Abdullah Khalid

Quantum Information Scientist

Habib University, Karachi

IBA

12th November 2021

Are quantum computers faster than classical computers?

(Human) Computer

1788

1700s

1950s

Mechanical Computer

1940s

Electronic Computers

Total world computing capacity

2 x 10²⁰ – 1.5 x 10²¹ FLOPS

Computers solve computational problems

Decision

Search

Optimization

Decision Problems

Multiplication

Input: integers P and Q

Output: integer R = P x Q

Factorization

Input: integer R

Ouput: prime numbers P and Q

             such that R = P x Q

R = 21

digits = 2 = problem size

R = 498556150811

digits = 12 = problem size

General number field sieve algorithm

Sampling Problems

Binomial sampling

Input: n, p

Output: a sample from the binomial probability distribution

A random number generator!

"The underlying physical laws ... of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble." 1929

Simulation Problems

Simulating atoms, molecules and materials

Paul Dirac

Note: Turing published a universal model of computation in 1936

Extended Church-Turing Thesis

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

Church-Turing Thesis (simplified)

Any algorithmic process can be simulated using a Turing machine.

Turing Machine = very simple computer

Quantum Computers

Birth of Quantum Computers

Simulating atoms, molecules and materials

"Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy." Richard Feynman, 1982

Visions of Quantum Computing

Simulating atoms, molecules and materials (via Feynman)

Simulate this

By controlled experiments on this

Physicist's Extended Church-Turing Thesis

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

David Deutsch 1985

Chemistry

Biology

Computer science

Computing Machine = Physical System

=> Computational complexity is determined by physical laws

A physical universal computing machine depends on the underlying physical laws of the universe

Turing Machines

Quantum computers

Quantum Computers: The transport analogy

Laptop

Super computer

Quantitative

Qualitative

Quantum computer

Solve computational problem = Go from A to B

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

But they don't!

Decision Problems Complexity Classes

BQP (bounded-error quantum polynomial time )

= set of problems efficiently solvable by a quantum computer

Factorization

Quantum Computing Today

Prototype quantum computers exist on the cloud for testing

Are quantum computers practically faster than classical computers?

Road to Quantum Computers

Nature | Vol 574 | 24 OCTOBER 2019

Quantum Random Circuit

Sampling problem

Input: Circuit C (randomly selected from a special set of circuits)

Output: a sample from the output probability distribution of C

Difficult for classical computer

Outputs = 2ⁿ Output strings, each with different probability

Soon after: Arxiv: 1910:09534 22 Oct 2019

2.5 days only to simulate on a super computer, using our better classical algorithm!

Arxiv: 2111:03011 (4 Nov 2021)

Text

Even better classical algorithm that can do the same number of samples in a few dozen seconds on the fastest supercomputer

Thank you

Questions?

What should Pakistan do to prepare for the quantum computing future?

1. Invest in quantum computing and cryptography research.
    
2. Build quantum cryptography infrastructure.
    
3. Invest in policy research.
    
4. Participate in international encryption standards committees.