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 10^{20} – 1.5 x 10^{21} 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

## 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

Rivest–Shamir–Adleman

Key: 10101011101...

Security ∝ number of digits

Recommended key size: 4096 bits

(for security till 2030)

## Cracking RSA

## 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!

### Quantum computers can

## simulate atoms, molecules and materials,

### exponentially faster than classical computers.

### Quantum computers can

## maybe do machine learning and optimization

### exponentially faster than classical computers.

### Quantum computers can

## break all currently used asymmetric encryption protocols

### exponentially faster than classical computers.

arXiv:1909.07353

## Cryptographic Algorithms in Use

### Quantum computers CANNOT

~~do industrial optimization~~

predict the stock market

optimize airline schedules

predict the stock market

optimize airline schedules

~~NP-Complete problems~~

### exponentially faster than classical computers.

## 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?

Quantum Supremacy | Quantum Advantage | |
---|---|---|

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 |

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

## Google's superconducting chip

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?

### Verification that device works

## 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

# Thank you

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

## Second Option: Quantum Key Distribution

$5000-50,000

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

- Invest in quantum computing and cryptography research.

- Build quantum cryptography infrastructure.

- Invest in policy research.

- Participate in international encryption standards committees.

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

By abdullahkhalids

# Are quantum computers faster than classical computers?

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