1. CS252 Graduate Computer Architecture Lecture 28 Esoteric Computer Architecture DNA Computing & Quantum Computing Prof John D. Kubiatowicz http://www.cs.berkeley.edu/~kubitron/cs252

2. 5/11/2009cs252-S09, Lecture 28 2 DNA Computing Can we use DNA to do massive computations? –Organisms do it –DNA has very high information density: »4 different base pairs: Adenine/Thymine Guanine/Cytosine »Always paired on opposite strands  Energetically favorable –Active operations: »Copy: Split strands of DNA apart in solution, gain 2 copies »Concatenate: eg: GTAATCCT will combine XXXXXCATT with AGGAYYYYY »Polymerase Chain Reaction (PCR): amplifies region of molecule between two marker molecules ©1999 Access Excellence @ the National Health Museum

3. 5/11/2009cs252-S09, Lecture 28 3 DNA Computing and Hamiltonian Path Given a set of cities and costs between them (possibly directed paths): –Find shortest path to all cities –Simpler: find single path that visits all cities DNA Computing example is latter version: –Every city represented by unique 20 base-pair strand –Every path between cities represented by complementary pairs: 10 pairs from source city, 10 pairs from destination –Shorter example: AAGT for city 1, TTCG for city 2 Path 1->2: CAAA Will build: AAGTTTCG..CAAA.. –Dump “city molecules” and “path molecules” into testtube. Select and amplify paths of right length. Analyze for result. –Been done for 6 cities! (Adleman, ~1998!)

4. 5/11/2009cs252-S09, Lecture 28 4 Even more promising uses of DNA Self-assembly of components –DNA serves as substrate –Attach active elements in middle of components. –Final step – metal deposited over DNA Other interesting structures could be built Active Region DNA Bonding

5. 5/11/2009cs252-S09, Lecture 28 5 Use Quantum Mechanics to Compute? Weird but useful properties of quantum mechanics: –Quantization: Only certain values or orbits are good »Remember orbitals from chemistry??? –Superposition: Schizophrenic physical elements don’t quite know whether they are one thing or another All existing digital abstractions try to eliminate QM –Transistors/Gates designed with classical behavior –Binary abstraction: a “1” is a “1” and a “0” is a “0” Quantum Computing: Use of Quantization and Superposition to compute. Interesting results: –Shor’s algorithm: factors in polynomial time! –Grover’s algorithm: Finds items in unsorted database in time proportional to square-root of n. –Materials simulation: exponential classically, linear-time QM

6. 5/11/2009cs252-S09, Lecture 28 6 Quantization: Use of “Spin” Particles like Protons have an intrinsic “Spin” when defined with respect to an external magnetic field Quantum effect gives “1” and “0”: –Either spin is “UP” or “DOWN” nothing between North South Spin ½ particle: (Proton/Electron) Representation: |0> or |1>

7. 5/11/2009cs252-S09, Lecture 28 7 Kane Proposal II (First one didn’t quite work) Bits Represented by combination of proton/electron spin Operations performed by manipulating control gates –Complex sequences of pulses perform NMR-like operations Temperature < 1° Kelvin! Phosphorus Impurity Atoms Single Spin Control Gates Inter-bit Control Gates

8. 5/11/2009cs252-S09, Lecture 28 8 Now add Superposition! The bit can be in a combination of “1” and “0”: –Written as:  = C 0 |0> + C 1 |1> –The C’s are complex numbers! –Important Constraint: |C 0 | 2 + |C 1 | 2 =1 If measure bit to see what looks like, –With probability |C 0 | 2 we will find |0> (say “UP”) –With probability |C 1 | 2 we will find |1> (say “DOWN”) Is this a real effect? Options: –This is just statistical – given a large number of protons, a fraction of them (|C 0 | 2 ) are “UP” and the rest are down. –This is a real effect, and the proton is really both things until you try to look at it Reality: second choice! –There are experiments to prove it!

9. 5/11/2009cs252-S09, Lecture 28 9 A register can have many values! Implications of superposition: –An n-bit register can have 2 n values simultaneously! –3-bit example:  = C 000 |000>+ C 001 |001>+ C 010 |010>+ C 011 |011>+ C 100 |100>+ C 101 |101>+ C 110 |110>+ C 111 |111> Probabilities of measuring all bits are set by coefficients: –So, prob of getting |000> is |C 000 | 2, etc. –Suppose we measure only one bit (first): »We get “0” with probability: P 0 =|C 000 | 2 + |C 001 | 2 + |C 010 | 2 + |C 011 | 2 Result:  = (C 000 |000>+ C 001 |001>+ C 010 |010>+ C 011 |011>) »We get “1” with probability: P 1 =|C 100 | 2 + |C 101 | 2 + |C 110 | 2 + |C 111 | 2 Result:  = (C 100 |100>+ C 101 |101>+ C 110 |110>+ C 111 |111>) Problem: Don’t want environment to measure before ready! –Solution: Quantum Error Correction Codes!

