2. Adiabatic quantum computer (AQC) Andrii Rudavskyi Supervisor: prof. Petra Rudolf

3. Outline… Adiabatic quantum algorithm Problems which can be solved How to make AQC work? Qubit, couplers, detectors Examples of real device

4. Initialize ground state Slowly alter Hamiltonian Read solution encoded in final Hamiltonian ground state Adiabatic quantum algorithm

5. NP-complete − problems which cannot be solved within polynomial time: Factorization of integers Search in unsorted databases Travelling salesman problem Image recognition Artificial intelligence What kind of problems can be solved?

6. where, NP-hard Ising model; describes real physical systems Use quantum physics to solve math CUBO-Quadratic unconstrained binary optimization

7. Qubit − quantum unit which encodes the state Coupler − device which couples qubits Device which measures the result of computation Qubits Couplers What do we need to construct AQC?

8. Superconductors: Semiconductor planar technology is highly developed and can be implemented in superconductors Generate almost no heat Superconductor logic is very fast What kind of hardware to use?

9. Superconducting current and magnetic field created by it cannot be arbitrary. They are quantized Single wave function Analogy with Bohr atomic orbits Superconducting flux qubit

10. Superconducting current and magnetic field created by it cannot be arbitrary. They are quantized Single wave function Analogy with Bohr atomic orbits We cannot change magnetic flux through the loop Superconducting flux qubit

11. Dielectric

12. Superconductor Dielectric I Josephson junction Separate superconductors have different phase. φ – phase difference Current through the junction Energy of the junction

13. Josephson junction in the loop

14. Superconducting quantum interference device (SQUID) a b

15. Josephson persistent-current qubit Science 285, 1037 (1999) Calculate Josephson energy of the loop Two stable minima of energy correspond to opposite currents

16. Coupling Coupling via inducting coil SQUID controls strength of coupling

17. Two-Qubit system FM coupling Non coupling AFM coupling

18. Conclutions: AQC − good alternative to conventional quantum computer All logical elements are easily built with help of well developed lithographic planar technology 28-qubit AQC is already built and 1000 is not far off

19. Thank you for attention!