Quantum Computing with Para-hydrogen

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1 Quantum Computing with Para-hydrogen Muhammad Sabieh Anwar International Conference on Quantum Information, Institute of Physics, Bhubaneswar, March 12, 28 Joint work with: J.A. Jones (Oxford) and S.B. Duckett (York)

5 Contents Entanglement in two qubit mixed states Quantum computing with mixed states? The problem of initialization Pure and entangled states with para-hydrogen Purity sharing

6 Entanglement in two qubit mixed states

7 Entanglement: Pure States Separable ψ AB = φ A χ B = ( 1 ) / 2 ( 1 ) / 2 ( = ( 1 ) / 2 i 1 ) / 2 = ( i 1 1 i 11 ) / 2 Entangled ψ AB φ A χ B ϕ = ( 11 ) / 2 ϕ = ( 11 ) / 2 Bell or EPR States ψ = ( 1 1 ) / 2 ψ = ( 1 1 ) / 2

8 Entanglement and Density Matrices 1 Density matrix ρ ρ AB = k λ k ψ AB ψ AB Pure and mixed states Density matrices of the Bell States 1/ 2 ( 11 ) / 2 ρ = 1/ 2 1/ 2 1/ 2 ( 1 1 ) / 2 ρ = 1/ 2 1/ 2 1/ 2 1/ 2

9 Entanglement and Density Matrices 2 Maximally mixed state Maximally mixed state 11 ) / ( 1/ 1/ 1/ 1/ = = ρ 1 ) / ( = Another mixed state Another mixed state 2 2) / 1 ) / )( 1 ( ( 1/ 1/ 1/ 3/ = = ρ

10 Entanglement and Density Matrices 3 Separable density matrix ρ η ( ρ ρ AB = k A B ) k k Convex sum of direct product states Entangled density matrix ρ η ( ρ ρ AB k A B ) k k

11 Detecting and Quantifying Entanglement 1 Can we find a separable decomposition of? ρ = ρ 11 ) / ( 1/ 1/ 1/ 1/ = = ρ ) / ( = ψ ψ ψ ψ ϕ ϕ ϕ ϕ Ensemble fallacy D. T. Pegg, J. Jeffers J. Mod. Opt. 52, 1835 (25)

12 Detecting and Quantifying Entanglement 2 2 ) / ( 2 1/ 2 1/ = = ρ 2 ) / ( = ψ ψ ψ ψ

13 Test for Separability PPT Test ψ ρ = ψ T ρ = 1/ ψ 1/ 2 = 2( 1/ 2 = 1/ 2 1/ / 2 ) 1/ 2 1/ 2 1/ 2 Eigenvalues of ρ T are {1/2,1/2,1/2,-1/2}. ρ is non-separable or entangled. A. Peres Phys. Rev. Lett. 77, 113 (1996)

14 Separability of the Werner State Eigenvalues Eigenvalues of PPT of of PPT of ρ are {1/(1-3ε),1/(1 ε), 1/(1 ε), 1/(1 ε)}. ρ is non is non-separable or entangled only if separable or entangled only if ε > 1/3 > 1/3. ρ = (1-ε)1/ / ε ψ - >< ψ - Werner or pseudopure state = = ε ε ε ε ε ε ρ ε ε ε ε ε ε T

15 The problem of initialization

16 Requirements for Practical QC Existence of Qubits Initialization Universal Quantum Networks Read-out or Measure Decoherence D.P. DiVincenzo quant-ph/277 (2)

17 Initialization 1 NMR states are highly mixed. Pure Mixed > 1> = = 1 ρ Ideal initial state

18 Initialization 2 1> E > Thermal equilibrium state.251 ρ = ρ eq = exp(-βh)/z where β=ħ/(k B T) E = γħb z = ħω = J k B T= 1-21 J at 1T, 3K Population difference only ~ k B T >> E ={{1/B,1/,1/,1/-B}}= }}=1/B/(I/(I z S z ) where B = ħω / kt.

