Quantum versus Thermal annealing, the role of Temperature Chaos
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- Britney Gray
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1 Quantum versus Thermal annealing, the role of Temperature Chaos Víctor Martín-Mayor Dep. Física Teórica I, Universidad Complutense de Madrid Janus Collaboration In collaboration with Itay Hen (Information Sciences Institute, USC). CPRCS 2014, Capri, September V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
2 Foreword Monte Carlo is an extremely bad method; it should be used only when all alternative methods are worse. (Alan Sokal, 1989). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
3 Foreword Monte Carlo is an extremely bad method; it should be used only when all alternative methods are worse. (Alan Sokal, 1989). Such desperate problems are common in Theoretical Physics. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
4 Foreword Monte Carlo is an extremely bad method; it should be used only when all alternative methods are worse. (Alan Sokal, 1989). Such desperate problems are common in Theoretical Physics. SG simulations are extremely computer intensive but simple: the Janus collaboration has dared to produce dedicated hardware. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
5 Foreword Monte Carlo is an extremely bad method; it should be used only when all alternative methods are worse. (Alan Sokal, 1989). Such desperate problems are common in Theoretical Physics. SG simulations are extremely computer intensive but simple: the Janus collaboration has dared to produce dedicated hardware. Janus is a great success, but classical Monte Carlo is hitting an algorithmic wall (temperature chaos). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
6 Foreword Monte Carlo is an extremely bad method; it should be used only when all alternative methods are worse. (Alan Sokal, 1989). Such desperate problems are common in Theoretical Physics. SG simulations are extremely computer intensive but simple: the Janus collaboration has dared to produce dedicated hardware. Janus is a great success, but classical Monte Carlo is hitting an algorithmic wall (temperature chaos). Is quantum computing our breakthrough? V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
7 Plan of the presentation 1 Desperate problem, desperate solutions: the Janus computer. 2 The temperature chaos algorithmic wall. 3 A more conventional approach to temperature chaos. 4 D-wave, the chimera lattice and temperature chaos. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
8 The Janus Collaboration Team from 5 universities in Spain and Italy: Universidad Complutense de Madrid: M. Baity-Jesi, L.A. Fernandez, V. Martin-Mayor, A. Muñoz Sudupe Universidad de Extremadura: A. Gordillo-Guerrero, J.J. Ruiz-Lorenzo Università di Ferrara: M. Pivanti, S.F. Schifano, R. Tripiccione La Sapienza Università di Roma: A. Maiorano, E. Marinari, G. Parisi, F. Ricci-Tersenghi, D. Yllanes, B. Seoane Universidad de Zaragoza: R.A. Baños, A. Cruz, J.M. Gil-Narvión, M. Guidetti, D. Iñiguez, J. Monforte-Garcia, D. Navarro, S. Perez-Gaviro, A. Tarancon, P. Tellez. Physicists and engineers dedicated to the design and exploitation of special-purpose computers, optimised for Monte Carlo simulations in condensed matter physics. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
9 Desperate problems, desperate solutions: Janus (I) Even with binary spins, simulation of spin-glasses is heavy in two respects: 1 Many ( 10 3 ) problem instances embarrassingly parallel. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
10 Desperate problems, desperate solutions: Janus (I) Even with binary spins, simulation of spin-glasses is heavy in two respects: 1 Many ( 10 3 ) problem instances embarrassingly parallel. 2 Single instance simulation very long. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
11 Desperate problems, desperate solutions: Janus (I) Even with binary spins, simulation of spin-glasses is heavy in two respects: 1 Many ( 10 3 ) problem instances embarrassingly parallel. 2 Single instance simulation very long. For modest system sizes (i.e. N = 32 3 = spins): Typical instance: 4.5 standard-cpu years (i.e updates). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
