1. Objectives Approach Status Linear: LOQC + Cluster state approaches Nonlinear: Q. Zeno and QND-driven Theoretical efforts to reduce resources, quantify and optimise error thresholds New technologies: frequency uncorrelated photons, adaptive-optic mode matching, micro- and waveguide optics, fast low-loss feed-forward capabilities 3 & 4-qubit computation demonstrated, including universal gates, realised Shor’s algorithm. Compact, bright, robust entangled photon source, T = 98.3 ± 3.3%, S mermin = 2.968 ± 0.023. Invented general technique to reduce # of universal gates. Realised first-ever Toffoli, CU, gates. Invented technique to measure error-prob-per-gate. Exp’lly identified OQC path to fault-tolerance. Collaborations underway for micro-, nano- and adaptive optics. QCCM: Optical Quantum Computing Andrew White, University of Queensland http://quantum.info/ Develop optical quantum computing using both linear and nonlinear methods. Evaluate scalability of optical quantum computing. 82.5% ±1.5% 97.7% ±1.5% Ideal Experiment Model 85.1%

2. Yr 1Demonstration of cluster states with 3 or 4 qubits (>70% fidelity) Yr 2 Logic operations using cluster states (without feed-forward) (>70% fidelity) Lanyon et al., Experimental Demonstration of Shor’s Algorithm with Quantum Entanglement, PRL 99, 250505 (2007). F = 68 ± 4%. Yr 1Two-photon absorption analysis and experiments Myers and Gilchrist, Photon-loss-tolerant Zeno controlled-SIGN gate, PRA 75, 052339 (2007) Yr 2Improved sources of entangled photons, realizing HOM visibility above 95% continuous: Biggerstaff et al, Experimental violation of Bell’s original inequality, PRL, under review (2008). T = 98.3 ± 3.3%. pulsed: under development, HOM V ~ 78%. Yr 1Develop more efficient methods for device characterization Lanyon et al., PRL 99, 250505 (2007). Weinhold et al., Error budgets for quantum logic gates: the road to fault tolerance, Nature Physics, under review (2008). Yr 2Construction of error-models for the major errors in cluster state and parity encoding LOQC architectures/schemes Weinhold et al, Nature Physics, under review (2008). F=96.7 ± 1.5% Yr 1Demonstration of an entangling circuit using micro-optics (>80% fidelity) Yr 2Design and test integrated optics circuits Effort moved to Bristol with Associate-Professor J. L. O’Brien Yr 2Analysis of quantum logic based on weak nonlinearities Yr 2Encode a logical qubit in 3 or 4 physical qubits (>70% fidelity) Yr 2Theoretical analysis of techniques to make cluster states robust against noise Underway at Vienna. R. Prevedel et al., PRL 99, 250503 (2007). Yr 4Feasibility analysis of a scaleable optical quantum computer Weinhold et al., Nature Physics, under review (2008) Lanyon et al., Quantum computing using shortcuts through higher dimensions, Nature Physics, submitted (2008). UQ Milestones

3. quantum.info Dr Marco Barbieri Dr Marcelo Almeida Ben Lanyon Prof. Alexei Gilchrist Till Weinhold Dr Nathan Langford Devon Biggerstaff Geoff Gillett Rohan Dalton Prof. Kevin Resch Prof. Jeremy O’BrienDr Geoffrey Pryde Dr Bill Munro Prof. Daniel James Prof. Paul Kwiat Dr Stephen Bartlett Dr Andrew Doherty new Postdoc In July Dr Mike Goggin Dr Thomas JenneweinJames Owens Prof. Andrew White

4. Introduction to optical quantum computing

5. quantum.info Optical qubits need photons Spontaneous Parametric Downconversion Conditional 1-photon per mode Takeuchi, Optics Letters 26, 843 (2001) Kurtsiefer et al., J. Mod. Opt. 48, 1997 (2001) Well behaved spatial modes Coupled into single-mode fibres: true TEM 00 Bright output normalised brightness Kwiat, Type II 1995  0.0044 Kwiat, Type I 1999  1.98 Takeuchi 2001  33.3 Kurtsiefer 2001  13.3 White 2003  70.4 Kim 2006  500 Jennewein 2007  ~10 4 White 2007  ~10 5

