Liquid State NMR Quantum Computing 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

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

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

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

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

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

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

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

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

Physical Realizations of QC @ Tehran, Jan. 2009

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

Physical Realizations of QC @ Tehran, Jan. 2009

Physical Realizations of QC @ Tehran, Jan. 2009

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

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

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

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

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

Physical Realizations of QC @ Tehran, Jan. 2009

Physical Realizations of QC @ Tehran, Jan. 2009

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

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

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

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

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

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

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

Physical Realizations of QC @ Tehran, Jan. 2009

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

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

Physical Realizations of QC @ Tehran, Jan. 2009

Physical Realizations of QC @ Tehran, Jan. 2009

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

Physical Realizations of QC @ Tehran, Jan. 2009 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

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

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

Physical Realizations of QC @ Tehran, Jan. 2009 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

Physical Realizations of QC @ Tehran, Jan. 2009 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

Physical Realizations of QC @ Tehran, Jan. 2009 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