Confluence Results for a Quantum Lambda Calculus with Measurements

A strong confluence result for Q*, a quantum @l-calculus with measurements, is proved. More precisely, confluence is shown to hold both for finite and infinite computations. The technique used in the confluence proof is syntactical but innovative. This makes Q* different from similar quantum lambda calculi, which are either measurement-free or provided with a reduction strategy.

[1]  Gilles Dowek,et al.  Linear-algebraic lambda-calculus: higher-order, encodings, and confluence , 2008, RTA.

[2]  Benoît Valiron,et al.  A Lambda Calculus for Quantum Computation with Classical Control , 2005, TLCA.

[3]  Maribel Fernández The Lambda Calculus , 2009 .

[4]  Steven Roman Advanced Linear Algebra , 1992 .

[5]  Harumichi Nishimura,et al.  Computational complexity of uniform quantum circuit families and quantum Turing machines , 2002, Theor. Comput. Sci..

[6]  André van Tonder,et al.  A Lambda Calculus for Quantum Computation , 2003, SIAM J. Comput..

[7]  Harold T. Hodes,et al.  The | lambda-Calculus. , 1988 .

[8]  Terese Term rewriting systems , 2003, Cambridge tracts in theoretical computer science.

[9]  Umesh V. Vazirani,et al.  Quantum Complexity Theory , 1997, SIAM J. Comput..

[10]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[11]  Harumichi Nishimura,et al.  Perfect computational equivalence between quantum Turing machines and finitely generated uniform quantum circuit families , 2009, Quantum Inf. Process..

[12]  Manuel Gadella,et al.  Measurements and Confluence in Quantum Lambda Calculi With Explicit Qubits , 2011, Electron. Notes Theor. Comput. Sci..

[13]  Alex K. Simpson Reduction in a Linear Lambda-Calculus with Applications to Operational Semantics , 2005, RTA.

[14]  Ugo Dal Lago,et al.  On a measurement-free quantum lambda calculus with classical control , 2009, Math. Struct. Comput. Sci..

[15]  Raymond Laflamme,et al.  An Introduction to Quantum Computing , 2007, Quantum Inf. Comput..

[16]  Claude Kirchner,et al.  Probabilistic Rewrite Strategies. Applications to ELAN , 2002, RTA.

[17]  Peter Selinger,et al.  Towards a quantum programming language , 2004, Mathematical Structures in Computer Science.

[18]  Philip Wadler,et al.  A Syntax for Linear Logic , 1993, MFPS.

[19]  Chris Hankin,et al.  Probabilistic /lambda-calculus and Quantitative Program Analysis , 2005, J. Log. Comput..

[20]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[21]  Christopher Isham,et al.  Lectures On Quantum Theory: Mathematical And Structural Foundations , 1995 .