12 Desperate problems, desperate solutions: Janus (I) Even with binary spins, simulation of spin-glasses is heavy in two respects: 1 Many ( 10 3 ) problem instances embarrassingly parallel. 2 Single instance simulation very long. For modest system sizes (i.e. N = 32 3 = spins): Typical instance: 4.5 standard-cpu years (i.e updates). Worst in 10 3 instances: 800 standard-cpu years (i.e updates). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
13 Desperate problems, desperate solutions: Janus (I) Even with binary spins, simulation of spin-glasses is heavy in two respects: 1 Many ( 10 3 ) problem instances embarrassingly parallel. 2 Single instance simulation very long. For modest system sizes (i.e. N = 32 3 = spins): Typical instance: 4.5 standard-cpu years (i.e updates). Worst in 10 3 instances: 800 standard-cpu years (i.e updates). Fortunately, the spin update (the core algorithm) is very simple and (in principle) trivial to parallelize. But... V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
14 Desperate problems, desperate solutions: Janus (I) Even with binary spins, simulation of spin-glasses is heavy in two respects: 1 Many ( 10 3 ) problem instances embarrassingly parallel. 2 Single instance simulation very long. For modest system sizes (i.e. N = 32 3 = spins): Typical instance: 4.5 standard-cpu years (i.e updates). Worst in 10 3 instances: 800 standard-cpu years (i.e updates). Fortunately, the spin update (the core algorithm) is very simple and (in principle) trivial to parallelize. But... Modern architectures (GPU, Xeon, Xeon-φ) efficient only for larger N astronomical number of updates ( e cn, probably). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
15 Desperate problems, desperate solutions: Janus (II) Parallelizable problem Parallelise within each instance We divide the lattice in a checkerboard scheme, all sites of the same colour can be updated simultaneously Memory bandwith: 13 bits to update one bit! Only solution: Memory local to the processor. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
16 Desperate problems, desperate solutions: Janus (II) Parallelizable problem FPGA opportunity window: Large on-chip memory (several Mbits). Huge bandwidth on-chip distributed memory ( bits in and out per clock cycle). Large amount of logic 1024 Spin-Update Engines. Janus 1 (2008): 1000 boost in spin-glasses simulations. Green computer: energy consumption per update. Janus 2: Fall 2014 V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
17 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
18 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) Spin-glasses in a magnetic field (Juan s talk, tomorrow). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
19 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) Spin-glasses in a magnetic field (Juan s talk, tomorrow). Isothermal aging (from 1 picosecond to 0.1 seconds) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
20 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) Spin-glasses in a magnetic field (Juan s talk, tomorrow). Isothermal aging (from 1 picosecond to 0.1 seconds) Clustering correlation functions in equilibrium. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
21 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) Spin-glasses in a magnetic field (Juan s talk, tomorrow). Isothermal aging (from 1 picosecond to 0.1 seconds) Clustering correlation functions in equilibrium. Quantitative correspondence: equilibrium, finite size non-equilibrium, finite time. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
22 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) Spin-glasses in a magnetic field (Juan s talk, tomorrow). Isothermal aging (from 1 picosecond to 0.1 seconds) Clustering correlation functions in equilibrium. Quantitative correspondence: equilibrium, finite size non-equilibrium, finite time. Precision estimates of critical exponents. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
23 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) Spin-glasses in a magnetic field (Juan s talk, tomorrow). Isothermal aging (from 1 picosecond to 0.1 seconds) Clustering correlation functions in equilibrium. Quantitative correspondence: equilibrium, finite size non-equilibrium, finite time. Precision estimates of critical exponents. Ultrametricity in the spin-glass phase.... V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