10. 5/11/2009cs252-S09, Lecture 28 10 Spooky action at a distance Consider the following simple 2-bit state:  = C 00 |00>+ C 11 |11> –Called an “EPR” pair for “Einstein, Podolsky, Rosen” Now, separate the two bits: If we measure one of them, it instantaneously sets other one! –Einstein called this a “spooky action at a distance” –In particular, if we measure a |0> at one side, we get a |0> at the other (and vice versa) Teleportation –Can “pre-transport” an EPR pair (say bits X and Y) –Later to transport bit A from one side to the other we: »Perform operation between A and X, yielding two classical bits »Send the two bits to the other side »Use the two bits to operate on Y »Poof! State of bit A appears in place of Y Light-Years?

11. 5/11/2009cs252-S09, Lecture 28 11 Model: Operations on coefficients + measurements Basic Computing Paradigm: –Input is a register with superposition of many values »Possibly all 2 n inputs equally probable! –Unitary transformations compute on coefficients »Must maintain probability property (sum of squares = 1) »Looks like doing computation on all 2 n inputs simultaneously! –Output is one result attained by measurement If do this poorly, just like probabilistic computation: –If 2 n inputs equally probable, may be 2 n outputs equally probable. –After measure, like picked random input to classical function! –All interesting results have some form of “fourier transform” computation being done in unitary transformation Unitary Transformations Input Complex State Measure Output Classical Answer

12. 5/11/2009cs252-S09, Lecture 28 12 The Security of RSA Public-key cryptosystems depends on the difficult of factoring a number N=pq (product of two primes) –Classical computer: sub-exponential time factoring –Quantum computer: polynomial time factoring Shor’s Factoring Algorithm (for a quantum computer) 1)Choose random x : 2  x  N-1. 2)If gcd(x,N)  1, Bingo! 3)Find smallest integer r : x r  1 (mod N) 4)If r is odd, GOTO 1 5)If r is even, a  x r/2 (mod N)  (a-1)  (a+1) = kN 6)If a = N-1 GOTO 1 7)ELSE gcd(a ± 1,N) is a non trivial factor of N. Hard Security of Factoring Easy

13. 5/11/2009cs252-S09, Lecture 28 13 Finding r with x r  1 (mod N) Quantum Fourier Transform Finally: Perform measurement –Find out r with high probability –Get |y>|a w’ > where y is of form k/r and w’ is related

14. 5/11/2009cs252-S09, Lecture 28 14 ION Trap Quantum Computer: Promising technology IONS of Be+ trapped in oscillating quadrature field –Internal electronic modes of IONS used for quantum bits –MEMs technology –Target? 50,000 ions –ROOM Temperature! Ions moved to interaction regions –Ions interactions with one another moderated by lasers Cross- Sectional View Top View Top Proposal: NIST Group

15. 5/11/2009cs252-S09, Lecture 28 15 Ion Trap Quantum Computer - Data = an ion - Gate = a location Two-Qubit Gate Ballistic Movement - Apply pulse sequences to electrodes - Electrostatic forces move ion Q1 Q2 - Intersections similar, but more complicated pulse sequences Major Components

16. 5/11/2009cs252-S09, Lecture 28 16 Ballistic Movement Network One-Qubit Gate Two-Qubit Gate Memory Cell One-Qubit Gate Memory Cell R R R R Interconnection Network Q2Q3 Q4Q5 Q1 Problem: Noise accumulation!

17. 5/11/2009cs252-S09, Lecture 28 17 Noise Accumulation from Movement Noise may increase error by factor of 100 Qubit Error Distance Moved in Gates

18. 5/11/2009cs252-S09, Lecture 28 18 D? Movement Option 2: Teleportation D D E2E1 Source LocationTarget Location 1. Generate EPR pair 3. Transmit two classical bits Teleportation Benefits Problem: EPR pairs become noisy - Error Correction of data (arbitrary state): ~100 ms Purification of EPR pair (known state): ~120 µs - Pre-distribution of EPR pairs Goal: Transfer the state, not the data ion 2. Local Ops 4. Local OpsEntanglement

19. 5/11/2009cs252-S09, Lecture 28 19 One-Qubit Gate Q2 Two-Qubit Gate Q3 Two-Qubit Gate Q4Q5 Memory Cell Q1 One-Qubit Gate Memory Cell R R R R Interconnection Network EPR Pair Distribution Network EPR Pair Generators

20. 5/11/2009cs252-S09, Lecture 28 20 Setting Up a Teleportation Link GPP EPR Qubits Recycled Qubits For Data Teleportation Purification = Amplification of EPR pair link - Two EPR pairs  One “purer” pair, one junk pair - Chance of failure Need to send multiple pairs STRONGEREntanglement

21. 5/11/2009cs252-S09, Lecture 28 21 Chained Teleportation GTT GTGTGTGT PP Teleportation Adjacent T nodes linked for teleportation Positive Features - T node linking not on critical path - Pre-purification (Link Amplification): part of link setup

