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Measurements in Proof Nets as Higher-Order Quantum Circuits [chapter]

Akira Yoshimizu, Ichiro Hasuo, Claudia Faggian, Ugo Dal Lago
2014 Lecture Notes in Computer Science  
We build on the series of work by Dal Lago and coauthors and identify proof nets (of linear logic) as higher-order quantum circuits.  ...  The calculus MLLqm attains a pleasant balance between expressivity (it is higher-order and accommodates all quantum operations) and concreteness of models (given as token machines, i.e. in the form of  ...  Proof nets are "extended quantum circuits" in the following sense: (some) wires in proof nets can be naturally identified with those in quantum circuits; and at the same time higher-order computation is  ... 
doi:10.1007/978-3-642-54833-8_20 fatcat:kvgmkacuqvb6vhkxrxgijy334a

Hybrid Classical-Quantum method for Diabetic Foot Ulcer Classification [article]

Azadeh Alavi, Hossein Akhoundi
2021 arXiv   pre-print
In order to develop a self monitoring mobile application, it is necessary to be able to classify such ulcers into either of the following classes: Infection, Ischaemia, None, or Both.  ...  In this work, we compare the performance of a classical transfer-learning-based method, with the performance of a hybrid classical-quantum Classifier on diabetic foot ulcer classification task.  ...  In addition, it is non trivial to note that we have employed an elementary circuit for the proof of concept, in the future work we will study more elaborate measurements that can lead to increasing the  ... 
arXiv:2110.02222v1 fatcat:bhmbkjoidnfrvh3doopplacipm

Ground State Connectivity of Local Hamiltonians [chapter]

Sevag Gharibian, Jamie Sikora
2015 Lecture Notes in Computer Science  
The study of ground state energies of local Hamiltonians has played a fundamental role in quantum complexity theory.  ...  In this paper, we take a new direction by introducing the physically motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from quantum stabilizer  ...  Tier 3 Grant "Random numbers from quantum processes," (MOE2012-T3-1-009).  ... 
doi:10.1007/978-3-662-47672-7_50 fatcat:gkbjune5nbeqlovgmblxp4x2aa

How to Bake Quantum into Your Pet Petri Nets and Have Your Net Theory Too [article]

Heinz W. Schmidt
2021 arXiv   pre-print
services, based in partial-order dependencies and concurrent executions.  ...  In this paper, we establish a connection between Petri nets and quantum systems, such that net theory and the component architecture of nets may help in the synthesis and analysis of abstract software  ...  Proofs Proof (Th. 1). Let C be a quantum circuit diagram over n qubits and A its 2 n × 2 n complex operator matrix. A represents an operator in the complex Hilbert space H 2 n .  ... 
arXiv:2106.03539v1 fatcat:uzupyd2javewhbbofitopjfrti

Algorithmic Complexity and Entanglement of Quantum States

Caterina E. Mora, Hans J. Briegel
2005 Physical Review Letters  
We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.  ...  We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states.  ...  Piani for their help in editing the manuscript. This work was supported in part by the FWF, the DFG, and the EU (IST-2001-38877, -39227, OLAQUI, SCALA).  ... 
doi:10.1103/physrevlett.95.200503 pmid:16384044 fatcat:k27pd4ejkzflxpbiraqmvbprte

Methods for simulating string-net states and anyons on a digital quantum computer [article]

Yu-Jie Liu, Kirill Shtengel, Adam Smith, Frank Pollmann
2021 arXiv   pre-print
To achieve this we design a set of linear-depth quantum circuits to generate ground states of general string-net models together with quantum circuits to simulate the creation and braiding of abelian and  ...  Moreover, this set of efficiently prepared topologically ordered states has potential applications in the development of fault-tolerant quantum computers.  ...  A proof of the isometry property is given in Appendix C.  ... 
arXiv:2110.02020v1 fatcat:vg3wh3iccjcdpfqp7uyangj3x4

A Co-Design Framework of Neural Networks and Quantum Circuits Towards Quantum Advantage [article]

Weiwen Jiang, Jinjun Xiong, Yiyu Shi
2020 arXiv   pre-print
We discover that, in order to make full use of the strength of quantum representation, it is best to represent data in a neural network as either random variables or numbers in unitary matrices, such that  ...  QuantumFlow consists of novel quantum-friendly neural networks (QF-Nets), a mapping tool (QF-Map) to generate the quantum circuit (QF-Circ) for QF-Nets, and an execution engine (QF-FB).  ...  Acknowledgements This work is partially supported by IBM and University of Notre Dame (IBM-ND) Quantum program.  ... 
arXiv:2006.14815v2 fatcat:k2w2dypi2fhj3kx2mij2brf5oi

A co-design framework of neural networks and quantum circuits towards quantum advantage

