## A lambda calculus for quantum computation with classical control (2005)

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Venue: | IN PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON TYPED LAMBDA CALCULI AND APPLICATIONS (TLCA), VOLUME 3461 OF LECTURE NOTES IN COMPUTER SCIENCE |

Citations: | 47 - 6 self |

### BibTeX

@INPROCEEDINGS{Selinger05alambda,

author = {Peter Selinger and Benoît Valiron},

title = {A lambda calculus for quantum computation with classical control},

booktitle = {IN PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON TYPED LAMBDA CALCULI AND APPLICATIONS (TLCA), VOLUME 3461 OF LECTURE NOTES IN COMPUTER SCIENCE},

year = {2005},

pages = {354--368},

publisher = {Springer}

}

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### Abstract

### Citations

1485 |
Quantum Computation and Quantum Information
- Nielsen, Chuang
- 2000
(Show Context)
Citation Context ...ory of computation based on the laws of quantum physics, rather than of classical physics. Quantum computing has become a fast growing research area in recent years. For a good introduction, see e.g. =-=[9,10]-=-. Due to the laws of quantum physics, there are only two kinds of basic operations that one can perform on a quantum state, namely unitary transformations and measurements. Many existing formalisms fo... |

856 | Algorithms for Quantum Computation: Discrete Log and Factoring - Shor - 1994 |

695 | Quantum Theory, the Church–Turing Principle and the Universal Quantum Computer
- Deutsch
- 1985
(Show Context)
Citation Context ...nd outside of the formalism. In these models, a quantum computer is considered as a purely quantum system, i.e., without any classical parts. One example of such a model is the quantum Turing machine =-=[3,6]-=-, where the entire machine state, including the tape, the finite control, and the position of the head, is assumed to be in quantum superposition. Another example is the quantum lambda calculus of van... |

294 |
The Lambda Calculus: Its Syntax and Semantics, volume 103
- Barendregt
- 1984
(Show Context)
Citation Context ... will be |i〉 ⊗ |ψi〉. 3 The untyped quantum lambda calculus 3.1 Terms Our language uses the notation of the intuitionistic lambda calculus. For a detailed introduction to the lambda calculus, see e.g. =-=[2]-=-. We start from a standard lambda calculus with booleans and finite products. We extend this language with three special quantum operations, which are new, meas, and built-in unitary gates. new maps a... |

125 |
The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines
- Benioff
- 1980
(Show Context)
Citation Context ...nd outside of the formalism. In these models, a quantum computer is considered as a purely quantum system, i.e., without any classical parts. One example of such a model is the quantum Turing machine =-=[3,6]-=-, where the entire machine state, including the tape, the finite control, and the position of the head, is assumed to be in quantum superposition. Another example is the quantum lambda calculus of van... |

112 | Towards a quantum programming language
- Selinger
- 2003
(Show Context)
Citation Context ...s. In such a model, the control structures of the machine are classical, and only the data being operated upon is quantum. This situation is summarized by the slogan “quantum data, classical control” =-=[12]-=-. Several programming languages have been proposed to deal with such a model [4,11]. The present paper is based on the work of [12].s2 P. Selinger, B. Valiron In this paper, we propose a higher-order ... |

63 | Non-deterministic quantum programming
- Zuliani
- 2004
(Show Context)
Citation Context ... the data being operated upon is quantum. This situation is summarized by the slogan “quantum data, classical control” [12]. Several programming languages have been proposed to deal with such a model =-=[4,11]-=-. The present paper is based on the work of [12].s2 P. Selinger, B. Valiron In this paper, we propose a higher-order quantum programming language, i.e., one in which functions can be considered as dat... |

53 | A lambda calculus for quantum computation
- Tonder
- 2004
(Show Context)
Citation Context ...the entire machine state, including the tape, the finite control, and the position of the head, is assumed to be in quantum superposition. Another example is the quantum lambda calculus of van Tonder =-=[14,15]-=-, which is a higher-order, purely quantum language without an explicit measurement operation. On the other hand, one might imagine a model of a quantum computer where unitary operations and measuremen... |

