1. Paraty - II Quantum Information Workshop 11/09/2009 Fault-Tolerant Computing with Biased-Noise Superconducting Qubits Frederico Brito Collaborators: P. Aliferis, D. DiVincenzo, J. Preskill, M. Steffen and B. Terhal. DF- UFPE (Brazil)

2. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits Outline  The physical system: –Superconducting flux qubit  Encoding scheme for a biased-noise case: –Dephasing Vs. relaxation  Comments 2 Paraty - II Quantum Information Workshop11/09/2009

3. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 3 Paraty - II Quantum Information Workshop11/09/2009 - IBM Qubit Koch et al. PRL 96, 127001 ‘06; PRB 72, 092512 ‘05.  Oscillator Stabilized Flux Qubit - Three Josephson Junctions, Three loops - High-Quality Superconducting Transmission Line (Q ~ 10 4 ) - T 2 = 2.7µs (memory point); T 1 = ~10ns (measurement point).

4. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 4 Paraty - II Quantum Information Workshop11/09/2009 Energy f  c 

5. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 5 Paraty - II Quantum Information Workshop11/09/2009 - Qubit Potential L R L R L R Burkard et al PRB 69, 064503 ‘04; - Coupling qubit-Transmission Line Brito et al NJP 10, 033027 ‘08

6. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 6 Paraty - II Quantum Information Workshop11/09/2009 - Level Dynamics Portal “Parking” Regime “S-Line”

7. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 7 Paraty - II Quantum Information Workshop11/09/2009 Adiabatic Process R,0 L,0 S,1 S,0

8. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 8 Paraty - II Quantum Information Workshop11/09/2009 - Physical sources of noise  1/f noise.  Johnson noise from resistances in the circuit.  Instrumental jitter in pulse timing and amplitude. - DC Pulse Gates  Low-bandwidth operations.  Operations are scalable.  Leakage.  Fast gates.

9. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 9 Paraty - II Quantum Information Workshop11/09/2009 Phase-Gate: exp( i  z )  const tt Both qubits Phase: 2.75 x 10 -3 Relaxation: 3.5 x 10 -7 Leakage : 3.77 x 10 -7 Noise characterization Noise bias

10. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 10 Paraty - II Quantum Information Workshop11/09/2009 “|+>” Measurement and Preparation Gates Non- Adiabatic Process Qubit A   = 2  3.1 GHz  Qubit B   = 2  ¾ 3.1 GHz  Phase: 2.75 x 10 -3 2.75 x 10 -3 Relaxation: 3.5 x 10 -7 3.5 x 10 -7 Leakage : 3.77 x 10 -7 1.5 x 10 -5 Noise characterization Noise bias

11. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 11 Paraty - II Quantum Information Workshop11/09/2009 - Two-qubit Gate: - Two qubit species: different transmission lines        - Qubit-qubit mutual inductance is “always on”

12. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 12 Paraty - II Quantum Information Workshop11/09/2009 - CPHASE gate – Noise characterization 0 5 10 15 20 25 30 35 t(ns) Qubit A   = 2  3.1 GHz  Qubit B   = 2  ¾ 3.1 GHz  Phase: 1.96 x 10 -3 4.6 x 10 -3 Relaxation: 3.5 x 10 -6 3.5 x 10 -6 Leakage : 3.5 x 10 -6 3.5 x 10 -6 Noise bias

13. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 13 Paraty - II Quantum Information Workshop11/09/2009 - The IBM qubit  The noise is highly biased.  Phase errors are stronger than all other types of errors by a factor of 10 3.  For all other types of errors, the dominant contribution is due to relaxation to the ground state: T 1 process.  Hadamard gate: error rate as low as 0.4%.  BUT, no physical implementation of a CNOT gate with error rate better than 5%.

14. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 14 Paraty - II Quantum Information Workshop11/09/2009 - The IBM qubit  Simple implementations of a logical CNOT gate have error rates of the order of (a) 1.25% and (b) 2.3%. (a) (b)  But, those implementations break the noise asymmetry, converting phase errors into errors of other types! - For example, a  z error during the implementation of a H gate will be converted to some linear combination of a  z,  x, and  y error.

15. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 15 Paraty - II Quantum Information Workshop11/09/2009 If =, and, - Biased-noise Qubits  Can we exploit this noise asymmetry to improve the threshold for quantum computation? If we use an n -qubit repetition code, a first guess would lead us to the following logical errors : : ; ; = phase error prob. = error prob. (n=7)

16. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 16 Paraty - II Quantum Information Workshop11/09/2009  So, what do we need to implement that? a)A universal set of elementary operations whose implementation induces noise that is biased towards dephasing. b)All gates must commute with    so that the noise bias is maintained.  Our quantum computer will execute NJP 11, 013061 (2009) –The preparation of the state –The CPHASE gate; –And measurements in the equator of the Bloch sphere: biased noisemore balanced effective noise with str. below effective noise with arbitrarily small str.

17. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 17 Paraty - II Quantum Information Workshop11/09/2009 - Logical CNOT Logical input data qubits preparation measurement = = Aliferis et al quant-ph/0710.1301 Ancilla qubit

18. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 18 Paraty - II Quantum Information Workshop11/09/2009 - Logical CNOT  The logical state of each block is teleported to a new block and phase errors are corrected.  The circuit prevents the propagation of leakage errors between input and output qubits (teleportation).  Measurements with ancilla qubits must be repeated several times to correct errors.  A logical teleportation preceding every logical gate prevents leakage propagation between logical gates

19. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 19 Paraty - II Quantum Information Workshop11/09/2009 - The IBM qubit: Phase errors: 4.62 x 10 -3 All other erros: 3.98 x 10 -3 ( n,k ) = (5,7) Logical CNOT: An improvement by a factor of about 3 over the best alternative method we have for implementing a CNOT. Our physical-level error rates are, in principle, very close to those needed for effective fault-tolerant quantum computation!

20. Fault-Tolerant Computing With Biased-Noise Superconducting Qubits 20 Paraty - II Quantum Information Workshop11/09/2009 - Comments  Can our analysis be applied for other qubits? –We think so! Indeed, for most qubits, dephasing is much stronger than relaxation, Future experiments could focus on improving T 1. Provided this is achieved, dephasing noise can be suppressed by using the encoding and fault-tolerant circuits we have described here. NJP 11, 013061 (2009); NJP 10, 033027 (2008)