PERFORMING UNITARY ITERATION AND INDEXED OPERATIONS

Methods, systems and apparatus for performing indexed operations using a unary iteration quantum circuit. In one aspect, a method includes encoding an index value in an index register comprising index qubits; encoding the index value in a control register comprising multiple control qubits; and repeatedly computing and uncomputing the control qubits to perform, conditioned on the state of the control qubits, the operation on one or more target qubits corresponding to the index value, wherein during the encoding, computing and uncomputing: the multiple control qubits are made available in sequence, and the multiple control qubits correspond to a one-hot encoding of the encoded index value.