This mini-course will introduce participants to an exciting frontier for quantum computing theory: namely, questions involving the computational complexity of preparing a certain quantum state or applying a certain unitary transformation. Traditionally, such questions were considered in the context of the Nonabelian Hidden Subgroup Problem and quantum interactive proof systems, but they are muc...

This mini-course will introduce participants to an exciting frontier for quantum computing theory: namely, questions involving the computational complexity of preparing a certain quantum state or applying a certain unitary transformation. Traditionally, such questions were considered in the context of the Nonabelian Hidden Subgroup Problem and quantum interactive proof systems, but they are muc...

We propose an information theoretically secure secret-key quantum money scheme in which the verification of a coin is classical and consists of only one round; namely, a classical query from the user to the bank and an accept/reject answer from the bank to the user. A coin can be verified polynomially (on the number of its qubits) many times before it expires. Our scheme is an improvement on Ga...

Quantum money is a cryptographic protocol in which a bank can create quantum states which anyone can verify but no one except possibly the bank can clone or forge. Aaronson [1] proposed a scheme for this, which we show to be insecure. On the positive side, we propose a new scheme, and conjecture that it is secure. Our scheme is inherently quantum, in the sense that there are no classical secret...

We investigate the security assumptions behind three public-key quantum money schemes. Aaronson and Christiano proposed a scheme based on hidden subspaces of vector space $$\mathbb {F}_2^n$$ in 2012. It was conjectured by Pena et al. (IACR international workshop cryptography, pp 194–213. Springer, 2015) that hard problem underlying can be solved quasi-polynomial time. confirm this conjecture, h...

The fisherman caught a quantum fish. Fisherman, please let me go, begged the fish, and I will grant you three wishes. The fisherman agreed. The fish gave the fisherman a quantum computer, three quantum signing tokens and his classical public key. The fish explained: to sign your three wishes, use the tokenized signature scheme on this quantum computer, then show your valid signature to the king...