Abdullah Khalid

Quantum Information Scientist

Guftugu Seminar Series

11th October 2019

Chemistry

Biology

Computer science

Computing Machine = Physical System

Decision

Search

Optimization

Input: integers P and Q

Output: integer R = P x Q

Input: integer R

Ouput: prime numbers P and Q

such that R = P x Q

R = 21

digits = 2

R = 498556150811

digits = 12 = problem size

General number field sieve algorithm

Multiplication

Factorization

Resources = time/memory

Problem size (n)

Hard/inefficient

Easy/efficient

"Top secret info"

"Top secret info"

"hf72h18v82ja9"

You

You

Military

Bank

Email provider

Military

Encryption/Decryption = Multiplication = Easy

Cracking = Factorization = Hard

Rivest–Shamir–Adleman

Key: 10101011101...

Security ∝ number of digits

Recommended key size: 4096 bits

(for security till 2030)

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

Simulating atoms, molecules and materials

Paul Dirac

Computing Machines = Physical Systems

=> Computational complexity is determined by physical laws

Simulating atoms, molecules and materials

Simulate this

By controlled experiments on this

Laptop

Super computer

Quantitative

Qualitative

Quantum computer

Solve computational problem = Go from A to B

arXiv:1909.07353

predict the stock market

optimize airline schedules

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

But they don't!

Breaking encryption on Quantum Computer

Text

NP-Complete Problems on Classical/Quantum Computer

Breaking encryption on Classical Computer

Resources

Problem size (n)

Quantum computers

Quantum supremacy devices

Solve a (useless) problem exponentially faster than a classical computer

Solve a (useful) problem exponentially faster than a classical computer

Analogy

Nature | Vol 574 | 24 OCTOBER 2019

**Computational problem**

Input: Circuit C

Output: a sample from the output probability distribution of C

Difficult for classical computer

Outputs = 2^{n} Output strings, each with different probability

53+1 qubits, depth = 20

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

arXiv:1909.07353

No proofs of security, but hope!

Secret key: 1011101111010... for symmetric key encryption

$5000-50,000