8 research outputs found
Modular quantum signal processing in many variables
Despite significant advances in quantum algorithms, quantum programs in
practice are often expressed at the circuit level, forgoing helpful structural
abstractions common to their classical counterparts. Consequently, as many
quantum algorithms have been unified with the advent of quantum signal
processing (QSP) and quantum singular value transformation (QSVT), an
opportunity has appeared to cast these algorithms as modules that can be
combined to constitute complex programs. Complicating this, however, is that
while QSP/QSVT are often described by the polynomial transforms they apply to
the singular values of large linear operators, and the algebraic manipulation
of polynomials is simple, the QSP/QSVT protocols realizing analogous
manipulations of their embedded polynomials are non-obvious. Here we provide a
theory of modular multi-input-output QSP-based superoperators, the basic unit
of which we call a gadget, and show they can be snapped together with LEGO-like
ease at the level of the functions they apply. To demonstrate this ease, we
also provide a Python package for assembling gadgets and compiling them to
circuits. Viewed alternately, gadgets both enable the efficient block encoding
of large families of useful multivariable functions, and substantiate a
functional-programming approach to quantum algorithm design in recasting QSP
and QSVT as monadic types.Comment: 15 pages + 9 figures + 4 tables + 45 pages supplement. For codebase,
see https://github.com/ichuang/pyqsp/tree/bet
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
Tools and Algorithms for the Construction and Analysis of Systems
This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers
Deductive Verification of Concurrent Programs and its Application to Secure Information Flow for Java
Formal verification of concurrent programs still poses a major challenge in computer science. Our approach is an adaptation of the modular rely/guarantee methodology in dynamic logic. Besides functional properties, we investigate language-based security. Our verification approach extends naturally to multi-threaded Java and we present an implementation in the KeY verification system. We propose natural extensions to JML regarding both confidentiality properties and multi-threaded programs