 Experimental Results. 7.5 Summary. Part III FogClear Components. 8. BUG TRACE MINIMIZATION. 8.1 Background and PreviousWork. 8.2 Analysis of Bug Traces. 8.3 Proposed Techniques. 8.4 Implementation Insights. 8.5 Experimental Results. 8.6 Summary. 9. FUNCTIONAL ERROR DIAGNOSIS AND CORRECTION. 9.1 Gate-Level Error Repair for Sequential Circuits. 9.2 Register-Transfer-Level Error Repair. 9.3 Experimental Results. 9.4 Summary. 10. INCREMENTAL VERIFICATION FOR PHYSICAL SYNTHESIS. 10.1 Background. 10.2 Incremental Verification. 10.3 Experimental Results. 10.4 Summary. 11. POST-SILICON DEBUGGING AND LAYOUT REPAIR. 11.1 Physical Safeness and Logical Soundness. 11.2 New ResynthesisTechnique-SafeResynth. 11.3 Physically-Aware Functional Error Repair. 11.4 Automating Electrical Error Repair. 11.5 Experimental Results. 11.6 Summary. 12. METHODOLOGIES FOR SPARE-CELL INSERTION. 12.1 Existing Spare-Cell Insertion Methods. 12.2 Cell Type Analysis. 12.3 Placement Analysis. 12.4 Our Methodology. 12.5 Experimental Results. 12.6 Summary. 13. CONCLUSIONS. Index. References.

Functional Design Errors in Digital Circuits: Diagnosis Correction and Repair

Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant input-output line-pairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting distributions of circuit sizes. We study circuit decompositions of reversible circuits where gates of the same type are next to each other. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover's search algorithm, and show a significant improvement over a previously proposed synthesis algorithm.

Reversible Logic Circuit Synthesis

Methods and apparatuses for approximate functional matching are described including identifying functionally similar subsets of an integrated circuit design or software program, distinguishing control inputs of the subsets from data inputs, and assigning combinations of logic values to the input control signals to capture co-factors for functional matching.

Approximate Functional Matching in Electronic Systems

The balanced partitioning problem divides the nodes of a [hyper]graph into groups ofapproximately equal weight (i.e., satisfying balance constraints) while minimizing thenumber of [hyper]edges that are cut (i.e., adjacent to nodes in different groups). Classiciterative algorithms use the pass paradigm [24] in performing single-node moves [16, 13]to improve the initial solution. To satisfy particular balance constraints, it is usual torequire that intermediate solutions satisfy the constraints. Hence, many possible movesare rejected.

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Iterative Partitioning with Varying Node Weights

Integrated circuits and electronic systems, as well as design technologies, are evolving at a great rate -- both quantitatively and qualitatively. Major developments include new interconnects and switching devices with atomic-scale uncertainty, the depth and scale of on-chip integration, electronic system-level integration, the increasing significance of software, as well as more effective means of design entry, compilation, algorithmic optimization, numerical simulation, pre- and post-silicon design validation, and chip test. Application targets and key markets are also shifting substantially from desktop CPUs to mobile platforms to an Internet-of-Things infrastructure. In light of these changes in electronic design contexts and given EDA's significant dependence on such context, the EDA community must adapt to these changes and focus on the opportunities for research and commercial success. The CCC workshop series on Extreme-Scale Design Automation, organized with the support of ACM SIGDA, studied challenges faced by the EDA community as well as new and exciting opportunities currently available. This document represents a summary of the findings from these meetings.

Igor L. Markov

Papers

Functional Design Errors in Digital Circuits: Diagnosis Correction and Repair

Reversible Logic Circuit Synthesis

Approximate Functional Matching in Electronic Systems

Iterative Partitioning with Varying Node Weights

Workshops on Extreme Scale Design Automation (ESDA) Challenges and Opportunities for 2025 and Beyond