The document discusses the variational quantum eigensolver (VQE) algorithm. It provides an outline that includes possible applications of VQE like the traveling salesman problem and supply chain optimization. It then explains key concepts of VQE including using a wavefunction and Hamiltonian to represent the energy of a quantum system. The document demonstrates running VQE on optimization problems using the CoCalc and QISKit playgrounds.

1. Quantum Computing
The Variational Quantum Eigensolver
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Vesselin G. Gueorguiev, PhD 1
Vesselin G. Gueorguiev
Ronin Institute &
Institute for Advanced Physical Studies

2. Outline
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 Possible Applications of VQE.
 Key VQE Concepts.
 The VQE playground exploration:
• Running on CoCalc by SageMath, Inc. ,
• Running within IBM QISKit.
 Few Optimization examples:
• Max-Cut problem,
• Traveling Salesman problem,
• Vehicle Routing.
 Conclusion and Open Discussion!

3. Possible Applications of VQC
the Traveling Salesman problem
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www.dogonews.com/2012/9/30/
www.pinterest.co.kr/pin/556827941406760594/

4. Possible Applications of VQC
Supply Chain optimization
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www.businessinsider.com/iphone-x-teardown-parts-cost-ihs-markit-2017-11
www.innovationtoronto.com/2012/05/track-where-your-stuff-comes-from-down-to-the-tiniest-part/

5. Possible Applications of VQC
Profit Optimization (Max-Cut)
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global profit function (wij=wji and xi = 0 or 1)
qiskit-tutorials/qiskit/optimization/max_cut_and_tsp.ipynb
Ising Hamiltonian (1925)
www.hs-augsburg.de/~harsch/anglica/Chronology/20thC/Ising/isi_fm00.html
xi  (1 - zii)/2

6. Key VQE Concepts
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The Q-bit represented
as a Bloch sphere
 Wavefunction: a mathematical description of a (quantum) state
 Hamiltonian: an operator that describes the energy of a system
 Quantum gates: operations performed on qubits!
Feed this energy to an optimizer that is run on a classical computer.
The optimizer then generates a new set of control parameters
that create a new trial wavefunction with lower energy.
https://developer.ibm.com/dwblog/2017/quantum-computing-qubit-vqe-variational-quantum-eigensolver/
https://grove-docs.readthedocs.io/en/latest/vqe.html

7. Key VQE Concepts
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The Q-bit represented
as a Bloch sphere
Quantum gates: operations performed on qubits!
CNOT

8. Key VQE Concepts
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Ising Hamiltonian
xi  (1 - zii)/2
 Hamiltonian (cost function) an operator that describes the energy of a system
H|ψ>=e |ψ>

9. Key VQE Concepts
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10. CoCal Playground
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Collaborative Calculation in the Cloud

11. QISKit Playground
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Playground for gaining intuition about Variational Quantum Eigensolver
https://github.com/JavaFXpert/vqe-playground
Learn Quantum Computation using Qiskit
https://community.qiskit.org/textbook/
Using QISKit jupiter notebooks:
http://localhost:8888/tree/qiskit-tutorials/qiskit/optimization
Qiskit/qiskit-iqx-tutorials https://github.com/Qiskit/qiskit-iqx-tutorials/
qiskit-iqx-tutorials/qiskit/advanced/aqua/optimization/
……/tree/master/qiskit/advanced/aqua/optimization
max_cut_and_tsp.ipynb
vehicle_routing.ipynb

12. Open Discussion
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