22. 5/11/2009cs252-S09, Lecture 28 22 Quantum Network Architecture Grid of T nodes Packet-switched network - Dimension-order routing TTTT TTTT PPPP PPPP G G G G G GG GGG, linked by G nodes Each qubit has associated message Gate

23. 5/11/2009cs252-S09, Lecture 28 23 Classical Control Quantum Datapath Layer - T Nodes and G Nodes (P Nodes and Gates not shown) Classical Control Layers - Messages Associated with Qubits - Teleportation and Purification Bits

24. 5/11/2009cs252-S09, Lecture 28 24 Running a Quantum Circuit Simple gates (transversal) More complex gates (non-transversal) –Exist in any universal set Quantum Error Correction (QEC) –10 -8 to 10 -6 error rates from gates, movement and idleness –Data must be encoded and periodically error corrected Ancilla (helper) qubits –Necessary for complex gates and for QEC –Computation with ancilla qubits > 90% of quantum program H CXCX H T T QEC T T Q0 Q1 time Serial Circuit Latency

25. 5/11/2009cs252-S09, Lecture 28 25 Running a Quantum Circuit Ancilla qubits are independent of data –Preparation may be pulled offline –Ancilla qubits should be ready just in time to avoid noise from idleness H CXCX H T T QEC Q0 Q1 Parallel Circuit Latency

26. 5/11/2009cs252-S09, Lecture 28 26 Running at The Speed of Data Ideally, execution time determined solely by data time hardware Ancilla encoding Operations involving data qubits

27. 5/11/2009cs252-S09, Lecture 28 27 Limited Ancilla Bandwidth 32-bit Quantum Carry-Lookahead Adder –Varying rate at which encoded zero ancillae are provided for QEC –Conclusion: design architecture with “ancilla factories” Encoded Ancilla Bandwidth Available (Ancillae per ms) Execution Time of a 32-Bit QCLA (μs)

28. 5/11/2009cs252-S09, Lecture 28 28 Ancilla Factory Design I “In-place” ancilla preparation Encoded AncillaVerification Qubits Ancilla factory consists of many of these –Encoded ancilla prepared in many places, then moved to output port –Movement is costly! In-place Prep In-place Prep In-place Prep In-place Prep 0 Prep Cat Prep 0 Prep Cat Prep 0 Prep Cat Prep Verify ? ? ? Bit Correct Phase Correct QEC Ancilla Generation Circuit

29. 5/11/2009cs252-S09, Lecture 28 29 Idealized Qalypso Architecture Dense data region –Data qubits only –Local communication Shared Ancilla Factories –Distributed to data as needed –Fully multiplexed to all data –Output ports ( ): close to data –Input ports ( ): may be far from data, since recycled qubits have irrelevant state Goals –Design ancilla factories –Answer Question: How much hardware is needed for ancilla generation to run at the speed of data?

30. 5/11/2009cs252-S09, Lecture 28 30 Discussion of ISCA 2009 paper “A Fault Tolerant, Area Efficient Architecture for Shor’s Factoring Algorithm” –Mark Whitney, Nemanja Isailovic, Yatish Patel, and John Kubiatowicz –ISCA 2009 How to compare layouts? (what is good)? –Probabilistic circuits  need metric that includes probability of failure –ADCR = Probabilistic version of area-delay product –Lower is better What to optimize? –Many different “datapath organizations” –Far too much error correction

31. 5/11/2009cs252-S09, Lecture 28 31 Datapath Organizations QLA: “Quantum Logic Array” –Every compute region has space for 2 bits and ancilla generation for 2 bits (to correct after every operation CQLA: “Compressed Quantum Logic Array” –Same compute regions as QLA, but ability to have less ancilla generation/bit for memory (idle bits less prone to error) Qalypso –Matching ancilla generation to needs

32. 5/11/2009cs252-S09, Lecture 28 32 Error Correction Optimization Selectively error correction placement –Standard techniques: correct after every error –Instead – only correct bits that are particularly “dirty” Error correction modeled after retiming optimization –Only place correction when approximate “EDist” parameter reaches threshold –Then, perform full mapping –Choose EDist by optimizing ADCR Very successful at reducing area/latency Even improves probability of success in some cases! –Why? Because error correction involves operations which can introduce error

33. 5/11/2009cs252-S09, Lecture 28 33 Shor’s Factoring Circuit Most of time spent in modular exponentiation –QFT is much smaller fraction of time –Easiest way to build modular exponentiation: with adders »Build multiplier instead? Not studied yet – would be very large Paper result: can factor in 7659 mm 2 –Previous result was 0.9 m 2

34. 5/11/2009cs252-S09, Lecture 28 34 Conclusion Computing can be done in a variety of ways –Normal silicon gates not required DNA Computing –Limited use “demonstration of concept” –Form of massive parallelism –Interesting consequences: self assembly Quantum Computing: –Computing using superposition and quantization –Ion Traps: a particularly promising technology CAD Tools for Quantum Computing –Can actually optimize circuits – just like classical case –ADCR = probabilistic version of Area-Delay product