# The lambda-q calculus can efficiently simulate quantum computers

@article{Maymin1997TheLC, title={The lambda-q calculus can efficiently simulate quantum computers}, author={Philip Z. Maymin}, journal={arXiv: Quantum Physics}, year={1997} }

We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We conclude by noting that the lambda-q calculus may be strictly stronger than quantum computers because NP-complete problems such as satisfiability are efficiently solvable in the lambda-q calculus but there is a widespread doubt that they are efficiently solvable…

## 22 Citations

Quantum Lambda Calculi with Classical Control: Syntax and Expressive Power

- Computer ScienceArXiv
- 2007

This work proves subject reduction, confluence and a standardization theorem, and proves the computational equivalence of the proposed calculus with a suitable class of quantum circuit families.

Programming complex systems

- Computer Science
- 1997

This paper proves that the lambda-q calculus is not only capable of solving satisfiability but can also simulate such complex systems as quantum computers.

On a measurement-free quantum lambda calculus with classical control

- MathematicsMathematical Structures in Computer Science
- 2009

A measurement-free, untyped λ-calculus with quantum data and classical control with operational and expressiveness issues, rather than (denotational) semantics is studied, and subject reduction and confluence, and a standardisation theorem are proved.

On quantum lambda calculi: a foundational perspective

- Computer ScienceMathematical Structures in Computer Science
- 2014

The ‘quantum data-classical control’ paradigm is considered, and a calculus which captures the three classes of quantum polytime complexity is proposed, showing an ICC-like approach in the quantum setting.

QPCF: Higher-Order Languages and Quantum Circuits

- Computer ScienceJournal of Automated Reasoning
- 2019

qPCF is a paradigmatic quantum programming language that extends PCF with quantum circuits and a quantum co-processor, and introduces qPCF syntax, typing rules, and its operational semantics.

NP in BQP by Partial Measurement

- Computer Science
- 1998

By allowing measurement (read-out) of some, but not all, qubits, this paper shows that NP-complete problems are efficiently solvable by quantum computers in polynomial time with bounded probability…

Quantum programming languages: survey and bibliography

- Computer ScienceMathematical Structures in Computer Science
- 2006

The study of quantum Programming languages is justified, the basics of quantum computing are presented, the literature in quantum programming languages is surveyed, and directions for future research are indicated.

Q#, a quantum computation package for the .NET platform

- Computer ScienceArXiv
- 2013

This simulator for quantum algorithms takes the form of a package or a programming library for Quantum computing, with a case study showing the ability of using it in the circuit model.

A Survey of Quantum Programming Languages: History, Methods, and Tools

- Computer ScienceSecond International Conference on Quantum, Nano and Micro Technologies (ICQNM 2008)
- 2008

An extensive but non-exhaustive look at work leading up to the current state-of-the-art in quantum computer programming, and an attempt to analyze the needed programming tools for quantum programmers to predict the direction in which the field is moving.

Quantum Programming Language: A Systematic Review of Research Topic and Top Cited Languages

- Computer Science
- 2019

This survey paper briefly gives an overview of state of the art in the field of quantum programming languages, their features and comparisons.

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