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## Quantum Computing

**Quantum Computing** is the study of how to use phenomena in quantum physics to perform much more efficient computations than what older, classical computer technologies are capable of. The basic unit of information in quantum computing is a qubit. ^{[1]}

# History

The idea of quantum mechanics can be traced back to research in 1900 by Max Planck who is considered the father of quantum theory. Quantum computers would come later in the 1980s and 1970s when Paul Benioff proved it was possible to build a computer that operated under the laws of quantum physics. ^{[2]}

# Overview

Unlike a traditional computer bit, a binary digit characterized as either 0 or 1, a qubit can be a coherent superposition of both 0 and 1. The power of a quantum computer increases with each qubit that is added. However, adding more transistors will not add power linearity, as it would with traditional computers. ^{[1]}

Superposition and entanglement are the two features of quantum mechanics used for quantum computations. These features empower quantum computers to handle operations at speeds that are exponentially higher as compared to traditional computers, while also consuming a lot less energy in the process. ^{[1]}

There is a debate in the cryptocurrency sector regarding the impact of quantum computing on network security, particularly in Bitcoin (BTC). This is because quantum computing could potentially pose a threat to the resilience of cryptography. As a result, developers and mathematicians are actively investigating the possibility of creating quantum-resistant cryptography to ensure that these networks remain secure. ^{[1]}

To address the potential threat of quantum computing, researchers in the field of cryptography are exploring and developing quantum-resistant cryptographic algorithms. These algorithms are designed to withstand attacks from both classical and quantum computers, ensuring the continued security of digital assets in a quantum computing era. The transition to quantum-resistant algorithms is a complex process requiring careful consideration and coordination within the cryptographic and blockchain communities. ^{[3]}

## Quantum Cryptography

Cryptography is the process of encrypting data, or converting plain text into scrambled text so that only someone who has the right “key” can read it. ^{[4]}

Quantum cryptography, by extension, uses the principles of quantum mechanics to encrypt data and transmit it in a way that cannot be hacked. It is a secure system against being compromised without the knowledge of the message sender or the receiver. That is, it is impossible to copy or view data encoded in a quantum state without alerting the sender or receiver. Quantum cryptography should also remain safe against those using quantum computing as well. ^{[5]}

Quantum cryptography uses individual particles of light, or photons, to transmit data over fiber optic wire. The photons represent binary bits. The security of the system relies on quantum mechanics. These secure properties include:

- particles can exist in more than one place or state at a time;
- a quantum property cannot be observed without changing or disturbing it; and
- whole particles cannot be copied.

These properties make it impossible to measure the quantum state of any system without disturbing that system. Photons are used for quantum cryptography because they offer all the necessary qualities: Their behavior is well understood, and they are information carriers in optical fiber cables. ^{[4]}^{[5]}

An example of quantum cryptography currently is quantum key distribution (QKD), which provides a secure method for key exchange. ^{[5]}

### How Quantum Cryptography Works

In quantum cryptography, the sender transmits photons through a filter, randomly assigning one of four polarizations and bit designations: Vertical (One bit), Horizontal (Zero bit), 45-degree right (One bit), or 45-degree left (Zero bit). These photons reach a receiver equipped with two beam splitters (horizontal/vertical and diagonal) to ascertain the polarization of each photon. ^{[4]}

Importantly, the receiver must guess which beam splitter to use for each photon, adding an element of uncertainty. After the photon stream is transmitted, the receiver informs the sender of the beam splitter used for each photon. The sender then compares this information with the sequence of polarizers used to send the key. Discarding photons read with the wrong beam splitter, the resulting sequence of bits forms the secure key. ^{[4]}

## Quantum Physics

Also known as quantum mechanics, quantum physics is a type of physics that only applies to things that are small enough for their rules to apply. Nearly everything behaves predictably in classical physics—calculations and measurements can be exact. Things become much more unpredictable once one starts studying objects at the size of quantum physics. ^{[2]}

Measurements and calculations in quantum physics are not guaranteed to be accurate—they can only be guessed using probabilities. At the quantum level, particles can start behaving like waves and suddenly change states depending on whether it is being observed. In the quantum realm, everything becomes uncertain. ^{[2]}

## Quantum Computers

Quantum computers leverage the principles of quantum mechanics to perform computations at speeds exponentially faster than classical computers for certain types of problems. One of the most significant implications for the field of cryptography is the ability of quantum computers to efficiently solve problems considered hard for classical computers, such as factoring in large numbers. ^{[2]}

In the context of cryptocurrencies, including Bitcoin and other blockchain-based systems, the concern is that quantum computers could break the cryptographic foundations on which these systems rely. For instance, if a sufficiently powerful quantum computer were to become available, it could potentially compromise the security of private keys used in cryptocurrency wallets. This could allow an attacker to derive private keys from their corresponding public keys, undermining the security of transactions and funds stored in those wallets. ^{[2]}^{[3]}

## Quantum Parallelism

Quantum parallelism is a fundamental feature of quantum computers, enabling them to assess a function for multiple input values simultaneously. This is accomplished by placing a quantum system in a superposition of input states and applying a unitary transformation that encapsulates the function to be evaluated. The resulting state holds the output values for all input states in the superposition, facilitating the simultaneous computation of multiple outputs. This property is key to the speedup of many quantum algorithms. ^{[5]}

Quantum Computing

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December 21, 2023

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## REFERENCES

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