Topics Introduction to Quantum omputing D-Wave Background D-Wave System Programming Environment Potential Applications opyright D-Wave Systems Inc. 1
D-Wave Software Environment APPLIATIONS Environment/ Libraries 1Qbit SDK Optimization QUORTRAN onstraint Satisfaction Q++ Sampling SAT, ML OMPILERS JADE/QuellE QSAGE ToQ l l l? TRANSLATORS Virtual QUBO QUBO LANL Assembler qbsolv INTERMEDIATE REPRESENTATION, ++, MATLAB Python SAPI QMI DW HOST LIBRARY AND OMMAND LINE INTERFAE SYSTEM INTERFAE AND ONTROL QUANTUM MAHINE INSTRTION TARGET SYSTEM PRODT PROTOTYPE ONEPT opyright D-Wave Systems Inc. 2
QUBIT q i Quantum bit which participates in annealing cycle and settles into one of two possible final states: 0,1 OUPLER q i q ) Physical device that allows one qubit to influence another qubit WEIGHT a i the qubit s tendency to collapse into its two possible final states; controlled by the programmer Real-valued constant associated with each qubit, which influences STRENGTH b ij the influence exerted by one qubit on another; controlled by the programmer Real-valued constant associated with each coupler, which controls OBJETIVE Obj Real-valued function which is minimized during the annealing cycle Obj(a i, b ij ; q i ) = 5 a i q i + 5 b ij q i The system samples from the q " that minimize the objective i ij q j opyright D-Wave Systems Inc. 3
The QMI for the 1000-qubit chip has (nominally): qubitweights intracell coupler strengths intercell coupler strengths 8 per cell x 12 x 12 16 per cell x 12 x 12 2 directions x 4 x 12 x 11 1152 2304 1056 Total size of the QMI is 1152 + 2304 + 1056 = 4412 parameters Each parameter can be specified to about 4-5 bits of precision Weights - a " Strengths - b "8 Quantum Machine Instruction (QMI) Quantum Processor Annealing ycles Qubits - q Qubits - " q Qubits - " q Qubits - " q " opyright D-Wave Systems Inc. 4
Generation L,M,N Qubits ouplers QMI coefficients Simulator 4,4,4 128 352 480 Rainier 4,4,4 128 352 480 Vesuvius 4,8,8 512 1472 1984 W1K 4,12,12 1K 3K 4K W2K 4,16,16 2K 6K 8K himera L,M,N 2LMN L = MN + L M 1 N +LM(N 1) 2LMN + L = MN + L M 1 N + LM(N 1) M L Unit ell L column cross opyright D-Wave Systems Inc. 5 N
Programming Environment Operates in a hybrid mode with a HP System or Data Analytic Engine acting as a co-processor or accelerator D-Wave system is front-ended on a network by a standard server User formulates problem as a series of Quantum Machine Instructions (QMIs) Front end sends QMI to quantum processor (QP) QP starts to sample from the distribution of bit-strings defined by the QMI Results are returned to the front-end and on to the user opyright D-Wave Systems Inc. 6
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Example: 4-coloring anada s provinces opyright D-Wave Systems Inc. 8
anada represented as a graph YT NU MB ON Q NL NT SK NB PE B AB NS AB Alberta B British olumbia MB Manitoba NB New Brunswick NL Newfoundland and Labrador NS Nova Scotia NT Northwest Territories NU Nunavut ON Ontario PE Prince Edward Island Q Quebec SK Saskatchewan YT Yukon opyright D-Wave Systems Inc. 9
Needle & Haystack : oloring anada (not to scale) # of colors Needle Haystack N/H 3 1728 3 @A = 1.6x10 E 0.0011 4 653184 4 @A = 6.7x10 H 0.0097 opyright D-Wave Systems Inc. 10
Encode colors and provinces via qubits Pick unary encoding for simplicity: 13 regions 4 colors (Blue, Green, Red, Yellow) reate 13x4 = 52 logical qubits Build QMI with these four tasks: 1. Turn on exactly one of the four color qubits for each region 2. Map logical color qubits for a region to physical qubits of a unit cell 3. Use intercell couplers to enforce neighbor constraints 4. lone regions as necessary so that anada can embed into a planar grid Each task contributes a portion of the final QMI Add individual contributions to get the total QMI opyright D-Wave Systems Inc. 11
Task 1: turn on one of four color qubits Blue qubit Q Q Green qubit Yellow qubit Q Q Red qubit Objective : O q b, q g, q r, q y = q b + q g + q r + q y 1 2 1(q b + q g + q r + q y ) +2(q b q g + q b q r + q b q y + q g q r + q g q y + q r q y ) opyright D-Wave Systems Inc. 12
Task 2: embed logical to physical qubits B Q Q G R Q Q logical Y physical opyright D-Wave Systems Inc. 13
Task 3: Intercell couplers constrain neighbors B British olumbia Alberta G R Y British olumbia Alberta opyright D-Wave Systems Inc. 14
Task 4: lone regions for planar embedding NT NT Northwest Territories British olumbia Alberta opyright D-Wave Systems Inc. 15 B AB
olors encoded in unit cells opyright D-Wave Systems Inc. 16
Scaling up... We cannot fit all the states into unit cells of the chip so we adopt a divide-and-conquer strategy Divide the US map into chunks. Process the first chunk and get valid colorings for the first chunk of states. Use these colorings to bias the second chunk. Repeat. chunk 1 chunk 2 chunk 3 opyright D-Wave Systems Inc. 17
...and up... 254 counties in Texas opyright D-Wave Systems Inc. 18
...and up opyright D-Wave Systems Inc. 3108 US counties 19
Implementations of map coloring ToQ Snippet (28 of 596 LO) entire program QMI : weights strengths opyright D-Wave Systems Inc. 20
Algorithms are being discovered for mapping applications to adiabatic quantum computers These algorithms are being turned into software tools This is greatly improving programmer productivity in the AQ environment......and closing the gap between applications and AQ power opyright D-Wave Systems Inc. 21
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Thank You Questions? Denny Dahl ddahl@dwavesys.com