[1] Kaye, R., Laflamme, R., & Mosca, M. (2007). An Introduction to Quantum Computing. Oxford University Press.
[2] Barenco, A., et al. (1995). "Elementary gates for quantum computation." Physical Review A, 52(5), 3457.
[3] Amy, M., Maslov, D., & Mosca, M. (2013). "Polynomial-time T-depth optimization of Clifford+T circuits via matroid partitioning." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 32(6), 818–830.
[4] Shende, V. V., Bullock, S. S., & Markov, I. L. (2006). "Synthesis of quantum logic circuits." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 25(6), 1000–1010.
[5] Gottesman, D. (1997). "Stabilizer codes and quantum error correction." PhD Thesis, California Institute of Technology.
[6] Qiskit Textbook. (2023). Learn Quantum Computation Using Qiskit. Online resource.
Quantum circuit optimization
| Type of study | Follow-up Master |
|---|---|
| Language of instruction | Czech |
| Code | 9600-1036/01 |
| Abbreviation | OKO |
| Course title | Quantum circuit optimization |
| Credits | 4 |
| Coordinating department | IT4Innovations |
| Course coordinator | prof. RNDr. Marek Lampart, Ph.D. |
Subject syllabus
Lectures:
1. Introduction to Quantum Circuits: Overview of basic quantum gates and circuits, motivation for optimization.
2.Quantum Complexity and Implementation Costs: Definitions of circuit complexity, quantum logic, and optimization objectives.
3. Classical Optimization Techniques in Quantum Contexts: Adapting classical optimization techniques to quantum circuits.
4. Minimization of Quantum Gates: Methods for reducing the number of gates.
5. Reduction of Quantum Circuit Depth: Techniques for minimizing circuit depth and their impact on quantum computers.
6. Quantum routing problem: Techniques of quantum circuit execution on a quantum computer with a limited physical layout of qubits.
7. Decomposition of Multi-Qubit Gates: Techniques for decomposing complex gates into simpler components.
8. Quantum Ansatz: Quantum ansatz as foundational building blocks in variational quantum algorithms, encoding problem-specific solutions into quantum circuits.
9. QAOA Optimization Algorithms: Quantum Approximate Optimization Algorithms and their impact on circuit design.
10. Variational Quantum Algorithms and Hybrid Approaches: Application of variational principles in circuit optimization.
11. Quantum Circuit Compilation: The role of quantum code compilers and their impact on optimization.
12. Software for Quantum Circuit Optimization: Practical demonstrations of software tools like Qiskit, Cirq, and others.
Exercises:
1. Solving Tasks on the Topic: Implementation of Basic Quantum Circuits: Construction and simulation of simple circuits containing gates such as Hadamard, CNOT, and Pauli operators using tools like Qiskit or Cirq.
2. Solving Tasks on the Topic: Calculating Quantum Complexity and Circuit Costs: Calculation of the number of gates used, circuit depth, and comparison of the efficiency of different circuit designs.
3. Solving Tasks on the Topic: Application of Classical Optimization Techniques in Quantum Circuits: Optimization of a simple circuit by reducing redundant gates.
4. Solving Tasks on the Topic: Minimization of Quantum Gates in Circuits: Transformation of multi-qubit gates into a sequence of two-qubit gates to achieve minimization.
5. Solving Tasks on the Topic: Reduction of Quantum Circuit Depth: Optimization of a circuit with a focus on parallel execution of gates and reduction of overall depth.
6. Solving Tasks on the Topic: Application of Quantum routing problem with determination of techniques of quantum circuit execution on a quantum computer with a limited physical layout of qubits.
7. Solving Tasks on the Topic: Decomposition of Multi-Qubit Gates into Simpler Universal Gates: Decomposition of the Toffoli gate into basic Clifford+T gates using Qiskit.
8. Solving Tasks on the Topic: Solving problems of application of quantum ansatz, its construction and integration into quantum circuits.
9. Solving Tasks on the Topic: Implementation and Optimization of the QAOA Algorithm: Design of QAOA for a simple problem, such as Max-Cut, and its optimization.
10. Solving Tasks on the Topic: Using Variational Quantum Algorithms for Circuit Optimization: Application of VQE (Variational Quantum Eigensolver) and analysis of its circuit complexity.
11. Solving Tasks on the Topic: Optimization of Circuits Using Quantum Compilers: Testing optimization functions of the Qiskit quantum compiler on a given circuit.
12. Solving Tasks on the Topic: Practical Use of Software Tools for Circuit Optimization: Creation and optimization of circuits in environments like Qiskit, Cirq, and other tools, and comparison of the outputs.
