Quantum money underpinned by the mathematics of knots could be impossible to forge.
In a quantum monetary system, money is represented as a collection of quantum bits – qubits – on a quantum computer. There is a secret procedure for creating the money that only the authority in charge, such as a mint, can perform. And copying the quantum money is impossible thanks to a law of physics called the no-cloning theorem. Effectively, if someone learned enough information about the quantum money to duplicate it, the qubits would change so much in the process that they would become unusable.
Physicist Stephen Wiesner first proposed the idea of quantum money in 1969 but there were details still to be worked out. One of them was a system by which people could check that quantum money stored on a quantum computer was actually created by the official authorities.
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at NTT Research, a computing and cryptography start-up in California, and his colleagues have now worked out how using a branch of mathematics called knot theory can help.
One thing mathematicians look at in knot theory is if one knot can be rearranged to match another – a surprisingly difficult problem, even for quantum computers.
Once two knots are found to be equivalent, mathematicians assign them the same value called an invariant. Zhandry and his colleagues examined a quantum monetary system where calculating these invariants, for knots and similar classification problems, is the basis for checking the money is genuine.
In their system, each unit of currency includes a collection of qubits, each with a corresponding knot, as well as a list of which invariants are present. A key part of the check is to analyse whether the qubits and their invariants match. This is relatively easy, but to come up with another list of knots that would also match is effectively impossible – and therefore so is forging the currency. Similar systems have been proposed in the past, but a detailed treatment of why they may work was lacking until now.
at the University of Texas at Austin says quantum money wouldn’t need a shared ledger of who owns what like cryptocurrencies have, known as the blockchain. Everyone could verify their money themselves by running a calculation on a quantum computer, perhaps in their home or at a shop.
However, in practice, creating such a monetary system may be just beyond current technology. Existing quantum computers are too small and too prone to error to run calculations like those in the new study, says at the University of California, San Diego. It may still be a few decades before quantum computers in laboratories start exchanging quantum money, let alone any quantum computing devices we could have in our homes or carry on us like wallets, he says.
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