DNA Computing Can we use DNA to do massive computations? Organisms do it DNA has very high information. Even more promising uses of DNA

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1 CS252 raduate Computer Architecture Lecture 28 Esoteric Computer Architecture DNA Computing & Quantum Computing Prof John D. Kubiatowicz DNA Computing Can we use DNA to do massive computations? Organisms do it DNA has very high information density:» 4 different base pairs: AdenineThymine uaninecytosine» Always paired on opposite strands Energetically favorable Active operations:» Copy: Split strands of DNA apart in solution, gain 2 copies» Concatenate: eg: TAATCCT will combine XXXXXCATT with AAYYYYY» Polymerase Chain eaction (PC): amplifies region of molecule between two marker molecules 1999 Access the National Health Museum cs252-s09, Lecture 28 2 DNA Computing and Hamiltonian Path iven 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: AAT for city 1, TTC for city 2 Path 1->2: CAAA Will build: AATTTC..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!) 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 Active egion DNA Bonding Other interesting structures could be Active built egion cs252-s09, Lecture cs252-s09, Lecture 28 4

2 Use Quantum Mechanics to Compute? Weird but useful properties of quantum mechanics: Quantization: Only certain values or orbits are good» emember 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 Transistorss 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! rover s algorithm: Finds items in unsorted database in time proportional to square-root of n. Materials simulation: exponential classically, linear-time QM Quantization: Use of Spin Spin ½ particle: (ProtonElectron) North South epresentation: 0> or 1> 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 cs252-s09, Lecture cs252-s09, Lecture 28 6 Kane Proposal II (First one didn t quite work) Single Spin Control s Inter-bit Control s Phosphorus Impurity Atoms Bits epresented by combination of protonelectron spin Operations performed by manipulating control gates Complex sequences of pulses perform NM-like operations Temperature < 1 Kelvin! cs252-s09, Lecture 28 7 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 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 eality: second choice! There are experiments to prove it! cs252-s09, Lecture 28 8

3 A register can have many values! Implications of superposition: An n-bit register can have 2 n values simultaneously! 3-bit example: = C >+ C >+ C >+ C >+ C >+ C >+ C >+ C > 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 C C C esult: = (C >+ C >+ C >+ C >)» We get 1 with probability: P 1 = C C C C esult: = (C >+ C >+ C >+ C >) Problem: Don t want environment to measure before ready! Solution: Quantum Error Correction Codes! cs252-s09, Lecture 28 9 Spooky action at a distance Consider the following simple 2-bit state: = C 00 00>+ C 11 11> Called an EP pair for Einstein, Podolsky, osen Now, separate the two bits: Light-Years? 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 EP 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 cs252-s09, Lecture Model: Operations on coefficients + measurements Input Complex State Unitary Transformations Measure Output Classical Answer 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 The Security of SA 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) Hard Security of Factoring 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, OTO 1 5) If r is even, a x r2 (mod N) (a-1)(a+1) = kn 6) If a = N-1 OTO 1 7) ELSE gcd(a ±1,N) is a non trivial factor of N cs252-s09, Lecture cs252-s09, Lecture 28 12

4 Finding r with x r 1 (mod N) k Quantum Fourier Transform \ k 1 \ r 1 r 1 w 0 y k cs252-s09, Lecture \ k x k\ w r y \ x \ w w ( ) \ w 0 0 r 1 k Finally: Perform measurement Find out r with high probability et y> a w > where y is of form kr and w is related r r x ION Trap Quantum Computer: Promising technology Cross- Sectional View Top IONS of Be+ trapped in oscillating quadrature field Internal electronic modes of IONS used for quantum bits MEMs technology Target? 50,000 ions OOM Temperature! Ions moved to interaction regions Ions interactions with one another moderated by lasers Top View Proposal: NIST roup cs252-s09, Lecture Ion Trap Quantum Computer Major Components - Data = an ion - = a location Ballistic Movement - Apply pulse sequences to electrodes - Electrostatic forces move ion - Intersections similar, but more complicated pulse sequences Two-Qubit One-Qubit Q2 One-Qubit Memory Cell Ballistic Movement Network Interconnection Network Two-Qubit Two-Qubit Q4 Q3 Q5 Memory Cell Q2 Problem: Noise accumulation! cs252-s09, Lecture cs252-s09, Lecture 28 16

