Quantum Hoare Logic with Ghost Variables

Unruh, Dominique

doi:10.1109/lics.2019.8785779

Cited by 28 publications

(34 citation statements)

References 26 publications

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“…This work has been promoted [25] and many variants have been proposed [30,52,57,58]. Besides, a quantum Hoare logic with ghost variables is introduced in [45] which is useful for dealing with mixed states/distributions. Practical tools have also been developed in recent years, including [18,35] in Isabelle/HOL, [27,28,39] in Coq; all of them are based on matrix representation and calculations.…”

Section: Related Workmentioning

confidence: 99%

EasyPQC: Verifying Post-Quantum Cryptography

Barbosa

Barthe

Fan³

et al. 2021

Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security

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EasyCrypt is a formal verification tool used extensively for formalizing concrete security proofs of cryptographic constructions. However, the EasyCrypt formal logics consider only classical attackers, which means that post-quantum security proofs cannot be formalized and machine-checked with this tool. In this paper we prove that a natural extension of the EasyCrypt core logics permits capturing a wide class of post-quantum cryptography proofs, settling a question raised by (Unruh, POPL 2019). Leveraging our positive result, we implement EasyPQC, an extension of EasyCrypt for post-quantum security proofs, and use EasyPQC to verify postquantum security of three classic constructions: PRF-based MAC, Full Domain Hash and GPV08 identity-based encryption.

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Section: Related Workmentioning

confidence: 99%

EasyPQC: Verifying Post-Quantum Cryptography

Barbosa

Barthe

Fan³

et al. 2021

Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security

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“…The mapping of quantum algorithms to quantum computers that respect the topological constraints imposed by specific quantum computers has also been investigated using automated reasoning methods [3], [4]. Formal methods and other logicbased symbolic reasoning systems have been used to reason about the correctness of quantum programs and quantum computing systems [5]- [7].…”

Section: Related Work a Quantum Computation And Reasoningmentioning

confidence: 99%

Automated Synthesis of Quantum Circuits Using Symbolic Abstractions and Decision Procedures

Velasquez

Jha

Ewetz

et al. 2021

2021 IEEE International Symposium on Circuits and Systems (ISCAS)

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Quantum algorithms are notoriously hard to design and require significant human ingenuity and insight. We present a new methodology called Quantum Automated Synthesizer (QUASH) that can automatically synthesize quantum circuits using decision procedures that perform symbolic reasoning for combinatorial search. Our automated synthesis approach constructs finite symbolic abstract models of the quantum gates automatically and discovers a quantum circuit as a composition of quantum gates using these symbolic models. Our key insight is that most current quantum algorithms work on a finite number of classical inputs, and hence, their correctness proof relies only on reasoning about a finite set of quantum states that can be represented using finite symbolic systems. We demonstrate the potential of our approach by automatically synthesizing four quantum circuits and re-discovering the Bernstein-Vazirani quantum algorithm using state-of-the-art decision procedures. Our synthesis approach only requires distinguishing between a finite set of symbolic quantum states; for example, the synthesis of the Bernstein-Vazirani quantum algorithm only requires reasoning about the following qubit states: |0 , |1 , −i|0 , i|1 , |+ , |− , e iπ/2 |1 , e iπ/4 |1 and a remaining symbolic state representing all other possible quantum states. Our approach leverages decision procedures and theorem provers to assist in the discovery of new quantum algorithms and is a step towards the automation of quantum algorithm design.

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“…Since the main focus is to show the use of quantum variables (and constructions based upon these), the language we analyze will not contain any features that are orthogonal to the question of variables such as loops. The ideas described can be easily extended to other Hoare logics that use subspaces as pre-/postconditions (i.e., von-Neumann-Birkhoff quantum logic [7]; used, e.g., in [34,39,33,18]). (And Hoare logics that use operators as pre-/postconditions [14,15,37,19,5] should be even easier to adapt because registers naturally translate operators from variables to overall program states.)…”

Section: Quantum Hoare Logicmentioning

confidence: 99%

Quantum and classical registers

Unruh¹

2021

Preprint

Self Cite

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We present a generic theory of "registers" in imperative programs and instantiate it in the classical and quantum setting. Roughly speaking, a register is some mutable part of the program state, e.g., mutable classical variables and quantum registers and wires in quantum circuits are examples of this. However, registers in our setting can also refer to subparts of other registers, or combinations of parts from different registers, or quantum registers seen in a different basis, etc. Our formalization is intended to be well suited for formalization in theorem provers and as a foundation for modeling quantum/classical variables in imperative programs.We implemented most results (including a minimal quantum Hoare logic and an analysis of quantum teleportation) in the Isabelle/HOL theorem prover.

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Quantum Hoare Logic with Ghost Variables

Cited by 28 publications

References 26 publications

EasyPQC: Verifying Post-Quantum Cryptography

EasyPQC: Verifying Post-Quantum Cryptography

Automated Synthesis of Quantum Circuits Using Symbolic Abstractions and Decision Procedures

Quantum and classical registers

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