Abdullah Khalid

Quantum Information Scientist

The Second Floor

3rd October 2019

1788

1700s

1950s

1940s

Total world computing capacity

2 x 10^{20} – 1.5 x 10^{21} FLOPS

Input: integers P and Q

Output: integer R = P x Q

Algorithms

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

Multiplication

Factorization

"Top secret info"

"Top secret info"

"hf72h18v82ja9"

You

You

Military

Bank

Email provider

Military

Encryption/Decryption = Multiplication

Cracking = Factorization

Rivest–Shamir–Adleman

Key: 10101011101...

Security ∝ number of digits

Recommended key size: 4096 bits

(for security till 2030)

1600 onwards

1900 onwards

Newton Faraday

Einstein

Heisenberg

Born

Schrodinger

"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

Simulating atoms, molecules and materials

Human computer

Super computer

Quantitative

Qualitative

Quantum computer

Computational problem: Go from A to B

Simulating atoms, molecules and materials

Simulate this

By controlled experiments on this

predict the stock market

optimize airline schedules

Breaking encryption on Quantum Computer

Text

NP-Complete Problems on Classical Computer

NP-Complete Problems on Quantum Computer

Breaking encryption on Classical Computer

arXiv:1909.07353

arXiv:1909.07353

No proofs of security, but hope!

Secret key: 1011101111010...

Provably secure against quantum computers

$5000-50,000

- Invest in quantum computing and cryptography research.

- Build quantum cryptography infrastructure.

- Invest in policy research.

- Participate in international encryption standards committees.