Algorithmic Cooling in Liquid-state NMR Yuval Elias / Gilles Brassard Group NTRQ Meeting November 2015 Château Bromont Algorithmic Cooling in Liquid-state NMR Yuval Elias / Gilles Brassard Group NTRQ Meeting November 2015 Château Bromont Bonne-Fête Anniversaire Gilles! 15 15 15 15 http://menoummm.centerblog.net/6123670-Bonne-Fete-Anniversaire- https://s3.amazonaws.com/uploads.startups.fm/wp-content/uploads/ 2013/08/erwin-schrodinger.jpg Overview Novel Spin Cooling from Quantum Computing Spin cooling: enhancing polarization in NMR Polarization compression: generalized polarization transfer Open systems: heat-bath cooling, algorithmic cooling Heat-bath Cooling Experiments Model system: 13C-labeled trichloroethylene (TCE) 13C-labeled glutamate and glycine (Glu, Gly) Algorithmic Cooling Experiments AC in solid-state NMR AC in liquid-state NMR - building blocks AC in liquid-state NMR – process 1 (cooling C1) AC in liquid-state NMR – processes 2,3 (cooling C2, C3) Future prospects – Carbon-based Brain Spectroscopy Outline The advent of NMR quantum computing in the late 1990s led to renewed interest in entropy manipulations for spin cooling. Spin Cooling – Enhancing Polarization in NMR Polarization bias : excess polarization of spins aligned with field 1 2 0 EEEE T 0 hB 0 1 tanh2kT 2 kT 2 kT 0 2 Effective spin temperature: for any bias (also non-thermal) 11.7T (500 MHz), 25°C ~ 10-5 Spin-cooling: transient increase in polarization, beyond thermal Abragam and Goldman, Nuclear Magnetism: Order and Disorder (1982) Polarization Compression Shannon’s bound on total entropy Shannon, Bell Syst. Tech. J. (1948) H( X ) p log 1 i 2 pi Coin flip: H(fair) = 1; H(¼,¾) = 0.811; H(heads) = 0 Fair biased coin: flip twice, use first toss if different J. von Neumann, Appl. Math. Ser. (1951). NMR: rf pulses for optimal polarization transfer Sørensen, Prog. Nucl. Mag. Res. Spec. (1989) “Molecular scale heat engine”: loss-less data compression Schulman & Vazirani, Proc. 31st ACM Symp. Theory Comput. (1999) Polarization Compression – Shannon’s Bound Shannon’s bound on single spin entropy: 11 1 2 H(1) p logpp p log 1 ln4 Shannon’s bound for n spin-system: 2 2 H() n nH (1) n 1 11max (1)1 n n ln 4 ln 4 max Over a billion spins required to produce one pure spin! abc P(abc) 3 3-Bit Polarization Compression 000 pp3 001 p2 a 010 p2 p 3B-Comp 011 1 a = 1.50 100 p2 101 p1 b c = = 0.5 110 p1 a =b=c= 0 b c 0 3 111 pp0 132 3 321 0 0 P a03 p p p 22 a abc 3-bit compression with non-uniform bias: a 2 Elias, Fernandez, Mor & Weinstein, Isr. J. Chem. (2006) Spin Cooling in Open Systems selective-reset(cr): PT to selected computation spin c followed by reset of reset spin r 1 Environment Reset spin ( H), eq 40 PT PT WAIT 13 Computation spins ( C), eq = 0 Assumption: computation spins relax infinitely faster than reset spins Heat-bath Cooling of Spins Heat-bath cooling: one or more selective-reset steps cool spin-system entirely or partially Reset spin (1H), 4 H eq 0 SR(HC1) SR(HC2) C2 C1 13 Computation spins ( C), eq = 0 Improved cooling of both 