24 Desperate problems, desperate solutions: Janus (III) Main problems tackled with Janus ( ) Spin-glasses in a magnetic field (Juan s talk, tomorrow). Isothermal aging (from 1 picosecond to 0.1 seconds) Clustering correlation functions in equilibrium. Quantitative correspondence: equilibrium, finite size non-equilibrium, finite time. Precision estimates of critical exponents. Ultrametricity in the spin-glass phase.... Temperature chaos V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
25 Temperature chaos: the showstopper (I) Increasing computing speed x1000, not such a big deal Pre-Janus era: up to N = 16 3 spins. Janus era: up to N = 32 3 spins. Why? V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
26 Temperature chaos: the showstopper (I) Increasing computing speed x1000, not such a big deal Pre-Janus era: up to N = 16 3 spins. Janus era: up to N = 32 3 spins. Why? We need to talk a bit about algorithms: Simulating at fixed temperature, simply not enough. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
27 Temperature chaos: the showstopper (I) Increasing computing speed x1000, not such a big deal Pre-Janus era: up to N = 16 3 spins. Janus era: up to N = 32 3 spins. Why? We need to talk a bit about algorithms: Simulating at fixed temperature, simply not enough. Temperature needs to become dynamic. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
28 Temperature chaos: the showstopper (II) Simulated Annealing Simplest protocol: thermal energy 1 High T : easy exploration V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
29 Temperature chaos: the showstopper (II) Simulated Annealing Simplest protocol: thermal energy 1 High T : easy exploration 2 T -lowering protocol: Trapped at nearby local minimum. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
30 Temperature chaos: the showstopper (II) Simulated Annealing Simplest protocol: thermal energy 1 High T : easy exploration 2 T -lowering protocol: Trapped at nearby local minimum. Outdated algorithm. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
31 Temperature chaos: the showstopper (III) Parallel Tempering T raised or lowered: thermal energy 1 Low T : local exploration V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
32 Temperature chaos: the showstopper (III) Parallel Tempering T raised or lowered: thermal energy 1 Low T : local exploration 2 High T : global exploration V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
33 Temperature chaos: the showstopper (III) Parallel Tempering T raised or lowered: thermal energy 1 Low T : local exploration 2 High T : global exploration 3 No trapping better solution. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
34 Temperature chaos: the showstopper (III) Parallel Tempering T raised or lowered: thermal energy 1 Low T : local exploration 2 High T : global exploration 3 No trapping better solution. N T temperatures: simultaneous simulation of N T clones (one at each temperature). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
35 Temperature chaos: the showstopper (III) Parallel Tempering T raised or lowered: thermal energy 1 Low T : local exploration 2 High T : global exploration 3 No trapping better solution. N T temperatures: simultaneous simulation of N T clones (one at each temperature). Periodically, clones attempt to exchange their temperature. The rule preserves detailed balance. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
36 Temperature chaos: the showstopper (IV) It looks perfect! What can go wrong? V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
37 Temperature chaos: the showstopper (IV) It looks perfect! What can go wrong? Each clone performs a temperature Random Walk. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
38 Temperature chaos: the showstopper (IV) It looks perfect! What can go wrong? Each clone performs a temperature Random Walk. The simulation is long enough if all the clones visited all the temperatures several times. Mixing time: τ. Random Walk in temperatures of a clone A mixing Random Walk A stuck Random Walk i T i T Wallclock time (hours) Wallclock time (hours) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
39 Temperature chaos: the showstopper (V) Temperature chaos: Relevant minima, completely different at nearby temperatures. T -random walk refuses to go across. T T - dt V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
