CS252Graduate Computer Architecture

Lecture 28

Esoteric Computer ArchitectureDNA Computing & Quantum

Computing

Prof John D. Kubiatowicz

http://www.cs.berkeley.edu/~kubitron/cs252

5/11/2009 cs252-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

5/11/2009 cs252-S09, Lecture 28 3

DNA Computing and Hamiltonian Path

• Given a set of cities and costs between them (possibly directedpaths):– 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 2Path 1->2: CAAAWill 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!)

5/11/2009 cs252-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

Active Region

DN

A

Bon

ding

5/11/2009 cs252-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

5/11/2009 cs252-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>

5/11/2009 cs252-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!

PhosphorusImpurity Atoms

Single SpinControl Gates

Inter-bit Control Gates

5/11/2009 cs252-S09, Lecture 28 8

Now add Superposition!• The bit can be in a combination of “1” and

“0”:– Written as: = C0|0> + C1|1>– The C’s are complex numbers!

– Important Constraint: |C0|2 + |C1|2 =1

• If measure bit to see what looks like, – With probability |C0|2 we will find |0> (say “UP”)

– With probability |C1|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 (|C0|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!

5/11/2009 cs252-S09, Lecture 28 9

A register can have many values!• Implications of superposition:

– An n-bit register can have 2n values simultaneously!– 3-bit example:

= C000|000>+ C001|001>+ C010|010>+ C011|011>+ C100|100>+ C101|101>+ C110|110>+ C111|111>

• Probabilities of measuring all bits are set by coefficients:– So, prob of getting |000> is |C000|2, etc.– Suppose we measure only one bit (first):

» We get “0” with probability: P0=|C000|2+ |C001|2+ |C010|2+ |C011|2

Result: = (C000|000>+ C001|001>+ C010|010>+ C011|011>)» We get “1” with probability: P1=|C100|2+ |C101|2+ |C110|2+ |C111|2

Result: = (C100|100>+ C101|101>+ C110|110>+ C111|111>)

• Problem: Don’t want environment to measure before ready!– Solution: Quantum Error Correction Codes!

5/11/2009 cs252-S09, Lecture 28 10

Spooky action at a distance• Consider the following simple 2-bit state:

= C00|00>+ C11|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?

5/11/2009 cs252-S09, Lecture 28 11

Model: Operations on coefficients + measurements

• Basic Computing Paradigm:– Input is a register with superposition of many values

» Possibly all 2n inputs equally probable!– Unitary transformations compute on coefficients

» Must maintain probability property (sum of squares = 1)» Looks like doing computation on all 2n inputs simultaneously!

– Output is one result attained by measurement

• If do this poorly, just like probabilistic computation:– If 2n inputs equally probable, may be 2n 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

InputComplex

StateMeasure

OutputClassicalAnswer

5/11/2009 cs252-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 : xr 1 (mod N)4) If r is odd, GOTO 15) If r is even, a x r/2 (mod N) (a-1)(a+1) =

kN6) If a = N-1 GOTO 17) ELSE gcd(a ± 1,N) is a non trivial factor of

N.

Hard

Security of Factoring

EasyEasy

EasyEasyEasyEasy

5/11/2009 cs252-S09, Lecture 28 13

Finding r with xr 1 (mod N)

k

/\k /

\xkk

/\k /

\1

/\

/\x

y

r yw0w

w1r

( ) /\x

r0

r r1 k

0ww

1r

QuantumFourier

Transform

• Finally: Perform measurement– Find out r with high probability– Get |y>|aw’> where y is of form k/r and w’ is related

5/11/2009 cs252-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

5/11/2009 cs252-S09, Lecture 28 15

Ion Trap Quantum Computer

- Data = an ion

- Gate = a location

Tw

o-Qubit G

ate

• Ballistic Movement

- Apply pulse sequences to electrodes- Electrostatic forces move ion

Q1

Q2

- Intersections similar, but more complicated pulse sequences

• Major Components

5/11/2009 cs252-S09, Lecture 28 16

Ballistic Movement Network

One-Qubit Gate

Two-Qubit Gate

Two-Qubit Gate

Memory Cell

One-Qubit Gate

Memory Cell

R R

RR

Interconnection Network

Q2 Q3

Q4 Q5

Q1

• Problem: Noise accumulation!