13C by avoiding final reset Fernandez, Lloyd, Mor & Roychowdhury, Int. J. Quant. Inf. (2004) Algorithmic Cooling of Spins Heat-bath algorithmic cooling: bypass entropy bound combine polarization compression and heat-bath cooling! Reset spin (1H), 4 H eq 0 HBC Comp Scalable NMRQC C2 C1 13 Computation spins ( C), eq = 0 = 60 beyond H(3)! PAC – practicable algorithmic cooling Boykin, Mor, Roychowdhury, Vatan & Vrijen, PNAS (2002) Fernandez, Lloyd, Mor & Roychowdhury, Int. J. Quant. Inf. (2004) Mor, Roychowdhury, Fernandez, Lloyd & Weinstein, US Patent #6,873,154 (2005) Algorithmic Cooling – Second Cooling Level Reset spin (1H), 4 H eq 0 H 3B-Comp C4 C3 C2 C1 13 Computation spins ( C), 1 = 60 2 = 90 (160) PAC with n spins (3/2)n [2n] Fernandez, Lloyd, Mor & Roychowdhury, Int. J. Quant. Inf. (2004) Spin-cooling Algorithms For n spins, one reset spin and 2Q = n-1 computation spins, ideally: leftmost - reset spin; rightmost - coldest PAC algorithm : {1 1 3/2 3/2 9/4 9/4 27/8 ... (3/2)Q} 53 resets Optimal algorithm (PPA): {1 1 2 4 8 16 32 ... 2n-2} “Fibonacci” algorithm: {1 1 2 3 5 8 13 ... Fn} “Tribonacci” algorithm: {1 1 2 4 7 13 24 ... Tn} Semi-optimal 4PAC: {1 1 1.94 1.94 3.75 3.75 7.27 } 911 resets Semi -optimal 4Fib: {1 1 1.88 2.70 4.28 6.54 10.2 } Fernandez, Lloyd, Mor & Roychowdhury, Int. J. Quant. Inf. (2004) Schulman, Mor & Weinstein, Phys. Rev. Lett. (2005) Elias, Fernandez, Mor & Weinstein, Isr. J. Chem. (2006) Elias, Mor & Weinstein, Phys. Rev. A, (2011) Relaxation-Time Ratios Reset spins should repolarize much faster than computation spins relax Preserve enhanced polarization during reset (c,r) = T1 (c) / T1 (r) >> d * Nr (#reset-steps) Preferably - (c,r) > 10*Nr (typically d ~ 1-5) Elias, Mor & Weinstein, Phys. Rev. A, (2011) Brassard, Elias, Mor & Weinstein, EPJ+ (2014) Heat-bath Cooling Model System 3.5s Cl H 13C2-TCE C1 C2 20s C1 904 T1(C1) ~ 40s 13C 13C C2 103 0 C1 C2 H 9 201 Cl Cl Non-selective (“hard”) pulses chloroform-d / acetone–d6 Paramagnetic reagent Cr(acac)3 (13C,1H) 10 T2 >> 1/J < 1 kHz hard pulses Fernandez, Mor & Weinsten, Int. J. Quant. Inf. (2005) Brassard, Elias, Fernandez, Gilboa, Jones, Mor, Weinstein & Xiao, arXiv:quant-ph/0511156 (2005) Heat-bath Cooling – POTENT pulse sequence 1) 1st Selective Reset(C1H) 2) 2nd Selective Reset(C2H) POTENT pulse sequence: Cl H POlarization Transfer via ENvironment Thermalization 13 13 C C 1 2 1H Cl Cl * 13C H C2 H C2 13C C2 C1 d2 d3 T1(H) < d2,d3 < T1(C2) < T1(C1) Brassard, Elias, Fernandez, Gilboa, Jones, Mor, Weinstein & Xiao, arXiv:quant-ph/0511156 (2005), EPJP (2014) Annotated POTENT pulse sequence Brassard, Elias, Fernandez, Gilboa, Jones, Mor, Weinstein & Xiao, EPJP (2014) Heat-bath Cooling of TCE – Entropy Reduction C2 C1 1H Cl H 13C 13C After POTENT: C1 C2 1H Cl Cl Equilibrium: Brassard, Elias, Fernandez, Gilboa, Jones, Mor, Weinstein & Xiao, EPJP (2014) Heat-bath Cooling – Amino Acids (Gly, Glu) 1) Selective Reset(C1H) 13C -Glu/Gly Gd-DTPA (Magnevist) 2) PT(C2H) 2 D2O, K3PO4, pH~8 Truncated POTENT Glutamate (Glu) – major excitatory 