40 Temperature chaos: the showstopper (VI) τ : Operational definition of Temperature chaos. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
41 Temperature chaos: the showstopper (VI) τ : Operational definition of Temperature chaos. τ-pdf L = 32, T c 1.1 Extreme sample-to-sample fluctuations. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
42 Temperature chaos: the showstopper (VI) τ : Operational definition of Temperature chaos. τ-pdf L = 32, T c 1.1 Extreme sample-to-sample fluctuations. L and T sensitivity. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
43 Temperature chaos: the showstopper (VI) τ : Operational definition of Temperature chaos. τ-pdf L = 32, T c 1.1 Extreme sample-to-sample fluctuations. L and T sensitivity. At variance with standard T -chaos studies, it is easy to observe the effect. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
44 Contacting with conventional approach (I) Defining T -chaos through a Markov MC dynamics is: Mathematically clear. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
45 Contacting with conventional approach (I) Defining T -chaos through a Markov MC dynamics is: Mathematically clear. Cumbersome (analytical computations??). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
46 Contacting with conventional approach (I) Defining T -chaos through a Markov MC dynamics is: Mathematically clear. Cumbersome (analytical computations??). Unsatisfying: T -chaos is supposed to be a static effect! V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
47 Contacting with conventional approach (I) Defining T -chaos through a Markov MC dynamics is: Mathematically clear. Cumbersome (analytical computations??). Unsatisfying: T -chaos is supposed to be a static effect! However, it provides a useful definition. Instead, the static approach: Hard for some analytically tractable models. Sherrington-Kirkpatrick: Rizzo-Crisanti (2003) Migdal-Kadanoff: McKay, Nihat-Berker, Kirkpatrick, (1982). Numerically, very hard to identify. Scaling laws barely known (Katzgraber& Krzakala, 2007). We still lack predictions relevant for experiments. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
48 Contacting with conventional approach (II) Our main ingredients (Fernandez, V.M.-M,Parisi,Seoane, 2013) Janus data base (2010): O(10 3 ) samples, L 32, well thermalized at low temperatures. Wash-out thermal fluctuations (Ney-Nifle and Young, 1997) Look at whole distribution (not only average!) Large-deviation functional (the successful analytical approach for SK) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
49 Contacting with conventional approach (II) Our main ingredients (Fernandez, V.M.-M,Parisi,Seoane, 2013) Janus data base (2010): O(10 3 ) samples, L 32, well thermalized at low temperatures. Wash-out thermal fluctuations (Ney-Nifle and Young, 1997) Look at whole distribution (not only average!) Large-deviation functional (the successful analytical approach for SK) Consistency checks: Must correlate with dynamic approach Previously subtle effects should become visible. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
50 Contacting with conventional approach (III) Washing-out thermal fluctuations Useful technicality: the chaotic parameter X J T 1,T 2 = qt 2 1,T 2 J qt 2 1,T 1 J qt 2 2,T 2 J X J = 1 no chaos; X J = 0 strong chaos. Mind that, for T 1, T 2 < T c and large L, one expects XT J 1,T 2 qt 2 1,T 2 J qt 2 1,T 1 J qt 2 2,T 2 J 1. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
51 Contacting with conventional approach (IV) Average or full distribution? X T1 =0.7026,T 2 X J T 1 =0.7026,T L = 32 L = 24 L = 16 L = 12 L = 8 average S 050 S 150 S 250 S 350 S 450 S 550 S 650 S 750 S 850 S 950 Expectations: E J (X J T 1,T 2 ) = 0 if T 1 T 2 We are far from that. T 2 > T c : nothing happens. 0.2 σ (X T1 =0.7026,T 2 ) q XT J T 2 1,T 2 = 1,T 2 J qt 2 1,T 1 J qt 2 2,T 2 J T 2 V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
52 Contacting with conventional approach (IV) Average or full distribution? 1.0 X T1 =0.7026,T 2 X J T 1 =0.7026,T L = 32 L = 24 L = 16 L = 12 L = 8 average S 050 S 150 S 250 S 350 S 450 S 550 S 650 S 750 S 850 S 950 Expectations: E J (X J T 1,T 2 ) = 0 if T 1 T 2 We are far from that. T 2 > T c : nothing happens. In the slowest samples we identify chaotic events ( level-crossings in Quantum Mechanics). σ (X T1 =0.7026,T 2 ) I J = Tmax T min dt 2 X J T min,t T 2 V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