6. quantum.info Frequency encoding Optical qubits are degrees of freedom  Single qubits “1” = +i R = = HV Polarisation encoding Spatial encoding very low intrinsic decoherence at electromagnetic frequencies useful for qudits & quantum communication Langford, et al., PRL 93, 053601 (2004) Temporal encoding tt Path encoding “0” “1” “0”

7. quantum.info 3 Single qubit gates   |H|H ( | H   | V   / √2 Hadamard gate       |H|H  | H    | V  Arbitrary rotation gate ? Two-qubit gates Requires massive nonlinearity Impossible with existing nonlinear optics Milburn, PRL 62, 2124 (1988) Optical qubits are degrees of freedom  Single qubits “1” = +i R = = HV Spatial encoding very low intrinsic decoherence at electromagnetic frequencies useful for qudits & quantum communication Langford, et al., PRL 93, 053601 (2004) “0” Polarisation encoding

8. quantum.info Longest decoherence times of any architecture467 µs (141km)QCCM Vienna Entangling gates via measurement Knill, Laflamme and Milburn, Nature 409, 46 (2001) Fastest gate times of any architecture 145 nsQCCM Vienna

9. quantum.info + teleportation + error correction = scalable QC Internal ancillas Simplified 2-photon Ralph, Langford, Bell, & White, PRA 65, 062324 (2002) Simplified 2-photon Hofmann & Takeuchi, PRA 66, 024308 (2002) Linear-optical QND Kok, Lee & Dowling, PRA 66, 063814 (2002) External ancillas Gasparoni et al., PRL 93, 020504 (2004) Pittman et al., PRA 68, 032316 (2004) Walther et al., Nature 434, 169 (2005) KLM 4-photon Knill, Laflamme, & Milburn, Nature 409, 46 (2001) Entangled ancilla 4-photon Pittman, Jacobs, and Franson, PRL 88, 257902 (2002) Simplified 4-photon Ralph, White, Munro, & Milburn, PRA 65, 012314 (2001) Efficient 4-photon Knill, PRA 66, 052306 (2002) Entangled input 2-photon Pittman, Jacobs, and Franson, PRL 88, 257902 (2002) Proposed entangling gates

10. quantum.info CZ qubit Two scalable architectures Nielsen, PRL 93, 040503 (2004) conventional circuit Raussendorf and Briegel, PRL 86, 5188 (2001) qubit CZ Uz(1)Uz(1)Uz(2)Uz(2)Uz(3)Uz(3)Uz(4)Uz(4) Uz(1)Uz(1)Uz(2)Uz(2)Uz(3)Uz(3)Uz(4)Uz(4) Uz(1)Uz(1)Uz(2)Uz(2)Uz(3)Uz(3)Uz(4)Uz(4) single qubit gates two-qubit (entangling) gates flow of quantum information 11  2  3  4 11  2  3  4 11  2  3  4 cluster/graph circuit flow of measurement info entanglementqubit measurement cos   x + sin   y

11. quantum.info Graph states (clusters and parity encoding techniques) have greatly reduced the required resources and the loss-tolerance threshold for LOQC: Resources (Bell states, operations, etc.) for a reliable entangling gate Acceptable loss for a scalable architecture OQC Anti-Moore’s Law ?

12. Building an entangling gate “In theory, there is no difference between theory and practice. – Jan L.A. van de Snepscheut (1953-1994) “In theory, there is no difference between theory and practice. – Jan L.A. van de Snepscheut (1953-1994) But, in practice, there is.”

