The race to demonstrate quantum supremacy, and onward to quantum computers

Abdullah Khalid

Quantum Information Scientist

HUAIC

5th November 2019

Computational Problems

Decision

Search

Optimization

Decision Problems

Multiplication

Input: integers P and Q

Output: integer R = P x Q

Algorithms

Is left most digit 1 in binary?

Decision Problems

Factorization

Input: integer R

Ouput: prime numbers P and Q

             such that R = P x Q

 

 

 

 

 

Algorithms

R = 21

digits = 2

 

R = 498556150811

digits = 12

  • Dixon's algorithm
  • Continued fraction factorization
  • Quadratic sieve
  • Rational sieve
  • General number field sieve
  • Shanks's square forms factorization

Is left most digit of bigger prime 1 in binary?

Cryptography

"Top secret info"

"Top secret info"

"hf72h18v82ja9"

You

You

Military

Bank

Email provider

Military

Sampling Problems

Binomial sampling

Input: n, p

Output: a sample from the binomial probability distribution

 

A random number generator

 

 

 

 

 

Extended Church-Turing Thesis [1]

Any algorithmic process can be simulated efficiently using a probabilistic Turing machine.

Church-Turing Thesis

Any algorithmic process can be computed using a Turing machine.

[1] They didn't actually say it.

Physicist's Extended Church-Turing Thesis

Every finitely realizable physical system can be perfectly simulated by a universal computing machine operating by finite means - Deutsch 1985

Chemistry

Biology

Computer science

Computing Machine = Physical System

Computing Machines = Physical Systems

=> Computational complexity is determined by physical laws

Computational Complexity

Multiplication

Factorization

Resources

Problem size (n)

Decision Problems Complexity Classes

Factoring

Multiplication

Circuit model of classical computation

Width/Space = n

Depth/Time = m

Input: Any of 2n n-bit strings

Output: 1-bit string

Quantum Computers

Quantum Circuits

Text

Text

n-qubits => 2n outcomes

  • Solves same computational problems as classical computer
  • Algorithm is different because of architecture difference

Quantum Computers: The transport analogy

Human computer

Super computer

Quantitative

Qualitative

Quantum computer

Solve computational problem = Go from A to B

Quantum computers CANNOT

 

do industrial optimization
predict the stock market
optimize airline schedules

NP-Complete problems

 

exponentially faster than classical computers.

If this was true, quantum computers could solve NP-complete problems efficiently

 

 

But they don't!

 

 

 

Quantum computers can

 

simulate atoms, molecules and materials,

 

exponentially faster than classical computers.

Quantum computers can

 

maybe do machine learning and optimization

 

exponentially faster than classical computers.

Quantum computers can

 

break all currently used asymmetric encryption protocols

 

exponentially faster than classical computers.

Quantum vs Classical Computers

Breaking encryption on Quantum Computer

Text

NP-Complete Problems on Classical/Quantum Computer

Breaking encryption on Classical Computer

Resources

Problem size (n)

Decision Problems Complexity Classes

BQP (bounded-error quantum polynomial time )

= set of problems efficiently solvable by a quantum computer

Quantum computers difficult to build due to engineering challenges

Nature | Vol 574 | 24 OCTOBER 2019

Quantum Supremacy Quantum Advantage
A devices that: Solves any problem faster than classical Solves useful problems faster than classical
Requires Non-universal quantum computational device Universal Quantum Computer
Quantum error correction
Analogies Fission experiments Nuclear power stations
Wright brothers flight Commercial/military airplanes

Depth/Time = m

Width/Space = n

Quantum Random Circuit

Outputs = 2n Output strings, each with different probability

Form a random circuit using √ X , √ Y , √ W , and a combination of iSWAP and C-Z.

,

Quantum Random Circuit

Computation problem

Input: Circuit C

Output: a sample from the output probability distribution of C

Easy for quantum computer

Difficult for classical computer

Google's superconducting chip

53+1 qubits, depth = 20

How to verify a device which you claim can't even be classically simulated?

Linear cross-entropy benchmarking fidelity

  1. Collect finite samples x1, x2, x3, ...
  2. Calculate probabilities P(xi) of measuring xi given circuit C
  3. Calculate FXEB = 2n Avg(P(xi)) - 1

FXEB = 0 => uniform random distribution

FXEB = 1 => error-free quantum random circuit

Verification that device works

Is quantum supreme?

Google's claim: 10,000 years on a state of the art supercomputer, using the best classical algorithm they could think of.

 

 

IBM's claim: Sorry, 2.5 days only using our better classical algorithm!

Quantum device performance: 600 seconds to sample 3 million times

The race to demonstrate quantum supremacy, and onward to quantum computers

By abdullahkhalids

The race to demonstrate quantum supremacy, and onward to quantum computers

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