5/11/2009 cs252-S09, Lecture 28 17

Noise Accumulation from Movement

• Noise may increase error by factor of 100

Qu

bit

Err

or

Distance Moved in Gates

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

0 16 32 48 64

1.0E-4 inital error

1.0E-5 inital error

1.0E-6 inital error

1.0E-7 inital error

1.0E-8 inital error

5/11/2009 cs252-S09, Lecture 28 18

D?

Movement Option 2: Teleportation

D

D

E2E1

Source Location Target 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. LocalOps

4. Local OpsEntanglement

5/11/2009 cs252-S09, Lecture 28 19

One-Qubit Gate

Q2

Two-Qubit Gate

Q3

Two-Qubit Gate

Q4 Q5

Memory Cell

Q1

One-Qubit Gate

Memory Cell

R R

RR

Interconnection Network

EPR Pair Distribution Network

EPR PairGenerators

5/11/2009 cs252-S09, Lecture 28 20

Setting Up a Teleportation Link

G PP

EPR QubitsEPR Qubits

Recycled QubitsRecycled 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

STRONGER Entanglement

5/11/2009 cs252-S09, Lecture 28 21

Chained Teleportation

G TT G TGT G TGT

PP

TeleportationTeleportation

• Adjacent T nodes linked for teleportation

• Positive Features- T node linking not on critical path- Pre-purification (Link Amplification): part of link setup

5/11/2009 cs252-S09, Lecture 28 22

Quantum Network Architecture

• Grid of T nodes

• Packet-switched network - Dimension-order routing

T T T T

T T T T

P P P P

P P P P

G

G

G

G

G

G G

G G G

, linked by G nodes

• Each qubit has associated message

Gate Gate Gate Gate

Gate Gate Gate Gate

5/11/2009 cs252-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

5/11/2009 cs252-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

programH

CX

HT

T

QEC QEC QEC

QEC QEC QECT

T QEC

QEC

QEC

QEC

QEC

QECQ0

Q1

time Serial Circuit Latency

5/11/2009 cs252-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

HCX

H

T

T QEC

QEC

QEC

QEC

QEC

QECQ0

Q1

Parallel Circuit Latency

5/11/2009 cs252-S09, Lecture 28 26

Running at The Speed of Data

• Ideally, execution time determined solely by data

time

hardware

Ancilla encoding

Operationsinvolving

data qubits

5/11/2009 cs252-S09, Lecture 28 27

Limited Ancilla Bandwidth

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1 10 100 1000

• 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)

Exe

cutio

n T

ime

of a

3

2-B

it Q

CL

A (

μs)

5/11/2009 cs252-S09, Lecture 28 28

Ancilla Factory Design I

• “In-place” ancilla preparation

Encoded Ancilla Verification Qubits

• Ancilla factory consists of many of these– Encoded ancilla prepared

in many places, thenmoved to output port

– Movement is costly!

In-placePrep

In-placePrep

In-placePrep

In-placePrep

0 Prep

Cat Prep

0 Prep

Cat Prep

0 Prep

Cat Prep

Verify

Verify

Verify

?

?

?

BitCorrect

PhaseCorrect

QEC QEC

Ancilla Generation Circuit

5/11/2009 cs252-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?

5/11/2009 cs252-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

success

single

P

LatencyAreaADCR

5/11/2009 cs252-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

5/11/2009 cs252-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

5/11/2009 cs252-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 mm2

– Previous result was 0.9 m2

5/11/2009 cs252-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