### Google just built a quantum computer(?), and Pakistan is sitting ducks!

Abdullah Khalid

Quantum Information Scientist

Guftugu Seminar Series

11th October 2019

## What is a computer?

Chemistry

Biology

Computer science

Computing Machine = Physical System

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

R = 498556150811

digits = 12 = problem size

General number field sieve algorithm

## Computational Complexity

Multiplication

Factorization

Resources = time/memory

Problem size (n)

Hard/inefficient

Easy/efficient

### Application of computation: Cryptography

"Top secret info"

"Top secret info"

"hf72h18v82ja9"

You

You

Military

Bank

Email provider

Military

# RSA encryption protocol

Encryption/Decryption = Multiplication = Easy

Cracking = Factorization = Hard

Key: 10101011101...

Security ∝ number of digits

Recommended key size: 4096 bits

(for security till 2030)

## 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 Problem

Simulating atoms, molecules and materials

Paul Dirac

# Quantum Computers

Computing Machines = Physical Systems

=> Computational complexity is determined by physical laws

# Visions of Quantum Computing

Simulating atoms, molecules and materials

Simulate this

By controlled experiments on this

## Quantum Computers: The transport analogy

Laptop

Super computer

Quantitative

Qualitative

Quantum computer

Solve computational problem = Go from A to B

## break all currently used asymmetric encryption protocols

### exponentially faster than classical computers.

arXiv:1909.07353

## 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 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)

# Quantum Computing Today

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

## Quantum Random Circuit

Computational problem

Input: Circuit C

Output: a sample from the output probability distribution of C

Difficult for classical computer

Outputs = 2n Output strings, each with different probability

53+1 qubits, depth = 20

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

## 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

# How do we prepare for the coming quantum computing world?

## First Option: Post-Quantum Crypto Algorithms

arXiv:1909.07353

No proofs of security, but hope!

## Second Option: Quantum Key Distribution

Secret key: 1011101111010... for symmetric key encryption

\$5000-50,000

## Participate in international encryption standards committees.

#### Google just built a quantum computer(?), and Pakistan is sitting ducks! How to prepare for the coming quantum computing age.

By abdullahkhalids

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