These are lecture notes from a weeklong course in quantum complexity theory taught at the
Bellairs Research Institute in Barbados, February 21-25, 2016. The focus is quantum circuit …

Public key quantum money can be seen as a version of the quantum no-cloning theorem
that holds even when the quantum states can be verified by the adversary. In this work, we …

The digital currency Bitcoin has had remarkable growth since it was first proposed in 2008.
Its distributed nature allows currency transactions without a central authority by using …

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 …

We investigate the security assumptions behind three public-key quantum money schemes.
Aaronson and Christiano proposed a scheme based on hidden subspaces of the vector …

The construction of public key quantum money based on standard cryptographic
assumptions is a longstanding open question. Here we introduce franchised quantum …

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 …

We propose a new idea for public key quantum money. In the abstract sense, our bills are
encoded as a joint eigenstate of a fixed system of commuting unitary operators. We perform …

Publicly verifiable quantum money is a protocol for the preparation of quantum states that
can be efficiently verified by any party for authenticity but is computationally infeasible to …

At STOC 2012, Aaronson and Christiano proposed a noisy and a noiseless version of the
first public‐key quantum money scheme endowed with a security proof. This paper …