48 | Conventions for quantum pseudocode
- Knill
- 1996
(Show Context)
Citation Context ...easurement operation. On the other hand, one might imagine a model of a quantum computer where unitary operations and measurements can be interleaved. One example is the so-called QRAM model of Knill =-=[8]-=-, which is also described by Bettelli, Calarco and Serafini [4]. Here, a quantum computer consists of a classical computer connected to a quantum device. In this configuration, the operation of the ma... |

44 | Toward an architecture for quantum programming
- Bettelli, Calarco, et al.
- 2003
(Show Context)
Citation Context ...del of a quantum computer where unitary operations and measurements can be interleaved. One example is the so-called QRAM model of Knill [8], which is also described by Bettelli, Calarco and Serafini =-=[4]-=-. Here, a quantum computer consists of a classical computer connected to a quantum device. In this configuration, the operation of the machine is controlled by a classical program which emits a sequen... |

28 | Quantum computation, categorical semantics and linear logic. arXiv:quant-ph/0312174
- Tonder
- 2003
(Show Context)
Citation Context ...the entire machine state, including the tape, the finite control, and the position of the head, is assumed to be in quantum superposition. Another example is the quantum lambda calculus of van Tonder =-=[14,15]-=-, which is a higher-order, purely quantum language without an explicit measurement operation. On the other hand, one might imagine a model of a quantum computer where unitary operations and measuremen... |

13 | On the linear decoration of intuitionistic derivations
- Danos, Joinet, et al.
- 1995
(Show Context)
Citation Context ... absence of the principal type property, we need to design a type inference algorithm based on a different idea. The approach we follow is the one suggested by V. Danos, J.-B. Joinet and H. Schellinx =-=[5]-=-. The basic idea is to view a linear type as a “decoration” of an intuitionistic type. Our type inference algorithm is based on the following technical fact, given below: if a given term has an intuit... |

7 |
2004a) A functional programming language for quantum computation with classical control
- Valiron
(Show Context)
Citation Context ...id can be reduced to the question of finding an intuitionistic type for it and to explore a finite number of linear decorations for the type. This work is based on the second author’s Master’s thesis =-=[13]-=-. 2 Quantum computing basics We briefly recall the basic definitions of quantum computing; please see [9,10] for a complete introduction to the subject. The basic unit of information in quantum comput... |

4 |
A functional quantum programming language. Available at http://arXiv.org/abs/ quant-ph/0409065
- Altenkirch, Grattage
- 2004
(Show Context)
Citation Context ...ion system. Definition 2. A probabilistic reduction system is a tuple (X, U, R,prob) where X is a set of states, U ⊆ X is a subset of value states, R ⊆ (X \U)×X is a set of reductions, and prob : R → =-=[0, 1]-=- is a probability function, where [0, 1] is the real unit interval. Moreover, we impose the following conditions: – For any x ∈ X, Rx = { x ′ | (x, x ′ ) ∈ R } is finite. – � x ′ ∈Rx prob(x, x′ ) � 1 ... |

3 |
Lecture notes for Physics 229, quantum computation. Available from http://www.theory.caltech.edu/people/preskill/ph229/#lecture
- Preskill
- 1999
(Show Context)
Citation Context ...ory of computation based on the laws of quantum physics, rather than of classical physics. Quantum computing has become a fast growing research area in recent years. For a good introduction, see e.g. =-=[9,10]-=-. Due to the laws of quantum physics, there are only two kinds of basic operations that one can perform on a quantum state, namely unitary transformations and measurements. Many existing formalisms fo... |

1 | 10〉), let 〈p, p ′ 〉 = CNOT 〈p1, p0〉 in 〈 meas(Hp), meas p - Altenkirch, Grattage - 2004 |