13. quantum.info C 0 C 1 T 0 T 1 C 0 C 1 T 0 T 1 Two-qubit gate Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002)  phase shift CSIGN gate CNOT = H T + CSIGN + H T

14. quantum.info -1/3-1/3 1/31/3 1/31/3 CSIGN gate Two-qubit gate Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002)

15. quantum.info both transmitted both reflected -1/3-1/3 1/31/3 1/31/3 CSIGN gate Two-qubit gate Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002)

16. quantum.info -1/3-1/3 1/31/3 1/31/3 Control in Control out Target in Target out CNOT gate Ralph, Langford, Bell & White, PRA 65, 062324 (2002) Hofmann & Takeuchi, PRA 66, 024308 (2002) Scalable gate designs

17. quantum.info Jamin-Lebedeff interferometer: very stable, insensitive to x-y-z translation Non-classical interference O’Brien, Pryde, et al., Nature 426, 264 (2003) Scalable gate designs Interferometric gates C T R H = 1 / 3 R V = 1 Langford et al., PRL 95, 210504 (2005) Okamoto et al., PRL 95, 210505 (2005) Kiesel et al., PRL 95, 210506 (2005) Non-classical interference Partially-polarising beamsplitter gates 3 Single-path interference  Fixed beamsplitters 3 Adjustable beamsplitters  Dual-path interference both designs suitable for micro-optics*

18. quantum.info 2 photon cluster 1 2 Non-classical interference between  H  1 &  H  2 Non-classical interference between  V  2 &  H  3 3 photon cluster 3 3 Repeat unit 12 Building graph states

19. Yr 1Demonstration of cluster states with 3 or 4 qubits (>70% fidelity) Yr 2 Logic operations using cluster states (without feed-forward) (>70% fidelity) Lanyon et al., Experimental Demonstration of Shor’s Algorithm with Quantum Entanglement, PRL 99, 250505 (2007). F = 68 ± 4%. Yr 1Two-photon absorption analysis and experiments Myers and Gilchrist, Photon-loss-tolerant Zeno controlled-SIGN gate, PRA 75, 052339 (2007) Yr 2Improved sources of entangled photons, realizing HOM visibility above 95% continuous: Biggerstaff et al, Experimental violation of Bell’s original inequality, PRL, under review (2008). T = 98.3 ± 3.3%. pulsed: under development, HOM V ~ 78%. Yr 1Develop more efficient methods for device characterization Lanyon et al., PRL 99, 250505 (2007). Weinhold et al., Error budgets for quantum logic gates: the road to fault tolerance, Nature Physics, under review (2008). Yr 2Construction of error-models for the major errors in cluster state and parity encoding LOQC architectures/schemes Weinhold et al, Nature Physics, under review (2008). F=96.7 ± 1.5% Yr 1Demonstration of an entangling circuit using micro-optics (>80% fidelity) Yr 2Design and test integrated optics circuits Effort moved to Bristol with Associate-Professor J. L. O’Brien Yr 2Analysis of quantum logic based on weak nonlinearities Yr 2Encode a logical qubit in 3 or 4 physical qubits (>70% fidelity) Yr 2Theoretical analysis of techniques to make cluster states robust against noise Underway at Vienna. R. Prevedel et al., PRL 99, 250503 (2007). Yr 4Feasibility analysis of a scaleable optical quantum computer Weinhold et al., Nature Physics, under review (2008) Lanyon et al., Quantum computing using shortcuts through higher dimensions, Nature Physics, submitted (2008). UQ Milestones

20. Shor’s algorithm

21. quantum.info Shor’s algorithm Many cryptographic protocols on difficulty of finding the prime factors of a large number Factors a composite number, N, into constituent primes Beckman et al, PRA 54, 1034 (1996)Shor, Proc. 35th Ann. Symp. Found. Comp. Sci., 124, 1994 Problem! Factoring a k-bit number requires 72k 3 elementary quantum gates* elementary = 1, 2, and 3 qubit gates Randomly choose a co-prime, C, where 1<C<N Greatest common divisor of C & N must be 1 Use a quantum routine to find order, r, of C modulo N:C r mod N =1 Classical processing finds factors from r: GCD of C r/2 ±1 and N

22. quantum.info Full algorithm requires 4608 gates: Preskill’s solution compile argument function Beckman et al, PRA 54, 1034 (1996) N = 15 C=4 C=2 Partially-compiled version done in NMR, but… Vandersypen et al., Nature 414, 883 (2001) Braunstein et al., PRL 83, 1054 (1999) Menicucci et al., PRL 88, 167901 (2002) classical states: no entangled states classical dynamics: no entangling processes no quantum routine! 0 0 0 1 0 top rail redundant! order-2order-4 Compile further since function input=1, replace CSWAPs with CNOTs Factoring 15

