The measurement calculus

  title={The measurement calculus},
  author={Vincent Danos and Elham Kashefi and P. Panangaden},
  journal={J. ACM},
Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model that is based on unitary operations. Among measurement-based quantum computation methods, the recently introduced one-way quantum computer [Raussendorf and Briegel 2001] stands out as fundamental. We develop a rigorous mathematical model… 

Figures from this paper

Distributed Measurement-based Quantum Computation

Simulating the Measurement Calculus by Rewriting

This work proves an equivalence between the existence of a circuit-like reduct for a given pattern and the presence of flow in that pattern’s underlying geometry, which is a proof that the original pattern has flow in the sense of Danos and Kashefi.

The One Way to Quantum Computation

A rewrite theory is developed and a general standardization theorem is proved which allows all patterns to be put in a semantically equivalent standard form.

Distributed quantum programming

In this paper we explore the structure and applicability of the Distributed Measurement Calculus (DMC), an assembly language for distributed measurement-based quantum computations. We describe the

Towards a Quantum Calculus: (Work in Progress, Extended Abstract)

Measurement-based quantum computation

Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation

Measurement-Based Quantum Computation

  • T. Wei
  • Physics, Computer Science
    Oxford Research Encyclopedia of Physics
  • 2021
The measurement-based approach offers a potential alternative to the standard circuit approach to realize a practical quantum computer and provides useful connections to the emergence of time ordering, computational complexity and classical spin models, blind quantum computation, etc.

Types for quantum computing

Higher level tools for quantum mechanics will be better suited to computation than those presently employed in the field, and this work connects quantum mechanics to mainstream areas of computer science such as categorical logic, type theory, program language semantics, and rewriting.

5 Extended Measurement Calculus

This chapter is an investigation into the structure, scope and limits of quantum computation, and physicists have introduced novel ideas based on the use of measurement and entanglement to perform computation.

Optimization of One-Way Quantum Computation Measurement Patterns

A new scheme is proposed to perform the optimization techniques simultaneously on patterns with flow and only gflow based on their geometries, and it is shown that the time complexity of the proposed approach is improved over the previous ones.



Distributed Measurement-based Quantum Computation

Quantum complexity theory

This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.

Unifying quantum computation with projective measurements only and one-way quantum computation

Quantum measurement is universal for quantum computation. Two models for performing measurement-based quantum computation exist: the one-way quantum computater was introduced by Briegel and

Toward a quantum process algebra

This paper aims at defining a high level language allowing the description of classical and quantum programming, and their cooperation, and process algebras are chosen as a basis for this language.

Experimental one-way quantum computing

The implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.

Unified derivations of measurement-based schemes for quantum computation

We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel, [Phys. Rev. Lett. 86,

Quantum theory, the Church–Turing principle and the universal quantum computer

  • D. Deutsch
  • Physics, Philosophy
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1985
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible

Fault-tolerant quantum computation with cluster states

Two threshold theorems are proved which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value.

Communicating quantum processes

The syntax, operational semantics and type system of CQP are formally defined, and it is proved that the semantics preserves typing, and that typing guarantees that each qubit is owned by a unique process within a system.