Table of Contents
1
Introduction
2
Overview
3
Quibit and Quantum State
4
Quantum Gates
5
Algorithms
6
Design & Testing
7
Conclusion
8
References
9
Glossary
10
Contributors
INTRODUCTION
Introduction
OVERVIEW OF QUANTUM MACHINE LEARNING
OVERVIEW OF QUANTUM MACHINE LEARNING
QUIBIT AND QUANTUM STATE
QUIBIT AND QUANTUM STATE
- |ψ^{+}⟩=|00⟩ + |11⟩/ Ö2
- |ψ^{–}⟩=|00⟩ – |11⟩/ Ö2
- |ψ^{+}⟩=|01⟩ + |10⟩/ Ö2
- |ψ^{–}⟩=|01⟩ – |10⟩/ Ö2
QUANTUM GATES
QUANTUM GATES
- A computer developed totally of billiard balls and mirrors, provides a beautiful concrete realization of the principles of reversible computation, and;
- A technique based on the Toffoli gate (a reversible logic gate), which can perform any computation that a classical computer can.
- Pauli-X: ….. It maps |0⟩ to |1⟩ and |1⟩ to |0⟩. It is equivalent to a NOT gate.
- Pauli-Y: ….. It maps |0⟩ to i |1⟩ and |1⟩ to −i |0⟩.
- Pauli-Z: ….. Also called a phase-flip, it leaves the basis state |0⟩ unchanged and maps |1⟩ to −|1⟩.
- Hadamard: H ….. It creates a superposition by mapping |0⟩ to and |1⟩ to .
- Phase shift: ….. It leaves the basis state |0⟩ unchanged and maps |1⟩ to e^{iψ }|1⟩.
- Controlled NOT: …. It acts on 2 qubits and performs the NOT operation on the target qubit only when the control qubit is |1⟩.
- SWAP: …. It acts on 2 qubits and swaps these two qubits.
ALGORITHMS
ALGORITHMS
- |0⟩^{⊗}^{n}|1⟩ Initialize state.
- Create superposition using Hadamard gates.
- Calculate function f using U_{f}.
- Perform Hadamard transform
- Measure to obtain final output z.
- Initialize state to the state, and output qubit to |−⟩.
- Apply Hadamard gates to the input register.
- Apply Hadamard gates to the output register.
- → 0 if s_{i} =0 and 1 if s_{i}=1 Measure to obtain final output s.
- y=y.z mod 2
- z=(x⊕s).z mod 2
- z=x.z⊕s.z mod 2
- 0=s.z mod 2
- Performed on classical computers: The classical part reduces the factorization to a problem of finding the period of the function.
- Performed on quantum machines: The quantum part uses a quantum computer to find the period using the Quantum Fourier Transform (QFT).
- If n is even, prime, or a prime power, then exit.
- Pick a random integer x < n and compute gcd (x, n). If it is not 1, then we have achieved a factor of n.
- Quantum algorithm: Pick q as the smallest power of 2 with n2 ≤ q < 2n2 . Find period r of xa mod n. The measurement gives us a variable c, which has the property c/q≈d/r where d ∈ N, where q is the dimension of a Hilbert space.
- To find d, r via continued fraction expansion algorithm. d and r are only determined if gcd(d, r) = 1 (reduced fraction).
- If r is odd, go back to 2. If x^(r/2)≡ −1 mod n, go back to 2. Otherwise, the factors p, q = gcd( x^(r/2)± 1, n).
DESIGN & TESTING
DESIGN & TESTING
Parameters | Metal Corrosion | Brain Tumor |
Quantum Depth | 31 | 31 |
Number of Epochs | 100 | 200 |
Batch Size | 8 | 16 |
Learning Rate | 0.0004 | 0.001 |
Max Accuracy Achieved During Iterations | 100% | 96.62% |
Dataset | Metal Corrosion |
Best Accuracy | 100% |
Test Results | |
Accuracy Results | |
Loss Results | |
Evaluation Metrics |
Dataset | Brain Tumor (Multi-class) |
Best Accuracy | 96.62% |
Test Results | |
Accuracy Results | |
Loss Results | |
Evaluation Metrics |
CONCLUSION
CONCLUSION
REFERENCES
REFERENCES
- Menard, Alexandre, et al. “A game plan for quantum computing.” McKinsey Quarterly, February 6, 2020.