23. quantum.info Compile further since function input=1, replace CSWAPs with CNOTs argument function N = 15 C=4 C=2 Full compile since function output only two values, 4 0 =1 or 4 1 =4 0 0 0 1 0 1 N = 15 C=4 C=2 function register encodes r values in log C r qubits * * We experimentally implemented circuits marked with * order-2order-4 order-2order-4 Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007) Lu, Browne, Yang, and Pan PRL 99, 250504 (2007) * Factoring 15

24. quantum.info 4-photon source Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007) Shor’s Circuits

25. quantum.info Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007) 4-photon source Shor’s Circuits

26. quantum.info Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007) * order-2 order-4 Shor’s Circuits

27. quantum.info * order-2order-4 order-2 order-4 Shor’s Circuits Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007)

28. quantum.info order-2 F = 99.9 ± 0.3% S L = 99.9 ± 0.6% add redundant bit then reverse argument bits P 10 = 48 ± 3% P 00 = 52 ± 3% failure Order-finding algortihm is non-deterministic: output state is mixed 32 1 ±1 341 = 11, 31 128 1 ±1 5 461 = 43, 127 131072 1 ±1 43691, 5 726 623 061 = 131071 GCD of C r/2 ±1 and N GCD of 4 1 ±1 and 15 = 3,5 r=2 Algorithm outputs Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007)

29. quantum.info GCD of C r/2 ±1 and N GCD of 4 1 ±1 and 15 = 3,5 P 110 = 27 ± 2% order-2order-4 F = 99.9 ± 0.3% S L = 99.9 ± 0.6% F = 98.5 ± 0.6% S L = 98.1 ± 0.8% P 000 = 27 ± 2% P 100 = 24 ± 2% add redundant bit then reverse argument bits P 10 = 48 ± 3% r=6 GCD of 4 3 ±1 and 15 = 3,5 r=2 P 010 = 23 ± 2% algorithm works near perfectly …? Order-finding algortihm uses mixed output state: non-deterministic GCD of C r/2 ±1 and N GCD of 4 1 ±1 and 15 = 3,5 r=2 Algorithm outputs Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007)

30. quantum.info Circuit performance Algorithm performance cannot distinguish between: mixture from desired entanglement with function-register mixture from undesired entanglement with environment Circuit performance is crucial when used as sub-routine in a larger algorithm measure with quantum state tomography order-2 order-4 states are both entangled & mixed F GHZ = 59 ± 4%S L = 62 ± 4% W GHZ = 9 ± 4% F 2Bell = 68 ± 3%S L = 52 ± 4% T bd = 41 ± 5%T ce = 33 ± 5% circuit does not work perfectly Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007)

31. quantum.info Circuit outputs Process and state tomography impractical for large circuits requires 2 4n and 2 2n measurements Check correlations: state is argument and function registers are highly correlated after logical meas’t of argument function is measuring function register requires only 2 n measurements order-2 83 ± 4% 59 ± 5% 000 010 0000 0001 0100 0101 order-4 000 001 010 011 87 ± 3% 84 ± 4% 82 ± 5% 67 ± 6% performance: quantum algorithm ≠ underlying quantum circuit urgent need to develop efficient diagnostic methods for large quantum circuits Lanyon, Weinhold, Langford, Barbieri, James, Gilchrist, and White, PRL 99, 250505 (2007)

