ECE 497NC: Unconventional Computer Architecture

1
ECE 497NC Unconventional Computer Architecture
Nicholas Carter

• Lecture 12
• Quantum Computers II
• Implementation Issues

2
Outline

• Hurdles to building quantum computers
• Decoherence
• Error Correction
• Requirements for workable quantum computers
• NMR quantum computers
• Complete architecture proposal

3
Decoherence

• Quantum computations rely on being able to
  operate on a set of qubits in an
  entangled/superimposed state
• Allows computation on all possible inputs to a
  computation in parallel
• Problem Interaction of qubits with environment
  affects their state, causing them to not be
  entangled/superimposed
• Can partially address this by designing computer
  to reduce interaction with environment, but this
  may make it impractical (for example, running at
  very low temperatures)
• General result a quantum computation can only
  proceed for a limited period of time before a
  measurement must be performed
• Measurement forces the system into a more-stable
  classical state
• Measurement destroys superposition
• System limited by ratio of decoherence time to
  operation latency

4
Quantum Errors

• Digital systems provide noise protection by
  mapping an analog signal onto two discrete states
• Any error/noise that doesnt cause the system to
  mis-interpret a signal gets corrected by the next
  circuit that reads the signal
• Problem qubits are analog
• Need to be able to operate on qubits that are
  superpositions of multiple states
• Observation of qubits collapses them into one
  state or another
• Also, operations on qubits are unlikely to be
  perfect, another source of error
• Need error correction

5
Classic Error Correction

• Basic idea encode n bits of data as n m bits
  of error-detecting data.
• For codes where the original n bits remain
  unchanged, the m bits are called the syndrome.
• Example Hamming codes
• Well-understood trade-off between m and number of
  errors that can be corrected/detected
• Whenever data is read, regenerate the m syndrome
  bits
• Compare to syndrome from data to determine if
  error has occurred
• Depending on the code, may be able to correct
  errors as well as just detect

6
Quantum Error Correction

• Problem reading qubits in a superimposed state
  collapses them to one state or the other.
• Cant use coding algorithms that require
  examining the data bits to detect errors
• Solution use codes based on measurements that
  only determine information about errors, not
  about data
• Theoretical best code uses 5 qubits to encode 1
• Commonly-used code uses 7 qubits for each data
  qubit.
• Can recursively apply encoding technique to
  tolerate higher error probabilities
• For some codes, can build gates that operate on
  encoded data directly, without decoding
• Code used in paper requires about 153 physical
  gates to implement a fault-tolerant operation
• Implementation parameter error rate of
  technology determines how much logic can be done
  between error corrections, and thus overhead of
  error correction.

7
Requirements for Quantum Computer

• Need to have something to represent qubits
• Lots of physical phenomena that have two states
• Must be able to address individual qubits, and
  qubits must be able to interact
• Must be able to apply individual qubits as inputs
  to gates
• Need to have gates with gt1 input
• Must be able to initialize qubits to a known
  state
• Hard to write programs if you cant set inputs
• Must be able to observe/extract result from
  system
• Yep, the answers in there somewhere, just cant
  get it out
• Coherence time must be long compared to gate
  delay
• This basically determines how many operations we
  can do on a superposition before we have to do an
  observation
• Implementation detail visible to programmer

8
NMR-Based Quantum Computers

• Most advanced demonstrated technology for quantum
  computation
• Use nuclei with spin ½ as qubits
• Spin straight up 0gt
• Spin straight down 1gt
• Other directions indicate superpositions of 0gt
  and 1gt
• Long coherence times (seconds)
• Electron spins (alternate technology) have
  coherence times of nanoseconds
• In a magnetic field, spin direction precesses
  about the fields axis at a rate that is
  proportional to the field strength

9
NMR-Based Computers II

• Bond atoms that represent qubits into molecules
• Inter-atomic bonds provide mechanism for
  different qubits to interact.
• Each molecule becomes an n-qubit computing system
• Can operate on multiple molecules in parallel to
  reduce errors
• Asymmetry of molecule causes different atoms to
  precess at different frequencies
• Individual addressability