5 Qubit Error Noise Accumulation from Movement 1.0E E E E E E E Distance Moved in s Noise may increase error by factor of E-4 inital error 1.0E-5 inital error 1.0E-6 inital error 1.0E-7 inital error 1.0E-8 inital error cs252-s09, Lecture Movement Option 2: Teleportation Source Location 2. Local Ops Teleportation Benefits D 3. Transmit two classical bits Entanglement E cs252-s09, Lecture E2 1. enerate EP pair oal: Transfer the state, not the data ion Problem: EP pairs become noisy Target Location 4. Local Ops D? D - Error Correction of data (arbitrary state): ~100 ms Purification of EP pair (known state): ~120 µs - Pre-distribution of EP pairs EP Pair Distribution Network Setting Up a Teleportation Link One-Qubit Q2 One-Qubit EP Pair enerators Two-Qubit Q3 Two-Qubit Q4 Q5 Purification = Amplification of EP pair link - Two EP pairs One purer pair, one junk pair - Chance of failure Need to send multiple pairs P STONE EP QubitsEntanglementEP Qubits P Memory Cell Interconnection Network Memory Cell ecycled Qubits ecycled Qubits cs252-s09, Lecture For Data Teleportation cs252-s09, Lecture 28 20

6 T P Chained Teleportation Teleportation Teleportation T T T T T Adjacent T nodes linked for teleportation P Quantum Network Architecture T T T T P P P P T T T T P P P P Positive Features - T node linking not on critical path - Pre-purification (Link Amplification): part of link setup cs252-s09, Lecture rid of T nodes, linked by nodes Packet-switched network - Dimension-order routing Each qubit has associated message cs252-s09, Lecture Classical Control Quantum Datapath Layer - T Nodes and Nodes (P Nodes and s not shown) Classical Control Layers - Messages Associated with Qubits - Teleportation and Purification Bits unning a Quantum Circuit Simple gates (transversal) More complex gates (non-transversal) Exist in any universal set Quantum Error Correction () 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 Computation with ancilla qubits > 90% of quantum program Q0 T H T T T C X H time Serial Circuit Latency cs252-s09, Lecture cs252-s09, Lecture 28 24

7 unning 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 unning at The Speed of Data Ideally, execution time determined solely by data hardware Operations involving data qubits Q0 H T C X H Parallel Circuit Latency cs252-s09, Lecture T time Ancilla encoding cs252-s09, Lecture Limited Ancilla Bandwidth Ancilla Factory Design I Execution Time of a 32-Bit QCLA (μs) Encoded Ancilla Bandwidth Available (Ancillae per ms) 32-bit Quantum Carry-Lookahead Adder Varying rate at which encoded zero ancillae are provided for Conclusion: design architecture with ancilla factories cs252-s09, Lecture In-place ancilla preparation Ancilla eneration Circuit Encoded Ancilla Verification 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 cs252-s09, Lecture Prep Cat Prep 0 Prep Cat Prep 0 Prep Cat Prep Verify Verify Verify??? Bit Correct Phase Correct

8 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 oals Design ancilla factories Answer Question: How much hardware is needed for ancilla generation to run at the speed of data? 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 ADC = Probabilistic version of area-delay product Area Latencysingle ADC P success Lower is better What to optimize? Many different datapath organizations Far too much error correction cs252-s09, Lecture cs252-s09, Lecture Datapath Organizations Error Correction Optimization 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 generationbit for memory (idle bits less prone to error) Qalypso Matching ancilla generation to needs cs252-s09, Lecture 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 ADC Very successful at reducing arealatency Even improves probability of success in some cases! Why? Because error correction involves operations which can introduce error cs252-s09, Lecture 28 32

9 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 cs252-s09, Lecture 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 ADC = probabilistic version of Area-Delay product cs252-s09, Lecture 28 34