32. Yr 1Demonstration of cluster states with 3 or 4 qubits (>70% fidelity) Yr 2 Logic operations using cluster states (without feed-forward) (>70% fidelity) Lanyon et al., Experimental Demonstration of Shor’s Algorithm with Quantum Entanglement, PRL 99, 250505 (2007). F = 68 ± 4%. Yr 1Two-photon absorption analysis and experiments Myers and Gilchrist, Photon-loss-tolerant Zeno controlled-SIGN gate, PRA 75, 052339 (2007) Yr 2Improved sources of entangled photons, realizing HOM visibility above 95% continuous: Biggerstaff et al, Experimental violation of Bell’s original inequality, PRL, under review (2008). T = 98.3 ± 3.3%. pulsed: under development, HOM V ~ 78%. Yr 1Develop more efficient methods for device characterization Lanyon et al., PRL 99, 250505 (2007). Weinhold et al., Error budgets for quantum logic gates: the road to fault tolerance, Nature Physics, under review (2008). Yr 2Construction of error-models for the major errors in cluster state and parity encoding LOQC architectures/schemes Weinhold et al, Nature Physics, under review (2008). F=96.7 ± 1.5% Yr 1Demonstration of an entangling circuit using micro-optics (>80% fidelity) Yr 2Design and test integrated optics circuits Effort moved to Bristol with Associate-Professor J. L. O’Brien Yr 2Analysis of quantum logic based on weak nonlinearities Yr 2Encode a logical qubit in 3 or 4 physical qubits (>70% fidelity) Yr 2Theoretical analysis of techniques to make cluster states robust against noise Underway at Vienna. R. Prevedel et al., PRL 99, 250503 (2007). Yr 4Feasibility analysis of a scaleable optical quantum computer Weinhold et al., Nature Physics, under review (2008) Lanyon et al., Quantum computing using shortcuts through higher dimensions, Nature Physics, submitted (2008). UQ Milestones

33. quantum.info Improved Sources

34. quantum.info bright: 1,600 pairs.s -1 @ 2.5mW,   = 1 nm Photon Sources HWP PBS PPKTP DM fibre coupler IF polarization analysis diode laser T. Kim et al., PRA 73, 012316 (2005) fibre coupler 640 pairs (s.mW.nm) -1 Continuous entangled source entangled and very pure Purity 0.993 Tangle 0.983 Fidelity 0.995 very bright: 360,000 pairs.s -1 @ 6mW, no filters brightness = 60,000 pairs (s.mW) -1 * Pulsed sources, under development why so low ? no entanglement, HOM visibility ~ 78% Continuous source test entanglement with Bell and Mermin inequalities distingushability … compensation? Biggerstaff et al., PRL, under review (2008)

35. quantum.info Bell’s original formulation holds only when in real cases A B C B Bob Alice Bell’s and Mermin’s inequalities is the “correlation deficit” for a fraction Assume the worst: then: Our source: A B C A B C Mermin’s stronger inequality Worst case scenario: Quantum prediction: 3 Our source: 2.968±0.023 Classical prediction:2.0746 source is bloody entangled Biggerstaff et al., PRL, under review (2008)

36. Yr 1Demonstration of cluster states with 3 or 4 qubits (>70% fidelity) Yr 2 Logic operations using cluster states (without feed-forward) (>70% fidelity) Lanyon et al., Experimental Demonstration of Shor’s Algorithm with Quantum Entanglement, PRL 99, 250505 (2007). F = 68 ± 4%. Yr 1Two-photon absorption analysis and experiments Myers and Gilchrist, Photon-loss-tolerant Zeno controlled-SIGN gate, PRA 75, 052339 (2007) Yr 2Improved sources of entangled photons, realizing HOM visibility above 95% continuous: Biggerstaff et al, Experimental violation of Bell’s original inequality, PRL, under review (2008). T = 98.3 ± 3.3%. pulsed: under development, HOM V ~ 78%. Yr 1Develop more efficient methods for device characterization Lanyon et al., PRL 99, 250505 (2007). Weinhold et al., Error budgets for quantum logic gates: the road to fault tolerance, Nature Physics, under review (2008). Yr 2Construction of error-models for the major errors in cluster state and parity encoding LOQC architectures/schemes Weinhold et al, Nature Physics, under review (2008). F=96.7 ± 1.5% Yr 1Demonstration of an entangling circuit using micro-optics (>80% fidelity) Yr 2Design and test integrated optics circuits Effort moved to Bristol with Associate-Professor J. L. O’Brien Yr 2Analysis of quantum logic based on weak nonlinearities Yr 2Encode a logical qubit in 3 or 4 physical qubits (>70% fidelity) Yr 2Theoretical analysis of techniques to make cluster states robust against noise Underway at Vienna. R. Prevedel et al., PRL 99, 250503 (2007). Yr 4Feasibility analysis of a scaleable optical quantum computer Weinhold et al., Nature Physics, under review (2008) Lanyon et al., Quantum computing using shortcuts through higher dimensions, Nature Physics, submitted (2008). UQ Milestones

