Ancilla-based quantum simulation

Abstract

Abstract. We consider the simulation of the Bardeen, Cooper and Schrieffer (BCS) Hamiltonian, a model of low-temperature superconductivity, on a quantum computer. In particular, we consider conducting the simulation on the qubus quantum computer, which uses a continuous variable ancilla to generate interactions between qubits. We demonstrate an O(N 3 ) improvement over previous studies conducted on an NMR computer (Wu et al 2002 Phys. Rev. Lett. 89 057904 and Brown et al 2006 Phys. Rev. Lett. 97 050504) for the nearest-neighbour and completely general cases. We then proceed to show methods for minimizing the number of operations needed per time step using the qubus in three cases: the completely general case, the case of exponentially decaying interactions and the case of fixed range interactions. We make these results controlled on an ancilla qubit so that we can apply the phase estimation algorithm, and hence show that when N 5, our qubus simulation requires significantly fewer operations than a similar simulation conducted on an NMR computer.

Heterotic computing: past, present and future

“…types of gate sequences, extra efficiency savings become available [21,22] due to the extra degrees of freedom in the ancilla. The qubus quantum computer uses a quantum state known as a coherent state as the ancilla, which has two quadratures, which act as two coupled continuous variable quantum systems.…”

Quantum computation mediated by ancillary qudits and spin coherent states

“…We now give a brief review of qubus computation based on controlled displacements [21][22][23]. We take an interaction between a field-mode bus and the j th register qubit of the form,…”

“…The continuous-variable nature of the displacement operator for a field mode can have additional advantages in terms of the computational power of the model. In particular, certain gate sequences can be implemented using fewer bus-qubit interactions than if each gate was implemented individually [22,23] and these techniques can be used to implement certain quantum circuits with a lower scaling in the total number of interactions required in comparison to the standard quantum circuit model [26].…”

Qubus ancilla-driven quantum computation

“…We also applied the qubus to other algorithms, including quantum simulation of the BCS Hamiltonian [8]. As well as simulating the Hamiltonian itself, using the Trotter approximation for unitary evolution, the full simulation required a qubus implementation of the quantum Fourier transform (QFT) in order to perform phase estimation to obtain the result.…”

“…Performing a QFT on N qubits requires a total of (N 2 − N)/2 controlledrotation gates. With the qubus, these can be performed using a controlled-phase gate plus single-qubit corrections on each qubit [8]. In a naïve implementation, where each controlled-phase gate requires four operations to perform, we would require 2(N 2 − N) interactions with the bus.…”