10
Structure of System
Tube
RF Coils
Static field coils
11
Implementing Operations

• Key ideas
• Radio energy applied perpendicular to magnetic
  field causes spins to rotate around axis of RF
  field if RF frequency is a resonant frequency of
  the precession frequency
• Pulses of different durations cause different
  amounts of rotation
• Position of spin of atom A affects precession
  rate of nearby atom B by altering the magnetic
  field seen by B
• Differences between precession frequencies of
  different atoms in the molecule gtgt effect of
  nearby atom spins

12
Implementing Operations I

• Can flip state of bit with appropriately-timed RF
  pulse, or set into superposition with shorter
  pulse
• Can create multi-input gates by sending pulses at
  the frequency that the atom will precess at if
  appropriate other bits are in a given state.
• CNOT operation
• CNOT operation set of operations on individual
  qubits universal set of gates
• Machine language is now set of frequency of RF
  pulses, duration of pulses, and time between
  pulses
• Read state out by rotating qubit spins into
  horizontal plane, sensing the time-varying
  magnetic field they create as they precess

13
Results

• Used NMR technology to implement the core of
  Shors algorithm on permutations of a
  four-element set.
• Duration 50-500ms, depending on permutation

14
Full System Architecture

• Goal extend thoughts on ways to do computation
  with quantum to something like a full system
• Issues
• Data storage
• Communication/signalling
• Error correction overhead
• Basic idea Couple quantum computing system with
  classical computer
• Classical computer sequences operations through
  quantum computer, does dynamic compilation
• Classical computer also does checking of results
  for probabilistic computations
• System aimed at NP-complete problems where
  computing answer is hard but checking answer is
  easy.

15
Programming/Compiling

• Two-phase process
• Pre-compiler generates code that executes the
  algorithm with a specified error probability on
  an ideal quantum computer
• Dynamic compiler creates instruction stream to
  meet the error probability on the actual computer
• This compiler needs to know about the technology
• Also needs estimate of program run time
• errors is proportional to run time.
• Estimate either provided by user or generated
  using profiling
• For example, can start with very conservative
  (strong) error correction and use lower levels
  once the running time is known

16
Error Correction

• Problem 7-bit codes only tolerate certain
  amounts of error
• Can tolerate greater errors by recursive coding,
  at greatly increased cost
• Sawtooth overhead as error rates cross critical
  thresholds
• Solution Cluster operations
• Rather than performing error correction on each
  operation, group operations into clusters and
  only do error correction after each cluster.
• Allows fractional levels of recursion, bringing
  error correction cost much closer to ideal.

17
Architecture

• Quantum ALU/Ancilla generator
• Performs actual computations and error correction
• Implements set of universal quantum operations
• Quantum Memories
• Storage locations for qubits
• Assumed to have 2 orders of magnitude lower error
  rates than CPU
• Entropy Exchange Unit
• Source of qubits in 0gt or CAT state
• Important, because many algorithms require many
  qubits in one of these states or the other
• Inter-unit communication via quantum
  teleportation
• Allows exact state of qubits to be transmitted
• Extension to quantum teleportation allows
  conversion from one error-correcting code to
  another as part of teleportation

18
Conclusions/Thoughts

• Quantum computing is still way out there, though
  people are starting to demonstrate actual systems
• One issue current designs expose implementation
  issues to programmer
• Time that computation can run before decoherence
  becomes an issue
• Number of steps that can be performed before need
  to do a measurement
• Still big gaps between demonstrated results and
  the theoretical predictions people are using to
  do designs
• My gut feelings
• Well see quantum computers being built for
  specific problems in the next decade or two
• Quantum computing wont move into the mainstream
  unless a vastly better implementation technology
  is developed and a much larger set of problems
  that are good for quantum are discovered