37. quantum.info Shortcuts through higher dimensions

38. quantum.info Key quantum circuits Clifford: CX, CZ, CH, CP, CNOT… classically simulatable S = P 1/2 ToffoliH + + ValiantSWAP + classically simulatable universal gate set Josza 2006: what is the least quantum resource add-on to classical computation required for universal QC? In addition: controlled- U gates, used in phase estimation, quantum chemistry.. Toffoli gates, used in error correction, fault tolerance… 1 0 0 e i  P= Even small quantum algorithms require large numbers of CU and Toffoli gates multiplexed full adder multiplexed k-bit adder

39. quantum.info Harnessing higher dimensions Toffoli Scaling: Toffoli controlled-U Using traditional ~n 2 ~n 2 n qubits previous best12n-11 12n-10 n-1 ancilla qubits our new technique 2n-1 2n qubit-qudit transforms Works by coherently isolating some quantum information from gate actions Toffoli R = I CU R = Z  how does X a work? transforms qubit to qudit optical example Lanyon et al., Nature Physics, under review (2008)

40. quantum.info Harnessing higher dimensions Powerful technique for simply generating complex circuits: triple-control Toffoli, 3 TS doubly-controlled unitary, C 2 U triply-controlled unitary on k-qubits, C 3 (U k ) Lanyon et al., Nature Physics, under review (2008)

41. quantum.info Example with linear-optical gates C1C1 C1C1 C2C2 C2C2 T T Lanyon et al., Nature Physics, under review (2008)

42. quantum.info Toffoli Truth table inquisition, 81 ± 3% Coherent operation: state measurements Ideal Output  1,0+1,0 〉  0,0+1,0 〉 InputOutput  0+1,1,0 〉  0+1,0,0 〉 InputOutput 90±4% 75±6% 81±2% 80±3% Lanyon et al., Nature Physics, under review (2008)

43. quantum.info CT gate,  F p = 98.2±0.3% F p = 97.7±0.4% F p = 94.0±0.6% F p = 95.6±0.3% Controlled-unitary gates CJ gate,  CL gate,  CZ gate,  Lanyon et al., Nature Physics, under review (2008) technique allows more efficient use of universal resource, be they gate sets or clusters

44. Yr 1Demonstration of cluster states with 3 or 4 qubits (>70% fidelity) Yr 2 Logic operations using cluster states (without feed-forward) (>70% fidelity) Lanyon et al., Experimental Demonstration of Shor’s Algorithm with Quantum Entanglement, PRL 99, 250505 (2007). F = 68 ± 4%. Yr 1Two-photon absorption analysis and experiments Myers and Gilchrist, Photon-loss-tolerant Zeno controlled-SIGN gate, PRA 75, 052339 (2007) Yr 2Improved sources of entangled photons, realizing HOM visibility above 95% continuous: Biggerstaff et al, Experimental violation of Bell’s original inequality, PRL, under review (2008). T = 98.3 ± 3.3%. pulsed: under development, HOM V ~ 78%. Yr 1Develop more efficient methods for device characterization Lanyon et al., PRL 99, 250505 (2007). Weinhold et al., Error budgets for quantum logic gates: the road to fault tolerance, Nature Physics, under review (2008). Yr 2Construction of error-models for the major errors in cluster state and parity encoding LOQC architectures/schemes Weinhold et al, Nature Physics, under review (2008). F=96.7 ± 1.5% Yr 1Demonstration of an entangling circuit using micro-optics (>80% fidelity) Yr 2Design and test integrated optics circuits Effort moved to Bristol with Associate-Professor J. L. O’Brien Yr 2Analysis of quantum logic based on weak nonlinearities Yr 2Encode a logical qubit in 3 or 4 physical qubits (>70% fidelity) Yr 2Theoretical analysis of techniques to make cluster states robust against noise Underway at Vienna. R. Prevedel et al., PRL 99, 250503 (2007). Yr 4Feasibility analysis of a scaleable optical quantum computer Weinhold et al., Nature Physics, under review (2008) Lanyon et al., Quantum computing using shortcuts through higher dimensions, Nature Physics, submitted (2008). UQ Milestones

