Quantum annealing. Matthias Troyer (ETH Zürich) John Martinis (UCSB) Dave Wecker (Microsoft)

Beyond Moore s law: quantum devices Disruptive technology change: use quantum mechanics for computing!? Windows Q Quantum random number generators Quantum simulators Quantum computer 2

Quantum random number generators Create true random numbers using the laws of quantum mechanics 0 photo detectors 0 1 1. Photon source emits a photon 2. Photon hits semitransparent mirror photon source semi-transparent mirror 3. Photon follows both paths 4. The photo detectors see the photon only in one place: random selection 3

When will we have a quantum computer?? Windows Q 4

May 2011: \

From http://www.dwavesys.com

DPHYS Friday, March 22, 2013 (page 1)... if it performs as Lockheed and D-Wave expect, the design could be used to supercharge even the most powerful systems, solving some science and business problems millions of times faster than can be done today. (page 2) However,... scientists have not yet published scientific data showing that the system computes faster than today s conventional binary computers.... critics of D-Wave s method say it is not quantum computing at all, but a form of standard thermal behavior. 8

May 2013: D-Wave is 3600x faster than classical computers!? Experimental Evaluation of an Adiabiatic Quantum System for Combinatorial Optimization Catherine C. McGeoch Amherst College Amherst MA, USA ccm@cs.amherst.edu Cong Wang Simon Fraser University Burnaby BC, CA cwa9@cs.sfu.ca Special purpose heuristic device (D-Wave) needs 0.491s General purpose exact solver (CPLEX) needs 30 minutes on one CPU core It would of course be interesting to see if highly tuned implementations could compete... 9

Some magazines investigate deeper...... but isn t it business success that counts in the end? Log in Register Subscribe Digital & mobile World politics Business & finance Economics Science & technology Culture Blogs Deba Quantum computing Faster, slower or both at once? The first real-world contests between quantum computers and standard ones May 18th 2013 From the print edition Like 268 Tweet 25 CHIPMAKERS dislike quantum mechanics. Half a century of Moore s law means their products have shrunk to the point where they are subject to the famous weirdness of the quantum world. That makes designing them difficult. Happily, those same quantum oddities can be turned into features rather than bugs. For many years researchers have been working on computers that would rely on the strange laws of quantum mechanics to do useful calculations. They would do this by using binary digits which, instead of having a value of either one or zero, had both at 10

What is behind this? D-Wave is not a universal quantum computer but a special purpose quantum optimizer Does it work? Is it quantum or classical? Is it thousands of times faster than anything classical? We performed experiments on D-Wave devices to answer these questions 11

Binary quadratic optimization: an NP-hard problem Find the values xi (=0 or 1) which minimize the quadratic cost function a x x + ij i j ij b x i i where x {0,1} i i Finding the solution is exponentially hard (unless P=NP) 12

The Ising spin glass: an NP-hard problem Find the values xi (= -1 or +1) which minimize the quadratic cost function J x x + ij i j ij h x i i where x { 1,+1} i i Finding the solution is exponentially hard (unless P=NP) Many important problems can be expressed as binary quadratic optimization problems (or Ising spin glasses) with only polynomial overhead factoring integers: 15 = 3 x 5 traveling salesman problem portfolio optimization graph isomorphism... Can a quantum device solve these problems faster than a classical one? 13

Annealing and simulated annealing Annealing A 7000 year old neolithic technology Slowly cool a metal to improve its properties Simulated annealing Kirkpatrick, Gelatt and Vecchi, Science (1983) A 30 year old optimization technique Slowly cool a model in a Monte Carlo simulation to find the solution to an optimization problem We don t always find the global minimum and have to try many times 14

Quantum annealing Advantages of quantum mechanics A quantum particle can be everywhere at once and explore all of the configuration space Quantum annealing schedule Ψ(x) 2 Start with a constant potential V(x) The particle is everywhere with equal probability given by the square of the wave function Ψ(x) 2 Turning on the potential the wave function concentrates around the minima of the potential V(x) We have to anneal very slowly for the hard problems to let the particle tunnel to the global minimum 15

DPHYS The D-Wave device 16

Superconducting flux qubits The qubit is implemented by magnetic fluxes caused by circulating superconducting currents 0: magnetic flux flowing down 1: magnetic flux flowing up Programmable magnetic coupling allows to define the optimization problem J x x + ij i j ij h x i i i Credit: D-Wave Systems 17