53 Contacting with conventional approach (V) I J correlates with τ! We are on the right track... I (X T1 =0.7026,T 2 ) r = 0.766(13) averaged median 2 25 log τ exp V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
54 Contacting with conventional approach (VI) Large deviations functional 3D, T 1 = 0.7, T 2 = 0.84, (T c = 1.1). Ω L (ɛ, T 1, T 2 ) Probability[X J T 1,T 2 > ɛ] = e LD Ω L (ɛ) Ω > 0 chaos! p(x T1,T 2 ε) Ω L (ε) L = 32 L = 24 L = 16 L = 12 L = ε L = 32 L = L = 16 L = 12 L = ε 2 V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
55 Contacting with conventional approach (VI) Large deviations functional 3D, T 1 = 0.7, T 2 = 0.84, (T c = 1.1). p(x T1,T 2 ε) Ω L (ε) L = 32 L = 24 L = 16 L = 12 L = ε L = 32 L = L = 16 L = 12 L = ε 2 Ω L (ɛ, T 1, T 2 ) Probability[X J T 1,T 2 > ɛ] = e LD Ω L (ɛ) Ω > 0 chaos! Ω L approaches convergence within Janus L-range. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
56 Contacting with conventional approach (VI) Large deviations functional 3D, T 1 = 0.7, T 2 = 0.84, (T c = 1.1). p(x T1,T 2 ε) Ω L (ε) L = 32 L = 24 L = 16 L = 12 L = ε L = 32 L = L = 16 L = 12 L = ε 2 Ω L (ɛ, T 1, T 2 ) Probability[X J T 1,T 2 > ɛ] = e LD Ω L (ɛ) Ω > 0 chaos! Ω L approaches convergence within Janus L-range. L = 8, 12 chaos is extremely rare. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
57 Contacting with conventional approach (VI) Large deviations functional 3D, T 1 = 0.7, T 2 = 0.84, (T c = 1.1). p(x T1,T 2 ε) Ω L (ε) L = 32 L = 24 L = 16 L = 12 L = ε L = 32 L = L = 16 L = 12 L = ε 2 Ω L (ɛ, T 1, T 2 ) Probability[X J T 1,T 2 > ɛ] = e LD Ω L (ɛ) Ω > 0 chaos! Ω L approaches convergence within Janus L-range. L = 8, 12 chaos is extremely rare. Crude parameterization Ω T1,T 2 (ɛ) T 1 T 2 b ɛ β V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
58 Contacting with conventional approach (VI) Large deviations functional 3D, T 1 = 0.7, T 2 = 0.84, (T c = 1.1). p(x T1,T 2 ε) Ω L (ε) L = 32 L = 24 L = 16 L = 12 L = ε L = 32 L = L = 16 L = 12 L = ε 2 Ω L (ɛ, T 1, T 2 ) Probability[X J T 1,T 2 > ɛ] = e LD Ω L (ɛ) Ω > 0 chaos! Ω L approaches convergence within Janus L-range. L = 8, 12 chaos is extremely rare. Crude parameterization Ω T1,T 2 (ɛ) T 1 T 2 b ɛ β Weak-chaos scaling (Katzgraber& Krzakala, 2007) explained: ζ = D/b = 1.07(2) Chaos length: ξ C = L a unless β = 1. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
59 Contacting with conventional approach (VII) SK finally yields to numerics (Billoire 2014) Rizzo-Crisanti and Rizzo-Parisi compute Ω(q T 1,T 2 )... SK model 256 sites SK model 4096 sites V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
60 Contacting with conventional approach (VII) SK finally yields to numerics (Billoire 2014) Rizzo-Crisanti and Rizzo-Parisi compute Ω(q T 1,T 2 )... But Ω(X J T 1,T 2 > ɛ) Ω(q T 1,T 2 ) (see also Rizzo 2014) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
61 Contacting with conventional approach (VIII) Take-home messages Dynamic methods might be preferable in real calculations. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
62 Contacting with conventional approach (VIII) Take-home messages Dynamic methods might be preferable in real calculations. Three (rather than 2) scaling variables: N, T and ɛ. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
63 Contacting with conventional approach (VIII) Take-home messages Dynamic methods might be preferable in real calculations. Three (rather than 2) scaling variables: N, T and ɛ. Temperature chaos is generic for large problem size N. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
64 Contacting with conventional approach (VIII) Take-home messages Dynamic methods might be preferable in real calculations. Three (rather than 2) scaling variables: N, T and ɛ. Temperature chaos is generic for large problem size N. In practice, specially for small N: 1 The large majority of problem instances are easy (small τ). 2 For some of them, though, τ inordinately large. 3 The larger is N, the more frequently missbehaving instances appear difficult to assess algorithmic scaling with N. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
65 Is quantum-computing our breakthrough? (I) From an impressive insight (Richard P. Feynman, 1982) NP-problems, specially simulation of quantum systems: best solved on quantum computers... V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