45. quantum.info The road to fault tolerance

46. quantum.info Fault tolerance thresholds Calculating thresholds is difficult: based on error-per-gate assumptions are always necessary optimistic simple errors higher thresholds numerical Two approaches pessimistic complex errors lower thresholds analytical and numerical Knill, Nature 434, 39 (2005) Aliferis, Gottesman, & Preskill, Quant. Inf. Comput. 6, 97 (2006) independent random Pauli errors independent stochastic noise gremlin adds unwanted process on any qubit at any step with probability p in large circuits, errors unlikely to add in best or worst possible way completely-positive process, CP Pauli process X, Y, Z

47. quantum.info Choose basis where first element of  -matrix represents ideal gate Measuring error-per-gate probabilities Weinhold, Gilchrist, Doherty, Resch, and White, Nature Physics, under review (2007) Process for ideal CZ gate Minimum gate error is height is process fidelity error probabilities Can measure F p with process witness F p witness ~ 60 measurements tomography > 256 measurements F p is process fidelity: overlap between ideal & exp processes If coherences are zero, error-probability-per-gate is Otherwise need to solve much harder, needs dual optimisation technique State-of-the-art: lower and upper bounds to gate error

48. quantum.info F = (89.3 ± 0.1) % Model source assumes photons are perfectly indistinguishable mode-matching is same only source is different + gate model based on measured parameters Independent photons Weinhold, Gilchrist, Doherty, Resch, and White, Nature Physics, under review (2007) dependent photons: not scalable CZ F = (82.5 ± 1.5) % independent photons: scalable CZ Photon sources & scalabiliy

49. quantum.info 21.8% ±1.5% experiment ideal srce (2+3) 2.8 % all (1+2+3)18.6 % Two-qubit controlled-Z gate we model: ideal 0 % 1-F p Weinhold, Gilchrist, Doherty, Resch, and White, Nature Physics, under review (2007) 2.Beamsplitter reflectivities,  =1-2% 3.Photon loss, 90-97% 1. Independent downconversion, 0.3-0.8% higher order terms All values measured

50. quantum.info 82.5% ±1.5% 85.1% 97.7% ±1.5% Ideal ExpModel Independent photons & a single gate

51. quantum.info 21.8% ±1.5% experiment ideal srce (2+3) 2.8 % all (1+2+3)18.6 % we model: model predicts that with good photon source & optics experimental gate error is:  g ~ 3.2 ± 1.5 % c.f. Knill’s tolerance threshold:  0 ≤ 6 % 2.Beamsplitter reflectivities,  =1- 2% 3.Photon loss, 90-97% photon source   15.8% mode mismatch   3.2% ideal 0 % 1-F p Two-qubit controlled-Z gate 1. Independent downconversion, 0.3-0.8% higher order terms All values measured Weinhold, Gilchrist, Doherty, Resch, and White, Nature Physics, under review (2007) source and detector development is criticial ordered $150k cryostat for July 2008 (Oz funded)+ working with Sae Woo Nam

52. Yr 1Demonstration of cluster states with 3 or 4 qubits (>70% fidelity) Yr 2 Logic operations using cluster states (without feed-forward) (>70% fidelity) Lanyon et al., Experimental Demonstration of Shor’s Algorithm with Quantum Entanglement, PRL 99, 250505 (2007). F = 68 ± 4%. Yr 1Two-photon absorption analysis and experiments Myers and Gilchrist, Photon-loss-tolerant Zeno controlled-SIGN gate, PRA 75, 052339 (2007) Yr 2Improved sources of entangled photons, realizing HOM visibility above 95% continuous: Biggerstaff et al, Experimental violation of Bell’s original inequality, PRL, under review (2008). T = 98.3 ± 3.3%. pulsed: under development, HOM V ~ 78%. Yr 1Develop more efficient methods for device characterization Lanyon et al., PRL 99, 250505 (2007). Weinhold et al., Error budgets for quantum logic gates: the road to fault tolerance, Nature Physics, under review (2008). Yr 2Construction of error-models for the major errors in cluster state and parity encoding LOQC architectures/schemes Weinhold et al, Nature Physics, under review (2008). F=96.7 ± 1.5% Yr 1Demonstration of an entangling circuit using micro-optics (>80% fidelity) Yr 2Design and test integrated optics circuits Effort moved to Bristol with Associate-Professor J. L. O’Brien Yr 2Analysis of quantum logic based on weak nonlinearities Yr 2Encode a logical qubit in 3 or 4 physical qubits (>70% fidelity) Yr 2Theoretical analysis of techniques to make cluster states robust against noise Underway at Vienna. R. Prevedel et al., PRL 99, 250503 (2007). Yr 4Feasibility analysis of a scaleable optical quantum computer Weinhold et al., Nature Physics, under review (2008) Lanyon et al., Quantum computing using shortcuts through higher dimensions, Nature Physics, submitted (2008). UQ Milestones

