Recently, the cryptocurrency circle is full of clouds. The "second uncle coin" cryptocurrency pool is suspected to have a Rug Pull: the token price plummeted by more than 99% as the contract deployer laundered stolen money through Tornado cash, and the total profit from the scam is estimated to be as high as $1.3 million.

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The price of the token SUC has dropped 99.7%.

This event has certainly exposed the huge crypto and maintenance costs required for decentralized currencies. Recently, Andrey Khesin and Peter Shor of MIT, and Jonathan Lu of Harvard University have proposed a way to create a quantum currency - one that is completely decentralized and does not require a blockchain to record transactions: this would effectively address the difficulty of sustaining existing tokens This would effectively address the long-term pitfalls of unsustainable development of existing tokens. A preprint of the research results was published on the arXiv under the title "A publicly verifiable quantum currency from random lattices" [1]. Peter Shor is the author of the most famous Shor algorithm in quantum computing.

01What is quantum money?

Quantum money is a form of currency that uses the laws of quantum mechanics to ensure that the currency in question cannot be copied, but at the same time can be easily verified. These properties make it an ideal medium of exchange, just like ordinary cash, and without any risk of counterfeiting.

The idea was originally proposed by physicist Stephen Wiesner in 1970, using the concept that any attempt to measure an unknown quantum state would inevitably destroy it. In contrast, the process of measuring a known quantum state preserves it. wiesner realized that if the details of the quantum state were kept secret (by central banks, for example), this property could be used to guarantee the authenticity of quantum money, while ensuring that it could never be copied.

Since then, the idea of quantum money has become very influential, forming the basis for many experiments and quantum cryptography that have become the norm: a quantum money protocol must have a valid preparable monetary state, valid public authentication, and unforgeability.

02Quantum monetary states: vectors on lattice

However, Wiesner's quantum currency formulation has a drawback: the authentication process can only be performed by a trusted institution (e.g., a central bank) that would otherwise keep the details of the quantum state secret. However, the emergence of decentralized currencies like bitcoin and ethereum has raised concerns about monetary systems that do not require centralized control. Therefore, this new research has found a way to create quantum currencies that anyone can verify: quantum currencies can be made completely decentralized without the need for a blockchain to securely record transactions.

The security of this new approach comes from post-quantum encryption and is resistant to attacks by quantum computers.

One of the most promising problems involves the mathematical idea of a "lattice" (lattice), which is a multidimensional lattice formed by a set of vectors. The points in this lattice are connected by vectors of different lengths, and these vectors are easy to compute. However, the problem of finding the shortest vector in the lattice has proven to be difficult, especially when the lattice is random.

One approach is to calculate the distance between all points in a random lattice, and eventually the shortest distance vector will be found. But as the lattice becomes larger or contains more dimensions, this problem becomes intractable, even for quantum computers.

The method proposed in this research encodes a random lattice as a quantum property of a quantum monetary unit, which can be an array of atoms. Anyone wishing to replicate this currency would have to reproduce this random lattice. But this can only be done if the shortest vector is known, a task that not even a quantum computer can accomplish.

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The quantum currency states in this experiment are represented as a superposition of states on a Gaussian sphere (a vector mapping of each point on the surface of an object onto a sphere). The two coordinates in the figure are the first two coordinates of the points on the lattice: x1 and x2. The interval between each pair of points is s(0). An opponent can reach these points after measuring a lattice point and adding s(2); after adding s(1) enough times to approach another cluster of Gaussian spheres, the line of points shown will move downward without intersecting the Gaussian sphere.

This guarantees the safety of the funds. It is also easily verifiable, since the quantum state of the lattice has specific properties: any user can test it.

The end result is a physical system that cannot be replicated, but is easy to check. "Since our monetary states are physically tangible, they can be used as tangible but uncounterfeitable banknotes, but they can also be transferred as digital money through quantum channels." Khesin et al. said [2] that this is all done by the buyer and seller without any record of the transaction: just as it is done today with ordinary cash. "Verification of ownership can be done locally and offline, without the need for global synchronization through mechanisms such as blockchain."

03Quantum currency technology: is steadily, slowly evolving

This is an interesting endeavor with significant implications. One of the drawbacks of decentralized cryptocurrencies is the huge energy costs required to encrypt and maintain the blockchain. For example, for Bitcoin, this is currently considered to be more than the electricity consumed by the entire country of Argentina, and thus clearly unsustainable in the long run.

Quantum currency has the potential to work without such overhead. It is also naturally anonymous, just like cash. "Our quantum currency also has advantages that cannot be achieved with classical cryptocurrencies or physical notes." But it could only be adopted if the infrastructure exists and quantum information can be sent easily and cheaply, the researchers said. In other words, quantum currencies first require a full-blown quantum Internet, a technology that is steadily but slowly emerging.

The next step is to adapt the quantum currency algorithm to an anti-piracy protocol that protects quantum computing (i.e., a circuit) from being copied.

Reference link:

[1]https://arxiv.org/abs/2207.13135

[2]https://www.discovermagazine.com/technology/why-quantum-money-could-replace-blockchain-based-cryptocurrencies