Projects:
Students will design, implement, and optimize a non-trivial quantum circuit for a selected problem using tools such as Qiskit or Cirq. The project must demonstrate the ability to analyze circuit complexity (gate count, depth), apply optimization techniques (e.g., gate minimization, depth reduction, routing, decomposition), and evaluate the impact of these methods on the circuit’s efficiency and hardware feasibility.
1. Introduction to Quantum Circuits: Overview of basic quantum gates and circuits, motivation for optimization.
2.Quantum Complexity and Implementation Costs: Definitions of circuit complexity, quantum logic, and optimization objectives.
3. Classical Optimization Techniques in Quantum Contexts: Adapting classical optimization techniques to quantum circuits.
4. Minimization of Quantum Gates: Methods for reducing the number of gates.
5. Reduction of Quantum Circuit Depth: Techniques for minimizing circuit depth and their impact on quantum computers.
6. Quantum routing problem: Techniques of quantum circuit execution on a quantum computer with a limited physical layout of qubits.
7. Decomposition of Multi-Qubit Gates: Techniques for decomposing complex gates into simpler components.
8. Quantum Ansatz: Quantum ansatz as foundational building blocks in variational quantum algorithms, encoding problem-specific solutions into quantum circuits.
9. QAOA Optimization Algorithms: Quantum Approximate Optimization Algorithms and their impact on circuit design.
10. Variational Quantum Algorithms and Hybrid Approaches: Application of variational principles in circuit optimization.
11. Quantum Circuit Compilation: The role of quantum code compilers and their impact on optimization.
12. Software for Quantum Circuit Optimization: Practical demonstrations of software tools like Qiskit, Cirq, and others.
Exercises:
1. Solving Tasks on the Topic: Implementation of Basic Quantum Circuits: Construction and simulation of simple circuits containing gates such as Hadamard, CNOT, and Pauli operators using tools like Qiskit or Cirq.
2. Solving Tasks on the Topic: Calculating Quantum Complexity and Circuit Costs: Calculation of the number of gates used, circuit depth, and comparison of the efficiency of different circuit designs.
3. Solving Tasks on the Topic: Application of Classical Optimization Techniques in Quantum Circuits: Optimization of a simple circuit by reducing redundant gates.
4. Solving Tasks on the Topic: Minimization of Quantum Gates in Circuits: Transformation of multi-qubit gates into a sequence of two-qubit gates to achieve minimization.
5. Solving Tasks on the Topic: Reduction of Quantum Circuit Depth: Optimization of a circuit with a focus on parallel execution of gates and reduction of overall depth.
6. Solving Tasks on the Topic: Application of Quantum routing problem with determination of techniques of quantum circuit execution on a quantum computer with a limited physical layout of qubits.
7. Solving Tasks on the Topic: Decomposition of Multi-Qubit Gates into Simpler Universal Gates: Decomposition of the Toffoli gate into basic Clifford+T gates using Qiskit.
8. Solving Tasks on the Topic: Solving problems of application of quantum ansatz, its construction and integration into quantum circuits.
9. Solving Tasks on the Topic: Implementation and Optimization of the QAOA Algorithm: Design of QAOA for a simple problem, such as Max-Cut, and its optimization.
10. Solving Tasks on the Topic: Using Variational Quantum Algorithms for Circuit Optimization: Application of VQE (Variational Quantum Eigensolver) and analysis of its circuit complexity.
11. Solving Tasks on the Topic: Optimization of Circuits Using Quantum Compilers: Testing optimization functions of the Qiskit quantum compiler on a given circuit.
12. Solving Tasks on the Topic: Practical Use of Software Tools for Circuit Optimization: Creation and optimization of circuits in environments like Qiskit, Cirq, and other tools, and comparison of the outputs.
Projects:
Students will design, implement, and optimize a non-trivial quantum circuit for a selected problem using tools such as Qiskit or Cirq. The project must demonstrate the ability to analyze circuit complexity (gate count, depth), apply optimization techniques (e.g., gate minimization, depth reduction, routing, decomposition), and evaluate the impact of these methods on the circuit’s efficiency and hardware feasibility.
Literature
Advised literature
[1] Nielsen, M. A. (1998). Quantum Information Theory (Doctoral dissertation, The University of New Mexico).
[2] Farhi, E., Goldstone, J., & Gutmann, S. (2014). "A quantum approximate optimization algorithm." arXiv preprint arXiv:1411.4028.
[3] McClean, J. R., et al. (2016). "The theory of variational hybrid quantum-classical algorithms." New Journal of Physics, 18(2), 023023.
[2] Farhi, E., Goldstone, J., & Gutmann, S. (2014). "A quantum approximate optimization algorithm." arXiv preprint arXiv:1411.4028.
[3] McClean, J. R., et al. (2016). "The theory of variational hybrid quantum-classical algorithms." New Journal of Physics, 18(2), 023023.