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Title: Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model

Abstract

We provide a set of prescriptions for implementing a quantum circuit model algorithm as measurement based quantum computing (MBQC) algorithm1, 2 via a large cluster state. As means of illustration we draw upon our numerical modeling experience to describe a large graph state capable of searching a logical 8 element list (a non-trivial version of Grover's algorithm3 with feedforward). We develop several prescriptions based on analytic evaluation of cluster states and graph state equations which can be generalized into any circuit model operations. Such a resulting cluster state will be able to carry out the desired operation with appropriate measurements and feed forward error correction. We also discuss the physical implementation and the analysis of the principal 3-qubit entangling gate (Toffoli) required for a non-trivial feedforward realization of an 8-element Grover search algorithm.

Authors:
 [1];  [1];  [1];  [1]
  1. United States Air Force Research Laboratory, Wright-Patterson Air Force Base
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
Work for Others (WFO)
OSTI Identifier:
1286794
DOE Contract Number:
AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: SPIE Security and defense, Amsterdam, Netherlands, 20140922, 20140922
Country of Publication:
United States
Language:
English

Citation Formats

Alsing, Paul, Fanto, Michael, Lott, Capt. Gordon, and Tison, Christoper C. Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model. United States: N. p., 2014. Web.
Alsing, Paul, Fanto, Michael, Lott, Capt. Gordon, & Tison, Christoper C. Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model. United States.
Alsing, Paul, Fanto, Michael, Lott, Capt. Gordon, and Tison, Christoper C. 2014. "Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model". United States. doi:. https://www.osti.gov/servlets/purl/1286794.
@article{osti_1286794,
title = {Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model},
author = {Alsing, Paul and Fanto, Michael and Lott, Capt. Gordon and Tison, Christoper C.},
abstractNote = {We provide a set of prescriptions for implementing a quantum circuit model algorithm as measurement based quantum computing (MBQC) algorithm1, 2 via a large cluster state. As means of illustration we draw upon our numerical modeling experience to describe a large graph state capable of searching a logical 8 element list (a non-trivial version of Grover's algorithm3 with feedforward). We develop several prescriptions based on analytic evaluation of cluster states and graph state equations which can be generalized into any circuit model operations. Such a resulting cluster state will be able to carry out the desired operation with appropriate measurements and feed forward error correction. We also discuss the physical implementation and the analysis of the principal 3-qubit entangling gate (Toffoli) required for a non-trivial feedforward realization of an 8-element Grover search algorithm.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2014,
month = 1
}

Conference:
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  • We provide a set of prescriptions for implementing a circuit model algorithm as measurement based quantum computing via a large discrete cluster state constructed sequentially, from qubits implemented as single photons. We describe a large optical discrete graph state capable of searching logical 4 and 8 element lists as an example. To do so we have developed several prescriptions based on analytic evaluation of the evolution of discrete cluster states and graph state equations. We describe the cluster state as a sequence of repeated entanglement and measurement steps using a small number of single photons for each step. These prescriptionsmore » can be generalized to implement any logical circuit model operation with appropriate single photon measurements and feed forward error corrections. Such a cluster state is not guaranteed to be optimal (i.e. minimum number of photons, measurements, run time).« less
  • We introduce schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in Gross and Eisert [Phys. Rev. Lett. 98, 220503 (2007); quant-ph/0609149]. Our method makes use of tools from many-body physics--matrix product states, finitely correlated states, or projected entangled pairs states--to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem--how to realize quantum computation--was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting and presentmore » a large number of examples. We find computational schemes, which differ from the original one-way computer, for example, in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may, for example, exhibit nonvanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev's toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.« less
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