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. Mark Zhandry 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. Quantum money that uses the mathematics of knots could be unforgeable | New Scientist