66 Is quantum-computing our breakthrough? (I)... to (possibly) quantum-computing objects (2014). D-wave Two V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
67 Is quantum-computing our breakthrough? (I)... to (possibly) quantum-computing objects (2014). A quantum annealer should: 1 Read accurately an instance. D-wave Two 2 Add a strong transverse magnetic field. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
68 Is quantum-computing our breakthrough? (I)... to (possibly) quantum-computing objects (2014). A quantum annealer should: 1 Read accurately an instance. D-wave Two 2 Add a strong transverse magnetic field. 3 At low enough T... 4 With low noise... 5 Slowly take field 0. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
69 Is quantum-computing our breakthrough? (I)... to (possibly) quantum-computing objects (2014). A quantum annealer should: 1 Read accurately an instance. D-wave Two 2 Add a strong transverse magnetic field. 3 At low enough T... 4 With low noise... 5 Slowly take field 0. All requirements met? global minimum. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
70 Is quantum-computing our breakthrough? (II) D-wave solves a toy problem: Small problems N = 512 (actually, N = 503 in USC). V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
71 Is quantum-computing our breakthrough? (II) D-wave solves a toy problem: Small problems N = 512 (actually, N = 503 in USC). Chimera graph: non-planar but 2D-like. Two-dimensional penalties: Chimera Each blob: 8 q-bits V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
72 Is quantum-computing our breakthrough? (II) D-wave solves a toy problem: Small problems N = 512 (actually, N = 503 in USC). Chimera graph: non-planar but 2D-like. Two-dimensional penalties: No SG phase for T > 0 T c = 0 easier problems. Chimera Each blob: 8 q-bits V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
73 Is quantum-computing our breakthrough? (II) D-wave solves a toy problem: Small problems N = 512 (actually, N = 503 in USC). Chimera graph: non-planar but 2D-like. Two-dimensional penalties: Chimera No SG phase for T > 0 T c = 0 easier problems. Small decycling set Main graph in Selby heuristics: 78% in a single tree (no loops!) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
74 Is quantum-computing our breakthrough? (II) D-wave solves a toy problem: Small problems N = 512 (actually, N = 503 in USC). Chimera graph: non-planar but 2D-like. Two-dimensional penalties: Chimera No SG phase for T > 0 T c = 0 easier problems. Small decycling set T = 0 heuristics better than thermal methods (i.e. PT). Main graph in Selby heuristics: 78% in a single tree (no loops!) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
75 Is quantum-computing our breakthrough? (II) D-wave solves a toy problem: Small problems N = 512 (actually, N = 503 in USC). Chimera graph: non-planar but 2D-like. Two-dimensional penalties: Chimera No SG phase for T > 0 T c = 0 easier problems. Small decycling set T = 0 heuristics better than thermal methods (i.e. PT). T > 0 2D-methods better than Monte Carlo (Middleton 2011, square lattice: N = ). Main graph in Selby heuristics: 78% in a single tree (no loops!) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
76 Is quantum-computing our breakthrough? (II) D-wave solves a toy problem: Small problems N = 512 (actually, N = 503 in USC). Chimera graph: non-planar but 2D-like. Two-dimensional penalties: Chimera No SG phase for T > 0 T c = 0 easier problems. Small decycling set T = 0 heuristics better than thermal methods (i.e. PT). T > 0 2D-methods better than Monte Carlo (Middleton 2011, square lattice: N = ). Are we learning something? Main graph in Selby heuristics: 78% in a single tree (no loops!) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
77 Is quantum-computing our breakthrough? (III) In three spatial dimensions only thermal annealing works. Real question: Is there chaos in the chimera lattice? V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
78 Is quantum-computing our breakthrough? (III) In three spatial dimensions only thermal annealing works. Real question: Is there chaos in the chimera lattice? Middleton et al.: chaos in square lattice, but N = Chaos with only N = 503 q-bits? V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
