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Qubits > 1s and 0s

Explore Media - Michael A.

Qubits?

- Fundamentally different from classical computers!

Quantum Computing?

Classical computers utilize binary values...

Quantum computers use a mixture of binary, representing probabilities rather than definite values! [1, 3]

How?

- Qubits may exist as a 0 or 1, but also as a combination of either (superposition). [1]

-This phenomena may be found in multi-level

quantum fields

- ‘Spin’ (polarity) in a magnetic field

- Signal photons (wave-particle duality) [1, 2].

Title

Fancy Binary...

what does it mean?

The benefits of mastering quantum computing are groundbreaking

What does it mean?

Powerful Computation

Representing bits as 1, 0, or both:

A byte of data (8 bits) may represent one of 256 different combinations (numbers) at any given time.

- A qubyte can represent all of these combinations at once when in

superposition!

2 bytes can still only represent 1 number

- 16 qubits (2 qubytes) can represent all 65,536 combinations in parallel. [1]

Faster Calculation

Same clock speed, faster calculation?

All possible algorithmic quantum calculations are done on the same clock speed. [1]

Derived from quantum properties of probability and uncertainty.

- Quantum gates take superposition inputs, and generate a

probabilistic output (also in superposition).

- This implies that an observed output is a probability

[1,2,4]

Real World Application

Quantum computers may one day...

Model quantum physics [1, 5, 6]

- Multi-level physics simulation

- Simulated using quantum components

- Remove unwanted variables in real world simulations

Provide quick solutions to exceptionally difficult math problems [7, 8]

- Time consuming on classical computers

Further development in medicine [1]

- Classical computers still struggle to model complex organic systems

What has been accomplished?

Although less exciting than solving the mysteries of the universe, we are make progress with quantum physics and computing

Current Implementation

Linear Algebra

Faster solutions

In 2017 physicists demonstrated the ability to solve a simple system of equations using only quantum methods

"best solid-state platforms with excellent scalability and remarkable high fidelity." [6]

The Harrow, Hassidim, and Lloyd (HHL) algorithm was used to accomplish this task, and is theorized to be exponentially faster than classical calculations

HHL Quantum Circuit Used [6]

RNG

Google, Quantum Supremacy, and RNG

Quantum computers have been shown to outperform supercomputers in isolated tasks (quantum supremacy)

One such example is Google's quantum computer, which was able to model quantum number generation

This took the 53 qubits in Google's computer 2-3 minutes, and would have taken a classical supercomputer ~10,000 years [7]

Too much power?

While quantum computers may one day aid in medicine, physics, and humanitarian development - they may also pose a threat to our security

Concerns

RSA Encryption

RSA Encryption

Number

X

RSA Encryption uses large numbers and their prime factors to act as a public and private key for online users to access encrypted (otherwise unusable) data

As far as classical computers are concerned: it is far easier to multiple factors to match a number than it is to determine that number's prime factors [8]

It is for this reason that RSA encryption is used to keep data secure - as it would take an exceptional amount of computational work for computers to determine these factors

Prime Factors

Breaking Encryption

Quantum + Shor's Algorithm

There is an established formula known as Shor's Algorithm Able to define a better guess for prime factors of a number N, after an initial guess. [8,9]

g^(P/2)±1 = m*N Shor's Alrorithm (simplified) [8]

where g is any initial guess, p is some power, N is the number being factored, and m is some multiple of N

Computers still struggle to accomplish these computational steps in sum, but the exponential calculations preformed by quantum computers imply that modern encryption methods may one day be at risk. [8]

Refrences

Title

1. Kurzgesagt – In a Nutshell, “Quantum Computers Explained – Limits of Human Technology. [Online]. Available: https://www.youtube.com/watch?v=JhHMJCUmq28. [Accessed: 12- Feb-2021].

2. T. L. Dimitrova and A. Weis, “The wave-particle duality of light: A demonstration experiment,” American Association of Physics Teachers, 01-Jan-1970. [Online]. Available: https://aapt.scitation.org/doi/10.1119/1.2815364. [Accessed: 12-Feb-2021].

3. GMU, “Superposition Principle.” [Online]. Available: http://physics.gmu.edu/~dmaria/590%20Web%20Page/public_html/qm_topics/superp osition/superposition.html. [Accessed: 12-Feb-2021].

4. J. Nalick, “Untangling Quantum Entanglement,” Caltech Magazine, 11-Oct-2019. [Online]. Available: https://magazine.caltech.edu/post/untangling-entanglement. [Accessed: 12- Feb-2021].

5. Anton Pertov, “Did China Just Achieve Quantum Supremacy in Computing?” [Online]. Available: https://www.youtube.com/watch?v=BZcW_5D-euY. [Accessed: 12-Feb- 2021].

6. L. Zyga, “Solving systems of linear equations with quantum mechanics,” Phys.org, 09-Jun- 2017. [Online]. Available: https://phys.org/news/2017-06-linear-equations-quantum- mechanics.html. [Accessed: 12-Feb-2021].

7. E. Gibney, “Hello quantum world! Google publishes landmark quantum supremacy claim,” Nature News, 23-Oct-2019. [Online]. Available: https://www.nature.com/articles/d41586-019-03213-z. [Accessed: 12-Feb-2021].

8. Minute Physics, “How Quantum Computers Break Encryption | Shor's Algorithm Explained.” 01-Mar-2019 [Online]. Available: https://www.youtube.com/watch?v=lvTqbM5Dq4Q. [Accessed: 12-Feb-2021].

9. Quiskit, "Shor's Algorithm." [Online]. Available: https://qiskit.org/textbook/ch-algorithms/shor.html [Accessed: 18-Feb-2021]

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