2.7s (1.3s) neurotransmitter, Alzheimer’s disease O H 4s (2s) 30s (13s) 13 13 + C CNH3 2 1 - O R = H, CH2CH2COOD Glycine - inhibitory neurotransmitter (low conc.) T1(H) ~ T1(C2) < d2 << T1(C1) T2 >> 1/J Short spin-selective pulses (1 ms BURP) Elias, Gilboa, Mor & Weinstein, Chem. Phys. Lett. (2011) Cooling Amino Acids Beyond the Entropy Bound O H Glycine 297K Glutamatic acid 13 13 + C C NH3 1 2 After cooling O - R 1H 1 rec Acq 13Caliphatic HCC Equilibrium HCC 1 rec d3 Acq 13Ccarbonyl d3 ~7T1(H) = 10s (Glu) / 20s (Gly) Both spin-systems cooled (C1 by 1.900.01) Elias, Gilboa, Mor & Weinstein, Chem. Phys. Lett. (2011) Heat-bath Cooling of Both Backbone Carbons O H 13C2-glutamate 310K +50 µM Magnevist 13 13 + C C NH3 1 2 O - R Truncated POTENT 1 3 1 rec 1 1 3 Acq HCC d2 d5 d3 HCC E-BURP1 E-BURP1 E-BURP1 1 rec 3 Acq d14 2 d14 d5 I-BURP1 I-BURP1 d2 = 2-3T1(H), d3 ~ T2(H) = 0.5s-1s Both carbons cooled about 2.5-fold (to ~120K) Elias, Gilboa, Mor & Weinstein, Chem. Phys. Lett. (2011) Algorithmic Cooling in Solid State NMR H H 13C3-malonic acid Hm2 Hm1 13C Spin diffusion – fast repolarization Cm (msec), T1(13C) > 100 s HOO13C 13COOH C1 C2 Numerically optimized pulses 1) 1st Selective Reset (C1Hm1) 2) 2nd Selective Reset (C2Hm1) 3) Selective PT(CmHm1) Single crystal, ~3% labeled 4) 3-Bit Compression (C1,Cm,C2) Heat-bath – protons in crystal C1 cooled by factor of 4.0 ± 0.1 C2 cooled beyond heat-bath (4.59, …, 5.58) Baugh, Moussa, Ryan, Nayak & Laflamme, Nature (2005) Ryan, Moussa, Baugh & Laflamme, Phys. Rev. A (2008) Algorithmic Cooling in Liquid-state NMR – Building Block 1 Numerically-optimized pulses (GRAPE) SIMPSON open source simulation package PE (polarization exchange) : C2 cooled by 3.76 ± 0.02 Glaser, Reiss, Kehlet & Schulte-Herbrüggen, J. Magn. Reson. (2005) Tosner, Vosegaard, Kehlet, Khaneja, Glaserd & Nielsen, J. Magn. Reson. (2009) Atia, Elias, Mor & Weinstein, Int. J. Quant. Inf. Algorithmic Cooling in Liquid-state NMR – Building Block 2 Numerically-optimized pulses (GRAPE) SIMPSON open source simulation package COMP : C1 cooled by 2.76 ± 0.02 Glaser, Reiss, Kehlet & Schulte-Herbrüggen, J. Magn. Reson. (2005) Tosner, Vosegaard, Kehlet, Khaneja, Glaserd & Nielsen, J. Magn. Reson. (2009) Atia, Elias, Mor & Weinstein, Int. J. Quant. Inf. AC in Liquid-state NMR – Process 1 Overview Cl H 13 13 C C 1 2 Cl Cl Atia, Elias, Mor & Weinstein, arXiv:1411.4641v2 [quant-ph], submitted to Phys. Rev. A AC in Liquid-state NMR – Process 1 Process 1: D1=150s, D2=5s, D3=3s Atia, Elias, Mor & Weinstein, arXiv:1411.4641v2 [quant-ph], submitted to Phys. Rev. A AC in Liquid-state NMR – Process 1 Buildup Atia, Elias, Mor & Weinstein, arXiv:1411.4641v2 [quant-ph], submitted to Phys. Rev. A AC in Liquid-state NMR – Process 1 (7 Rounds) C1 cooled by factor of about 4.6, ICC1 = 21.25 ± 0.18 Atia, Elias, Mor & Weinstein, arXiv:1411.4641v2 [quant-ph], submitted to Phys. Rev. A AC in Liquid-state NMR – Process 2 Process 2: D1=150s, D2=5s, D3=3s, D4=5s Atia, Elias, Mor & Weinstein, arXiv:1411.4641v2 [quant-ph], submitted to Phys.