79 Is quantum-computing our breakthrough? (III) In three spatial dimensions only thermal annealing works. Real question: Is there chaos in the chimera lattice? Middleton et al.: chaos in square lattice, but N = Chaos with only N = 503 q-bits? Not at first sight Probability density (instances) e+06 τ (Metropolis sweeps) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
80 Is quantum-computing our breakthrough? (III) In three spatial dimensions only thermal annealing works. Real question: Is there chaos in the chimera lattice? Middleton et al.: chaos in square lattice, but N = Chaos with only N = 503 q-bits? Not at first sight... But look at that fat tail! 2 in 10 4 instances: τ τ -0.8 Probability density (instances) e+06 τ (Metropolis sweeps) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
81 Is quantum-computing our breakthrough? (IV) As usual, τ pinpoints peculiar samples... Overlap betwen Ground-State and 1 st Excited-State... 1e GS-GS, easy sample GS-ES 1e+07 1e+06 GS-GS, hard sample GS-ES q q V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
82 Is quantum-computing our breakthrough? (IV) As usual, τ pinpoints peculiar samples or energy-dependence with T. e = e T - e GS Same easy sample Same hard sample T e = e T - e GS Same easy sample Same hard sample exp[-2/t] V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
83 Is quantum-computing our breakthrough? (V) Meaningful algorithmic classification at fixed N: τ-scaling. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
84 Is quantum-computing our breakthrough? (V) Meaningful algorithmic classification at fixed N: τ-scaling. Parallel-Tempering: τ 1, Selby heuristics (2D!): τ b 0.3, D-wave: τ a Time to solution (seconds in Xeon) e-05 τ 0.3 PT (x 0.002) Selby s average Selby s median D-wave median,τ e+06 τ (Metropolis sweeps) V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
85 Conclusions The Janus computer: new window for spin-glasses. A new generation will soon enter into operation. Not everything in Spin-Glasses Physics is self-averaging. Temperature chaos is a clear example. Sometimes, studying dynamics (τ) might be the easiest way to learn about statics. Temperature chaos is a major obstacle. Is quantum annealing an alternative? V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
86 Conclusions The Janus computer: new window for spin-glasses. A new generation will soon enter into operation. Not everything in Spin-Glasses Physics is self-averaging. Temperature chaos is a clear example. Sometimes, studying dynamics (τ) might be the easiest way to learn about statics. Temperature chaos is a major obstacle. Is quantum annealing an alternative? D-wave is a candidate quantum-annealer. Object to be experimentally investigated, rather than a finished product. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
87 Conclusions The Janus computer: new window for spin-glasses. A new generation will soon enter into operation. Not everything in Spin-Glasses Physics is self-averaging. Temperature chaos is a clear example. Sometimes, studying dynamics (τ) might be the easiest way to learn about statics. Temperature chaos is a major obstacle. Is quantum annealing an alternative? D-wave is a candidate quantum-annealer. Object to be experimentally investigated, rather than a finished product. Currently, performance not competitive with Parallel Tempering. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
88 Conclusions The Janus computer: new window for spin-glasses. A new generation will soon enter into operation. Not everything in Spin-Glasses Physics is self-averaging. Temperature chaos is a clear example. Sometimes, studying dynamics (τ) might be the easiest way to learn about statics. Temperature chaos is a major obstacle. Is quantum annealing an alternative? D-wave is a candidate quantum-annealer. Object to be experimentally investigated, rather than a finished product. Currently, performance not competitive with Parallel Tempering. Reasons for failure intrinsic? Current investigation. V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
89 Many thanks to... The Janus collaboration, Alain Billoire, Itay Hen, The meeting organizers,... and to you (the audience), for your attention! V. Martin-Mayor (Física Teórica I, UCM) Quantum vs. Classical annealing Capri, September / 28
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