Weiwen Jiang, Jinjun Xiong, Yiyu Shi
2021 Nature Communications  
In QuantumFlow, we represent data as unitary matrices to exploit quantum power by encoding n = 2k inputs into k qubits and representing data as random variables to seamlessly connect layers without measurement  ...  designs a neural network suitable for quantum circuit.  ...  Acknowledgements This work is partially supported by IBM and University of Notre Dame (IBM-ND) Quantum program, and in part by the IBM-ILLINOIS Center for Cognitive Computing Systems Research.  ... 
doi:10.1038/s41467-020-20729-5 pmid:33495480 fatcat:p24jhbix3fdjljdkj7c4tgrsdu

A quantum relay chip based on telecommunication integrated optics technology

A Martin, O Alibart, M P De Micheli, D B Ostrowsky, S Tanzilli
2012 New Journal of Physics  
The two-photon interference pattern shows a net visibility of 80%, which validates the proof of principle of a "quantum relay circuit" for qubits carried by telecom photons.  ...  We investigate an integrated optical circuit on lithium niobate designed to implement the teleportation-based quantum relay scheme for one-way quantum communication at a telecom wavelength.  ...  Tascu for their help in the chip manufacturing, P. Baldi for discussions, M. Al Khalfioui for the micro-soldering of the electrodes, and G. Sauder for his support in software development.  ... 
doi:10.1088/1367-2630/14/2/025002 fatcat:3qnm533ag5eqvbdsj7laqq3iry

Generalization in quantum machine learning from few training data [article]

Matthias C. Caro, Hsin-Yuan Huang, M. Cerezo, Kunal Sharma, Andrew Sornborger, Lukasz Cincio, Patrick J. Coles
2021 arXiv   pre-print
Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing  ...  We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as √(T/N).  ...  They proved bounds on this complexity measure that depend on the size and depth of the circuit as well as on a measure of magic in the circuit. Ref.  ... 
arXiv:2111.05292v1 fatcat:yaitlnkgtjgvbnjz4gm5o6ka64

From quantum cloning to quantum key distribution with continuous variables: a review (Invited)

Nicolas J. Cerf, Philippe Grangier
2007 Journal of the Optical Society of America. B, Optical physics  
Quantum information processing with continuous variables is a paradigm that has attracted a growing interest over the past years, partly as a consequence of the prospects for high-rate quantum communication  ...  In this overview article, we introduce the concept of quantum continuous variables in optics and then turn to the fundamental impossibility of cloning continuousvariable light states, a result that lies  ...  Then she measures coherently all ancillae (with a quantum computer) in order to optimize her information on the block. • Coherent attacks.  ... 
doi:10.1364/josab.24.000324 fatcat:sua5wm4qjbht7kqgckatc6hzsm

Area laws and efficient descriptions of quantum many-body states [article]

Yimin Ge, Jens Eisert
2015 arXiv   pre-print
In this work, we show that this is in general not the case, except in one dimension.  ...  in the context of numerical simulations and analytical considerations.  ...  Quantum circuits Example 5 shows that states prepared by a polynomial quantum circuit with post-selected measurement results have a polynomial classical description.  ... 
arXiv:1411.2995v2 fatcat:mabfzwzeaje4lnlnz3foqpbati

Normalizer Circuits and Quantum Computation [article]

Juan Bermejo-Vega
2016 arXiv   pre-print
In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms.  ...  Our framework extends Gottesman's Pauli Stabilizer Formalism (PSF), wherein quantum states are written as joint eigenspaces of stabilizer groups of commuting Pauli operators: while the PSF is valid for  ...  In particular we show that every Pauli measurement can be implemented using only normalizer circuits and measurements in the standard basis, which will be a useful ingredient in our proof of theorem 3.7  ... 
arXiv:1611.09274v1 fatcat:y6tw3ta2mfb5fkpzdyrbrmuhwu

Saturation and recurrence of quantum complexity in random quantum circuits [article]

Michał Oszmaniec, Michał Horodecki, Nicholas Hunter-Jones
2022 arXiv   pre-print
From a technical perspective our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits  ...  In this work we prove the saturation and recurrence of the complexity of quantum states and unitaries in a model of chaotic time-evolution based on random quantum circuits, in which a local random unitary  ...  MO acknowledges financial support from the TEAM-NET project (contract no. POIR.04.04.00-  ... 
arXiv:2205.09734v1 fatcat:tdy6omwn5nbnpd5n7f5mluhjf4

The geometry of synchronization

Ugo Dal Lago, Claudia Faggian, Ichiro Hasuo, Akira Yoshimizu
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
This is realized by introducing proof-nets for SMLL, an extension of multiplicative linear logic with a specific construct modeling synchronization points, and of a multi-token abstract machine model for  ...  We graft synchronization onto Girard's Geometry of Interaction in its most concrete form, namely token machines.  ...  The third and fourth authors are supported by Grants-in-Aid for Young Scientists (A) No. 24680001, JSPS, and by Aihara Innovative Mathematical Modeling Project, FIRST Program, JSPS/CSTP.  ... 
doi:10.1145/2603088.2603154 dblp:conf/csl/LagoFHY14 fatcat:4fcfiu6ixjh2rih4zww37xv5ju
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