In AIP Publishing's AVS Quantum Science, the researchers describe a tool they created to determine how big a quantum computer needs to be to solve problems such as cracking the Bitcoin cryptocurrency and how long it takes.

Quantum computers are expected to be disruptive and could affect many industry sectors, including cryptocurrencies. As a result, researchers in the UK and the Netherlands decided to explore cracking Bitcoin's cryptocurrency (as well as simulating the molecule responsible for biological nitrogen fixation).

Many of the most promising quantum dominance use cases will require error correcting quantum computers. Error correction allows longer algorithms to be run by compensating for inherent errors within the quantum computer, but it comes at the cost of more physical quantum bits (quantum bits).

Ion Quantum Technology Group, University of Sussex Blueprint of a quantum computer with captured ions. Image credit: Ion Quantum Technology Group, University of Sussex

"Our tools automatically calculate error correction overhead based on key hardware specifications," Webber said. "To make quantum algorithms run faster, we can perform more operations in parallel by adding more physical quantum bits. We introduce additional quantum bits as needed to achieve the desired runtime, which is heavily dependent on the rate of operation at the physical hardware level."

Most quantum computing hardware platforms are limited because only quantum bits that are adjacent to each other can interact directly. In other platforms, such as some trapped ion designs, the quantum bits are not in fixed positions but can be physically moved – meaning that each quantum bit can interact directly with a large number of other quantum bits.

"We explored how best to exploit this ability to connect distant quantum bits with the goal of solving problems in less time with fewer quantum bits," Weber said. "We must continue to adapt error correction strategies to take advantage of the underlying hardware, which may allow us to solve far-reaching problems using smaller quantum computers than previously assumed."

Quantum computers have grown exponentially in their ability to crack many cryptocurrency technologies compared to classical computers. Most of the world's secure communications use RSA cryptocurrencies. RSA cryptocurrency and one of the (elliptic curve digital signature algorithms) used by Bitcoin will one day be vulnerable to quantum computing attacks, but today, even the largest supercomputers will never pose a serious threat.

Researchers estimate the size a quantum computer would need to be to crack the Bitcoin network's cryptocurrency in the small amount of time it would actually pose a threat – between its announcement and integration into the blockchain. The higher the fee paid for the transaction, the shorter that window would be, but it could range from a few minutes to a few hours.

"Today's most advanced quantum computers have only 50-100 quantum bits," Weber said. "We estimate that 3 to 300 million physical quantum bits are needed, suggesting that Bitcoin should currently be considered secure from quantum attacks, but devices of this size are generally considered achievable, and future advances may further reduce the requirements.

"The Bitcoin network could perform a 'hard fork' of the quantum-secure cryptocurrency technology, but this could lead to network scaling issues due to increased memory requirements."

The researchers highlighted the speed of improvement of quantum algorithms and error correction protocols.

"Four years ago, we estimated that a capture ion device would require one billion physical quantum bits to crack RSA cryptocurrency, which would require a device with an area of 100 x 100 square meters," Webber said. "Now, with the overall improvements, that could be significantly reduced to an area of just 2.5 x 2.5 square meters."

Large-scale error-correcting quantum computers should be able to solve important problems that cannot be solved by classical computers.

Ref: Mark Webber, Vincent Elfving, Sebastian Weidt, and Winfried K. Hensinger, "The Impact of Hardware Specifications on Achieving Quantum Advantage in Fault-Tolerant Mechanisms," January 25, 2022, AVS Quantum Science. DOI: 10.1116/5.0073075