Hardness and Optimality in QBF Proof Systems Modulo NP

Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof

Impact ◽

10.21820/23987073.2019.10.30 ◽

2019 ◽

Vol 2019 (10) ◽

pp. 30-32

Author(s):

Tomoyuki Morimae

Keyword(s):

Quantum Computing ◽

Quantum Information ◽

Theoretical Physics ◽

View Point ◽

Research Subjects ◽

Interactive Proof ◽

Open Problems ◽

Main Research ◽

Proof Systems ◽

Information Group

In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

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Disjoint NP-Pairs and Propositional Proof Systems

ACM SIGACT News ◽

10.1145/2696081.2696095 ◽

2014 ◽

Vol 45 (4) ◽

pp. 59-75 ◽

Cited By ~ 1

Author(s):

C. Glaßer ◽

A. Hughes ◽

A. L. Selman ◽

N. Wisiol

Keyword(s):

Proof Systems ◽

Propositional Proof Systems ◽

Propositional Proof

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Complete proof systems for algebraic simply-typed terms

ACM SIGPLAN Lisp Pointers ◽

10.1145/182590.182482 ◽

1994 ◽

Vol VII (3) ◽

pp. 220-226

Author(s):

Stavros S. Cosmadakis

Keyword(s):

Complete Proof ◽

Proof Systems

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A taxonomy of proof systems (part 1)

ACM SIGACT News ◽

10.1145/164996.165000 ◽

1993 ◽

Vol 24 (4) ◽

pp. 2-13 ◽

Cited By ~ 1

Author(s):

Oded Goldreich

Keyword(s):

Proof Systems

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Computational and Proof Complexity of Partial String Avoidability

ACM Transactions on Computation Theory ◽

10.1145/3442365 ◽

2021 ◽

Vol 13 (1) ◽

pp. 1-25

Author(s):

Dmitry Itsykson ◽

Alexander Okhotin ◽

Vsevolod Oparin

Keyword(s):

Lower Bounds ◽

Circuit Complexity ◽

Conjunctive Normal Form ◽

Proof Complexity ◽

Proof Systems ◽

Finite Set ◽

Propositional Proof Systems ◽

Classical Proof ◽

Exponential Size ◽

Infinite String

The partial string avoidability problem is stated as follows: given a finite set of strings with possible “holes” (wildcard symbols), determine whether there exists a two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in PSPACE, and this article establishes its PSPACE-completeness. Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form satisfiability problem, where each clause has infinitely many shifted variants. Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting proof lines (such as clauses, inequalities, polynomials, etc.). First, it is proved that there is a particular formula that has a short refutation in Resolution with a shift rule but requires classical proofs of exponential size. At the same time, it is shown that exponential lower bounds for classical proof systems can be translated for their shifted versions. Finally, it is shown that superpolynomial lower bounds on the size of shifted proofs would separate NP from PSPACE; a connection to lower bounds on circuit complexity is also established.

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