Discrimination of unitary transformations in the Deutsch-Jozsa algorithm

Abstract

We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form. We also use this to show that any quantum algorithm that solves the Deutsch-Jozsa problem starting with a quantum system in a particular class of initial, thermal equilibrium-based states of the type encountered in solution state NMR can only succeed with greater probability than a classical algorithm when the problem size exceeds $n\sim 10^5.$

7 pages, 1 figure

References in corpus (5)

• Benchmarking quantum control methods on a 12-qubit system
• Minimum-error discrimination between mixed quantum states
• Unambiguous discrimination among oracle operators
• Thermal Equilibrium as an Initial State for Quantum Computation by NMR
• Creation of entanglement in a scalable spin quantum computer with long-range dipole-dipole interaction between qubits

Cited by in corpus (2)

• Determining the parity of a permutation using an experimental NMR qutrit
• Multiple multi-control unitary operations: implementation and applications