Abdullah Khalid

Quantum Information Scientist

Habib University, Karachi

IBA

12th November 2021

1788

1700s

1950s

1940s

## Electronic Computers

Total world computing capacity

2 x 1020 – 1.5 x 1021 FLOPS

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

## Computational Complexity

Multiplication

Factorization

Resources = time/memory

Problem size (n)

Hard/inefficient

Easy/efficient

### Multiplication/Factorization dichotomy application: 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 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

# Birth of Quantum Computers

Simulating atoms, molecules and materials

# 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!

## break all currently used asymmetric encryption protocols

### exponentially faster than classical computers.

arXiv:1909.07353

## 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?

A quantum devices that: Solves one problem (possibly practically useless) exponentially 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

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

53+1 qubits, depth = 20

600 seconds to sample 3 million times

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

# 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

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

Questions?

# 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

## 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.

#### Are quantum computers faster than classical computers?

By abdullahkhalids

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