Is information processing a physical phenomenon

1
Is information processing a physical phenomenon?

• G.J. Milburn
• The University of Queensland

2
The BITatom of information.

• Transistor ON 1
• Transistor OFF 0
• Mutually exclusive alternatives.
• One bit.
• the information needed to store the result of a
  single coin toss.

C. Shannon
3
The BITatom of information.

• How much information is needed to store the
  result for the toss of two coins ?
• HH00, HT01, TH10, TT11
• Four outcomes ----- two bits.

4
Paths to a quantum computer.

• The beginning
• R.P. Feynman, 1982
• Simulating physics with computers,

5
Feynmans question.

• Can a quantum system be simulated efficiently
  by a conventional computer ?
• NO !

6
What is a quantum system ?

• THE QUANTUM PRINCIPLE.
• The physical universe is irreducibly random.
• Given complete knowledge of the state of a
  physical system, there is at least one
  measurement the results of which are completely
  random.

7
How is quantum physics possible ?

• CERTAINTY WITHIN UNCERTAINTY
• Given complete knowledge of a physical state
  there is at least one measurement the results of
  which are completely certain.

8
How is quantum physics possible ?

• We can compute the odds.
• The probability of any measurement can be
  calculated.
• Butto compute the odds we need a new
  mathematicsprobability amplitudes.
• Not 0 or 1 but 0 and 1.the superposition
  principle.

9
A quantum coin toss.

• A single photon at a beam splitter.

• 50 of light is reflected or transmitted.

10
A one photon bit ?
Probability of reflection 1/2 Probability of
transmission1/2 Prob. Count photon at
U1/2 Prob. Count photon at D 1/2 Is this
a coin-toss ? Does this encode one bit?
11
A one photon bit ?

• Toss a photon twice.

Is this like tossing a coin twice ?
12
A one photon bit? No.

• Experiment
• detection at U is certain.

• Irreducible randomness is made certain !

13
The one photon qubit.
State of photon after beam splitter ? Not
reflected or transmitted. Not logical 1 or
0. It is a superposition of both
possibilities. It is a qubit.
14
Quantum parallel input.

• superposition of binary strings.
• Length 2

Two physical qubits can encode four binary
numbers simultaneously. The output is a
superpostion of all biary strings of length two.
15
Quantum parallel computation
N physical qubits can encode 2N binary numbers
simultaneously A quantum computer can process
all 2N numbers in parallel on a single machine
with N physical qubits. Very hard to simulate
a quantum computer on a classical computer.
400 qubits 10120 bits (holographic
bound.Davies, 2006).
16
The Feynman processor.

• A physical computer operating by quantum rules.
• could it compute more efficiently than a
  conventional computer ?

17
Computational efficiency.

• Efficiency
• How many steps are required to compute a function
  (how many operations per second)?
• How does the number of steps depend on the size
  of the problem.

18
Computational efficiency example

• Find the prime factors of
• 2385269 (1001000110010101110101)
• How ?divide by 2.no
• Divide by 3.no
• And so on until
• Divide by 541yes... 2385269 541 x 4409
• In general to factor integer X, need
  steps.
• Add one digit to X, need about three times as
  many steps that is an exponential increase !

19
Deutsch and quantum parallelism.

• D. Deutsch, Oxford, 1985
• Quantum theory, the Church-Turing principle and
  the universal quantum computer.
• Prepare input as a superposition of all possible
  inputs.
• Run computer once to give all possible values of
  the calculation.

20
Quantum parallel input.

• Superposition of all calculations in a single
  machine.

21
Shor algorithm.

• Peter Shor, ATT, USA, 1993
• a quantum algorithm to find prime factors of
  large composites N
• public key cryptography no longer safe !
• Key step
• find the period of the function
• (x is random, but GCD(x,N)1)

22
Example.

• Factor 15.

• Order4
• Calculate
• Factors GCD(48,15)3, GCD(50,15)5

23
Factoring on a QC

• Finding the period is exponentially hard on a
  classical computer..or so we think!
• A QC can find it in one run (most of the time).
• Given the period, the rest is trivial for a
  classical computer.

24
The implications of efficient factoring.

• Current public key encryption assumes there is no
  efficient algorithm for finding the prime factors
  with a conventional computer.
• Shors algorithm is impossible in a classical
  world.
• If a QC is built, current encryption protocols
  are insecure

25
Computation is a physical process.

• Hardware determines the algorithm.
• Computers are physical objects and computations
  are physical processes. What computers can and
  cannot do are determined by the laws of physics
  alone and not by pure mathematics. Deutsch.
• computation is not a machine process..it is
  an abstract mathematical process that exists only
  relative to conscious observers.. Searle.

26
Synthetic reality

• Feynman, 1982
• Can physical reality be efficiently simulated ?
• Feynman-Deutsch principle
• Every finitely realisable physical system can
  be perfectly simulated by a universal (quantum)
  Turing machine operating by finite means.

27
Feynman-Deutsch principle and measurement.

• The virtual graduate student part one.

28
Bohrs insight.

• Quantum measurement theory
• ...however far the phenomenon transcend the
  scope of classical physical explanation, the
  account of all evidence must be expressed in
  classical terms (Bohr, 1934)

29
Feynman-Deutsch principle and measurement.

• The virtual graduate student part two.

30
Quantum measurement.

• Feynman-Deutsch principle
• (Measurement formulation)
• The results of all finitely describable
  physical measurement systems can be perfectly
  simulated by a universal quantum computer
  operating by finite means, producing finite
  measurement records.

31
Simulate consciousness on a QC ?

• Can we simulate Alice as well ?
• We do not know the operating system of the brain.
• Can we monitor the state of a QC from one step to
  the next ?
• NO !

32
Conclusion.

• Quantum computing machines enable new algorithms
  that cannot be realised in a classical world.
• The algorithms can be powerful physical
  simulators.
• The physics determines the algorithm.
• The hardware matters...