- Sandhu, Adarsh. “Quantum Computing: Technology with limitless possibilities looking for tough problems to solve.” Springer Nature, 2018.
- Adcock, Jeremy, et al. “Advances in quantum machine learning.” Quantum Engineering Centre for Doctoral Training, University of Bristol, December 10, 2015.
- TA-Swiss. Quantum Technologies, 2021
- Yanofsky, Noson S., and Mirco A. Mannucci. Quantum Computing for Computer Scientists. Cambridge University Press, August 2008.
- Tensorflow Quantum Computing, 2021. www.tensorflow.org
- José D. Martín-Guerrero, Lucas Lamata. “Quantum Machine Learning: A tutorial”, Neurocomputing, 2021.
- QuIC Seminar. “The Bernstein-Vazirani Algorithm.” Michigan State University.
- Watrous, John. “Lecture 6: Simon’s algorithm.” University of Waterloo, February 2, 2006.
- Grant Salton, Daniel Simon, and Cedric Lin. Exploring Simon’s Algorithm with Daniel Simon, 2021
- Erdi ACAR and Ihsan YILMAZ. COVID-19 detection on IBM quantum computer, 2020
- Junhua Liu,1, 2 Kwan Hui Lim. Hybrid Quantum-Classical Convolutional Neural Networks, 2021. arxiv.org
- Peter Young. The Bernstein-Vazirani Algorithm, 2019
- Chih-Chieh Chen, Shiue-Yuan Shiau, Ming-Feng Wu & Yuh-Renn Wu. Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines, 2019
- Andrea Mari, Thomas R. Bromley, Josh Izaac, Maria Schuld, Nathan Killoran. Transfer learning in hybrid classical-quantum neural networks, 2020
- Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin. PennyLane: Automatic differentiation of hybrid quantum-classical computations, 2020
- IBM Qiskit textbook. qiskit.org
- Changyu Dong. Math in Network Security
- Elisa Baumer, Jan-Grimo Sobez, Stefan Tessarini. Shor’s Algorithm, 2015
- Marcello Benedetti, Erika Lloyd, Stefan Sack, Mattia Fiorentini. Parameterized quantum circuits as machine learning models, 2019
- Post-Quantum Cryptography, NIST
- Carlos Bravo-Prieto, Ryan LaRose, M. Cerezo, Yigit Subasi, Lukasz Cincio, Patrick J. Coles. Variational Quantum Linear Solver, 2019
- Andi Sama. Hello Tomorrow,I am a Hybrid Quantum Machine Learning, 2020
- Aidan Pellow-Jarman. Near Term Algorithms for Linear Systems of Equations, 2021
- Aidan Pellow-Jarman, Ilya Sinayskiy. A Comparison of Various Classical Optimizers for a Variational Quantum Linear Solver, 2021
- Isaac Chuang and Michael Nielsen. Quantum Computation and Quantum Information, 2010
- QuIC Seminar. The Bernstein-Vazirani Algorithm
GLOSSARY
GLOSSARY
|0⟩ | Qubit state with vector output (1, 0) |
|1⟩ | Qubit state with vector output (0,1) |
σ_{x}, σ_{y} and σ_{z} | Pauli sigma matrices |
⊕ | Modulo two additions |
U | Unitary operator or matrix |
H | Hadamard gate |
α, β, γ, and δ | Real-valued number |
|ψ⟩ | Superpositions |
|+⟩ | Positive state phase |
|-⟩ | Negative state phase |
θ and ψ | Point on the unit’s three-dimensional sphere |
|ψ^{+}⟩ | Positive phase state |
|ψ^{–}⟩ | Negative phase state |
⊗ | Tensor product |
I | Identity Matrix |
H^{⊗}^{n} | Parallel action of n Hadamard gates |
R_{x} | Rotational X gate |
R_{y} | Rotational Y gate |
R_{z} | Rotational Z gate |
† | Hermitian conjugate |
Contributors
Arvind Ramachandra
Vice President of Technology & Cloud Services
Munish Singh
Deputy Manager, Research & Advisory AI/ML
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