Rodeo Algorithm for Quantum Computation

For closed quantum mechanical systems, the spectrum and eigenvectors of the corresponding Hamiltonian provide a great deal of information concerning dynamic and static properties. In cases where a good initial guess can be supplied, standard quantum phase estimation (QPE) can be used to bring a state closer to a desired eigenstate while simultaneously measuring the corresponding eigenvalue. However, though computationally efficient, standard QPE remains out of reach of current hardware capabilities, in part due to the number of ancilla qubits required to obtain ever higher degrees of precision. In my talk I will present a new approach to the problem of phase estimation, the Rodeo Algorithm, which can be viewed as a generalization of Kitaev’s original algorithm for QPE. Our approach maintains the basic underlying principle of interferometry but allows for a multi-qubit “arena” and stochastically varying phase shifts. I will demonstrate that this algorithm is well suited for NISQ era devices and has good scaling properties in terms of the number of iterations of a simple circuit.