19 Initialization 3 B Net Magnetic Moment Thermal Equilibrium

20 Pseudopure States Thermal equilibrium state 1 Ideal initial state Pseudopure state ρ ps = (1-ε)1/ ε ψ>< ψ ε is polarization. E = Thermal, mixed Maximally mixed Pure

21 Spin Temperature 1> > COLD 1> > COLD 1> > HOT

22 Problems with Pseudopure States Scalability Is NMR quantum mechanical at all? S.L. Braunstein et al. Phys. Rev. Lett. 83, (1999) J.A. Jones, Fortsch. der Physik 8, 99 (22).

23 Climbing Mount Scalable

24 Scalability Maximum pure state that can be extracted from thermal state ρ ps =(1-ε) 1 / 2 n ε ψ>< ψ Warren proposed a theoretical maximum on ε: ε ~ nb / (2 n ) where n is the number of qubits. 11> 1> 2 1> > W.S.Warren Science 277, 1688 (1997).

25 Scalability and Separability 1/(12 n/2 ) 1/(12 2n-1 ) n B / (2 n ) E ES S Present day NMR implementations work in region S. We can enter ES if n > 11 (room temperature, 1T). We may never enter E with thermal states!

26 Methods for Increasing Polarization High fields and low temperature B = ħω / kt Algorithmic concentration of polarization Polarization transfer from nuclear spins Polarization transfer from electron spins Chemically induced dynamical nuclear polarization (CIDNP)

27 Is an NMR Device a Quantum Computer? No entanglement What makes a quantum computer quantum? States or Dynamics? Scaling of the Hilbert space dimensionality? Superposition? Other models of better than classical computing.

28 The para-hydrogen approach

29 Para-hydrogen Induced Polarization 1 Need for non-thermal distributions Symmetrization postulate ψ> t = ψ> tr ψ> vib ψ> e ψ> ns ψ> r ψ> ns T 1 >= > T >=1/2 1/2 ( 1> 1>) S >=1/2 1/2 ( 1>- 1>) T -1 >= 1> ψ> r j=1,3,5, odd j=,2,, even (Y j m (π-θ, πϕ)=( )=(-1) j Y j m (θ, ϕ))

30 Para-hydrogen Induced Polarization 2 j ψ rot > ψ ns > o/p s symmetrical a asymmetrical p 1 a s o 2 s a p 3 a s o

31 Making Parahydrogen Para-hydrogen once is para-hydrogen forever!

32 Para-hydrogen Quantum Computer Cl The PASADENA Experiment H 12 C pairwise addition assymetric environment enhanced polarizations

33 Example PASADENA spectrum Rh H Before After

34 Experimental Setup

35 Schematic setup for the PASADENA Experiment

36 Some photographs depicting various units in the experiement

37 Flash Photolysis D. Blazina et al. Magn. Reson. Chem. 3, 2 (25)

38 PHIP Spectra Spin Temperature = 6. mk Effective Field =.5 MT ε =.916 1/ Tomography results Ideal singlet

39 The NMR Experiment M.S. Anwar et al. Phys. Rev. Lett. 93, 51 (2) M.S. Anwar et al. Phys. Rev. A 71, (25)

40 Grover s algorithm

41 Classical Deutsch s Algorithm: f(1)

42 Quantum Deutsch s Algorithm M.S. Anwar et al. Phys. Rev. A 7, 3232 (2)

43 Quantum Deutsch s Algorithm M.S. Anwar et al. Phys. Rev. A 7, 3232 (2)

44 Purity dilution

45 Purity Sharing 1 M.S. Anwar et al. Phys. Rev. A 73, (26)

46 Purity Sharing 2

47 Purity Sharing 3

Some Introductory Notes on Quantum Computing

Some Introductory Notes on Quantum Computing Markus G. Kuhn http://www.cl.cam.ac.uk/~mgk25/ Computer Laboratory University of Cambridge 2000-04-07 1 Quantum Computing Notation Quantum Computing is best