53. Nonlinear optical quantum computing

54. quantum.info Entangler Homodyne classical feedforward H H V V Measurement & nonlinearities 2004Barrett, et al.: amplify weak optical nonlinearities using measurement Barrett et al., PRA 71, 060302R (2005) H V 2004Nemoto & Munro: deterministic CNOT gate Nemoto and Munro, PRL 93, 250502 (2004) V H

55. quantum.info Measurement & nonlinearities  (2) nonlinearities: effect is 10 5 –10 8 times stronger than with intrinsic  (3) nonlinearities     (2) Cascaded  (2) nonlinearities = Kerr effect   (2) White, Mlynek and Schiller, Europhysics Letters 35, 425 (1996) –test with continuous pump –fs pulses probably too short, ps pulses?

56. quantum.info Research plan for Years 3 & 4 – Milestones Logic operations using cluster states with feed- forward, F > 80% Cluster state with 6-8 qubits, F>80% Adapt fault-tolerant constructions to specific error models in LOQC, evaluate required overhead Development of circuit design software Approximate methods for error characterization Two-photon absorption experiments: demonstrate >80% 2PA for Zeno gates, e.g., using fiber nanocavities. Theoretical optimization of techniques/materials for exploiting non-linearities in OQC, e.g. via quantum Zeno effect, QND; construction of error-models for the major errors in weak-nonlinearity OQC schemes Demonstration of Zeno logic gates Demonstration of QND device at single-photon level (system to be determined) Larger-scale circuits (5 qubits) using cluster states and/or Zeno gates, encode logical qubit Theoretical investigation and evaluation of techniques for reliable, single-mode single-photon sources Develop improved sources of entangled photons (i.e, controlled spectral properties for improved HOM- interference, >95% visibility, from independent sources, turnkey systems, etc.);generation of heralded entangled pairs (10 4 Hz, F>75%) Design, simulate & test micro-, integrated, and adaptive optics Research and assemble mode-matching enhancement system; improve spatial mode-matching efficiency from current 85% to as much as 98% with adaptive optics Transition to high-efficiency holographic elements, demonstrate mode-matching efficiency of 95% Incorporate sources, detectors, and memory from other programs Demonstration of a CNOT gate without nonlocal photon filtering (not in coincidence) Feasibility analysis for scalable OQC Yr 3 Analysis of quantum logic based on weak nonlinearities cascaded  (2) Kerr effect with coherent → single photon beams QCCM: Years 3 & 4 Yr 3 Generation of 5 and 6 qubit entanglement improved brightness PDC or adopt heralded sources á la Migdal, 5/6 qubit clusters with bulk and integrated optics Yr 4 Applying active feedback to cluster states active schemes under development

57. propose use this for next QCCM planning meeting http://quantum.info/cairns

58. quantum.info single photon detectors quantum state engineering quantum information processing quantum communication quantum control quantum metrology quantum measurement PRL 90 193601 (2003) Nature 426, 264 (2003) PRL 92, 190402 (2004) PRL 93, 053601 (2004) PRL 93, 080502 (2004) PRL 94, 220405 (2005) PRL 94, 220406 (2005) PRL 95, 048902 (2005) PRL 95, 210504 (2005) Nature 445, E4 (2007) PRL 98, 203602 (2007) PRL 98, 223601 (2007) PRL 99, 250505 (2007) PRL 100, in press (2007) …and submitted… PRL x 1 Nature Physics x 2 … IARPA / DTO / ARDA funded research 2003–08 Thank you!