Quantum Computing IICPSC 321

Andreas Klappenecker

Announcements

• Monday, November 29, 6:00pm-7:15pm, HRBB 113, review session for midterm exam

• Tuesday, November 30, midterm exam

• CPSC 640 Quantum Algorithms• Elephant walk

Quantum Bits

The Stern-Gerlach Experiment

Quantum Bits

Memory

Quantum Computing in a Nutshell

Operations on a Quantum Computer

Example

Teleportation

Teleportation – It’s Simple!

Teleportation, Step by Step

• Alice has two quantum bits• Bob has one quantum bit• Alice wants to teleport the state of

one quantum bit• Alice and Bob share entangled bits

• |00> + |11> = (1,0,0,1) normalized to length 1

Teleportation – Set up

Teleportation – Initial State

Step 1 - XOR

Step 2

Rewrite State

Measurement

Current Research Topics

Conclusion

• The basic model is simple• Everyone can write a simulator of a

quantum computer in a very short time

• The computational model is different – you need time to absorb that!

• Numerous potential technologies!

Prepare for the Exam

• Comprehensive Exam!• Emphasis more on newer topics

• Datapath and Control• Caching• Pipelines• I/O• Multithreading

• But also some older topics!

Prepare for the Exam

• Read the book• Chapters 5,6,7; skim through later

chapters and appendices• Skim through the previous chapters

1-4• Learn

Caching

• Given: A cache with some entries and a sequence of load/store instructions• Describe the evolution of the cache• When is it a hit or a miss?

• What are the different eviction strategies?• LRU• Random • many others …

Caching Basics

• What are the different cache placement schemes? • direct mapped• set associative• fully associative

• Explain how a 2-way cache with 4 sets works• If we want to read a memory block whose address is

addr, then we search the set addr mod 4• The memory block could be in either element of the

set• Compare tags with upper n-2 bits of addr

Implementation of a Cache

Sketch an implementation of a 4-way associative

cache

Measuring Cache Performance

• CPU cycle time• CPU execution clock cycles (including cache

hits)• Memory-stall clock cycles (cache misses)• CPU time = (CPU execution clock cycles +

memory stall clock cycles) x clock cycle time

• Memory stall clock cycles • read stall cycles (rsc)• write stall clock cycles (wsc)• Memory stall clock cycles = rsc + wsc

Measuring Cache Performance

• Write-stall cycle [write-through scheme]:• two sources of stalls:• write misses (usually require to fetch the block)• write buffer stalls (write buffer is full when write

occurs)• WSCs are sum of the two:

WSCs = (writes/prg x write miss rate x write miss penalty) + write buffer stalls

• Memory stall clock cycles similar

Cache Performance Example

• Instruction cache rate: 2%• Data miss rate: 4%• Assume that 2 CPI without any memory stalls• Miss penalty 40 cycles for all misses• Instruction count I• Instruction miss cycles = I x 2% x 40 = 0.80 x I

• gcc has 36% loads and stores• Data miss cycles = I x 36% x 4% x 40 = 0.58 x I

Pipelining

• Pipeline hazards• structural hazards [hardware cannot support the combination of instructions that we

want to execute during same clock cycle]• control hazards [need to make decision based on instruction that is still executing]• data hazards [instruction depends on results of a previous instruction that is still in

pipeline]

• Various remedies, for instance, • stall pipeline• forwarding• delayed branch block

Pipelined Version

Pipelining

Learn how to find out dependencies using pipeline diagramNeed to know the pipeline hazards inside outQ: Given a sequence of instructions, give a timing diagram [ Clock cycle | IF | ID | EX | MEM | WB ]

Timing Diagrams

Finding Dependencies

Dependencies that go backwards in time lead to a data hazard

Forwarding

Data hazard:

add $s0, $t0, $t1

sub $t2, $s0, $t3

Stalling the Pipeline

• and needs result of lw operation• hazard forces stalling of the pipeline • and and or ops need to repeat in clock cycle 4 what

they did in previous clock cycle

Typical Questions (Small Sample!)

• Chapter 6, problems 6.2, 6.3, 6.4• How much speed-up do you get by

pipelining? • How many cycles will it take to execute

this code? Problem 6.15 • Loop unrolling, problem 6.30

Verilog?

• I will ask little bits and pieces in mixed questions

• There will be no extensive Verilog programming on paper

• Little programming questions? Yes