Liquid State NMR Quantum Computing

1. Financial supports from Kinki Univ., MEXT and JSPS Liquid State NMR Quantum Computing Mikio Nakahara, Research Centre for Quantum Computing, Kinki University, Japan Physical Realizations of QC @ Tehran, Jan. 2009

2. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudopure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

3. 1. Introduction Physical Realizations of QC @ Tehran, Jan. 2009

4. Qubits in NMR Molecule Trichloroethylene Physical Realizations of QC @ Tehran, Jan. 2009

5. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudo-Pure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

6. NMR (Nuclear Magnetic Resonance )=MRI (Magnetic Resonance Imaging) Physical Realizations of QC @ Tehran, Jan. 2009

7. NMR Physical Realizations of QC @ Tehran, Jan. 2009

8. Schematic of NMR Physical Realizations of QC @ Tehran, Jan. 2009

9. Molecules used in NMR QC Physical Realizations of QC @ Tehran, Jan. 2009

10. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudopure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

11. 3.1 Single-Qubit Hamiltonian Physical Realizations of QC @ Tehran, Jan. 2009

12. Hamiltonian in Rotating Frame Physical Realizations of QC @ Tehran, Jan. 2009

13. Physical Realizations of QC @ Tehran, Jan. 2009

14. 2-Qubit Hamiltonian Physical Realizations of QC @ Tehran, Jan. 2009

15. Physical Realizations of QC @ Tehran, Jan. 2009

16. Physical Realizations of QC @ Tehran, Jan. 2009

17. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudopure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

18. 1-Qubit Gates Physical Realizations of QC @ Tehran, Jan. 2009

19. Example: Hadamard gate Physical Realizations of QC @ Tehran, Jan. 2009

20. Example: Hadamard gate 2 Physical Realizations of QC @ Tehran, Jan. 2009

21. Selective addressing Physical Realizations of QC @ Tehran, Jan. 2009

22. In resonance: . Physical Realizations of QC @ Tehran, Jan. 2009

23. Physical Realizations of QC @ Tehran, Jan. 2009

24. Physical Realizations of QC @ Tehran, Jan. 2009

25. 2-Qubit Gates: CNOT Physical Realizations of QC @ Tehran, Jan. 2009

26. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudopure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

27. Spins are in mixed state! Physical Realizations of QC @ Tehran, Jan. 2009

28. Preparation of a pseudopure state in terms of temporal average method Physical Realizations of QC @ Tehran, Jan. 2009

29. Temporal average method Physical Realizations of QC @ Tehran, Jan. 2009

30. Averaging three contributions Physical Realizations of QC @ Tehran, Jan. 2009

31. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudopure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

32. 6.1 Free Induction Decay (FID) |01〉 |00〉 |10〉 |11〉 Physical Realizations of QC @ Tehran, Jan. 2009

33. Free Induction Decay (FID) Physical Realizations of QC @ Tehran, Jan. 2009

34. Physical Realizations of QC @ Tehran, Jan. 2009

35. 6.2 Quantum State Tomography • We want to “measure” the density matrix. • Measure observable such as magnetizations to find linear combinations of the matrix elements of the density matrix. • Not enough equations are obtained. • Deform the density matrix with pulses to obtain enough number of equations. Physical Realizations of QC @ Tehran, Jan. 2009

36. 2-Qubit QST Physical Realizations of QC @ Tehran, Jan. 2009

37. Physical Realizations of QC @ Tehran, Jan. 2009

38. Physical Realizations of QC @ Tehran, Jan. 2009

39. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudopure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

40. DiVincenzo Criteria for NMR QC • A scalable physical system with well characterized qubits. • The ability to initialize the state of the qubits to a simple fiducial state, such as |00…0>. • Long decoherence times, much longer than the gate operation time. • A “universal” set of quantum gates. • A qubit-specific measurement capability. Physical Realizations of QC @ Tehran, Jan. 2009

41. Scalability • Selective addressing to each qubit becomes harder and hader as the # of qubits increases. Limited # of nuclear spices and overlap of resonance freqs. • Signal strength is suppressed as the # of qubits increases. Readout problem. Physical Realizations of QC @ Tehran, Jan. 2009

42. Initialization (pseudopure state) • # of steps required to prepare a pseudopure state increases exponentially as the # of qubits increases. • No real entanglement Physical Realizations of QC @ Tehran, Jan. 2009

43. Long decoherence time • Decoherence time • Single-qubit gate operation time • Two-qubit gate op. time • May execute Shor’s algorithm for 21=3X7. Physical Realizations of QC @ Tehran, Jan. 2009

44. A “universal” set of quantum gates. • One-qubit gates by Rabi oscillation. • Two-qubit gates by J-coupling. • Cannot turn off interactions; reforcusing technique becomes complicated as the # of qubits increases. Physical Realizations of QC @ Tehran, Jan. 2009

45. Measurement capability. • FID is a well-established techunique. • Quantum State Tomograpy and Quantum Process Tomography are OK. • S/N scales as , which limits the # of qubits to ~ 10. Physical Realizations of QC @ Tehran, Jan. 2009

46. Still… • NMR QC is commercially available. • It can execute small scale quantum algorithms. • It serves as a test bed for a real QC to come. • May ideas in other realizations are inspired from NMR. • We use NMR QC to demonstrate theoretical ideas, such as decoherence suppression, optimal control of a Hamiltonian etc. Physical Realizations of QC @ Tehran, Jan. 2009

47. Plan of Talk • 1. Introduction • 2. NMR • 3. NMR Hamiltonian • 4. Gate Operations • 5. Pseudopure State • 6. Measurement • 7. DiVincenzo Criteria • 8. Summary Physical Realizations of QC @ Tehran, Jan. 2009

48. Liquid state NMR QC is based on a well-established technology. Most of the materials introduced here have been already known in the NMR community for decades. • There are still many papers on NMR QC. • It is required to find a breakthrogh for a liquid state NMR to be a candidate of a working QC. • ENDOR, Solid state NMR… • Thank you for your attention. Physical Realizations of QC @ Tehran, Jan. 2009