DPHYS Lockheed Martin bought two D-Wave devices D-Wave One installed at USC in October 2011: D-Wave Two installed at USC in March 2013: 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 2 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62 3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125 66 70 74 78 82 86 90 94 98 102 106 110 114 118 122 126 67 71 75 79 83 87 91 95 99 103 107 111 115 119 123 127 128 132 136 140 144 148 152 156 160 164 168 172 176 180 184 188 129 133 137 141 145 149 153 157 161 165 169 173 177 181 185 189 130 134 138 142 146 150 154 158 162 166 170 174 178 182 186 190 131 135 139 143 147 151 155 159 163 167 171 175 179 183 187 191 192 196 200 204 208 212 216 220 224 228 232 236 240 244 248 252 193 197 201 205 209 213 217 221 225 229 233 237 241 245 249 253 194 198 202 206 210 214 218 222 226 230 234 238 242 246 250 254 195 199 203 207 211 215 219 223 227 231 235 239 243 247 251 255 256 260 264 268 272 276 280 284 288 292 296 300 304 308 312 316 257 261 265 269 273 277 281 285 289 293 297 301 305 309 313 317 258 262 266 270 274 278 282 286 290 294 298 302 306 310 314 318 259 263 267 271 275 279 283 287 291 295 299 303 307 311 315 319 320 324 328 332 336 340 344 348 352 356 360 364 368 372 376 380 321 325 329 333 337 341 345 349 353 357 361 365 369 373 377 381 322 326 330 334 338 342 346 350 354 358 362 366 370 374 378 382 323 327 331 335 339 343 347 351 355 359 363 367 371 375 379 383 384 388 392 396 400 404 408 412 416 420 424 428 432 436 440 444 385 389 393 397 401 405 409 413 417 421 425 429 433 437 441 445 386 390 394 398 402 406 410 414 418 422 426 430 434 438 442 446 387 391 395 399 403 407 411 415 419 423 427 431 435 439 443 447 448 452 456 460 464 468 472 476 480 484 488 492 496 500 504 508 449 453 457 461 465 469 473 477 481 485 489 493 497 501 505 509 450 454 458 462 466 470 474 478 482 486 490 494 498 502 506 510 451 455 459 463 467 471 475 479 483 487 491 495 499 503 507 511 108 of 128 qubits working 503 of 512 qubits working 1 Couplings can be defined on edges of the chimera graph implemented by the device J ij x x j + hi xi ij i i 18

Is D-Wave a quantum annealer? Many scientists doubt that D-Wave is a quantum device since the qubits are imperfect and the device is exposed to lots of thermal noise Hypothesis 1: D-Wave is a not quantum but just a classical annealer Experimental test: compare to a simulated classical annealer (Monte Carlo simulation) Hypothesis 2: D-Wave is a quantum annealer Experimental test: compare to a simulated quantum annealer (quantum Monte Carlo) Hypothesis 3: D-Wave is a quantum device and shows quantum speedup Experimental test: scaling with problem size is better than that of the classical codes 19

The experiments to test the machine Find the hardest problems that the machine can solve Random ±1 couplings on all edges of the chimera graph 1000s of choices of couplings 1000s of repetitions of the annealing 10s of problem sizes vary the annealing time and schedule hundred million experiments on D-Wave One billions of simulations classical and quantum Monte Carlo 20

Success probability histograms 1. Pick 1000 different random problems 2. For each problem run experiments and count how often the global minimum was reached 3. Plot a histogram of the probabilities of finding the global minimum Simulated classical annealer Simulated quantum annealer D-Wave One D-Wave One is inconsistent with a classical annealer D-Wave One is consistent with a simulated quantum annealer 21

Correlations between D-Wave and a simulated quantum annealer easy for both D-Wave and the simulated quantum annealer hard for both D-Wave and the simulated quantum annealer The same instances are hard and easy on D-Wave and the simulated quantum annealer 22

Scaling of the median time to solution with problem size Simulated Quantum Annealing generic Belief Propagation (exact) optimized parallelized GPU Simulated Annealing D-Wave Two D-Wave One 200 Monte Carlo updates per nanosecond This is for random ±1 couplings and the conclusion may be different for other benchmarks 23

We understand the D-Wave black box much better Special purpose device for combinatorial optimization problems Finds the global optimum out of 2 503 states (non-trivial!) a x x + ij i j ij b x i i i Evidence for quantum behavior Performance correlates well with a simulated quantum annealer but not with a simulated classical annealer Performance can (so far) be matched by highly optimized classical codes on a single GPU or CPU Observed scaling is the same as that of classical codes Can improved calibration change the conclusion? 24