Quantum computation mediated by ancillary qudits and spin coherent states

Abstract

Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 91, 012308 c (2015) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Models of universal quantum computation in which the required interactions between register (computational) qubits are mediated by some ancillary system are highly relevant to experimental realizations of a quantum computer. We introduce such a universal model that employs a d-dimensional ancillary qudit. The ancilla-register interactions take the form of controlled displacements operators, with a displacement operator defined on the periodic and discrete lattice phase space of a qudit. We show that these interactions can implement controlled phase gates on the register by utilizing geometric phases that are created when closed loops are traversed in this phase space. The extra degrees of freedom of the ancilla can be harnessed to reduce the number of operations required for certain gate sequences. In particular, we see that the computational advantages of the quantum bus (qubus) architecture, which employs a field-mode ancilla, are also applicable to this model. We then explore an alternative ancilla-mediated model which employs a spin ensemble as the ancillary system and again the interactions with the register qubits are via controlled displacement operators, with a displacement operator defined on the Bloch sphere phase space of the spin coherent states of the ensemble. We discuss the computational advantages of this model and its relationship with the qubus architecture.

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.…”

Hybrid quantum computing with ancillas

“…This illustrates the subtle nature of any advantages gained from using a higher-dimensional ancilla. In the context of a qubit register and QCV ancilla, this principle has been applied to design more intricate sequences of operations for increasing efficiencies in quantum simulation [75] and for making cluster states [74,76,78] with comparisons with what can be achieved using a qudit ancilla given in [70]. Equivalent ideas directly carry over to a register of qudits although this has yet to be investigated in detail.…”

“…By interacting with a second register subsystem, this then implements an entangling gate between the logical register subsystem residing in the ancilla and this second register subsystem (the gate is swap · CZ). A second interaction of the ancilla with the first register subsystem simply swaps the logical information back into the register and the overall effect is the application of swap · CZ to the two register systems [70,95]. Local gates may easily be applied to a register subsystem by swapping it into the ancilla, applying the gate, and swapping it back out [95] as shown in Fig.…”

Minimal ancilla mediated quantum computation

“…This model employs a field-mode ancilla to mediate two-qubit gates on pairs of register qubits with the interaction between the ancilla and a register qubit being a controlled displacement of the field-mode. Recently, we have developed an analogous model which employs a d-dimensional qudit ancilla [22] with a displacement operator defined in the discrete phase space of the qudit [23,24]. These models have been shown to require a lower number of operations to implement certain gate sequences than a direct implementation of the circuit model [19,22,25].…”

“…Recently, we have developed an analogous model which employs a d-dimensional qudit ancilla [22] with a displacement operator defined in the discrete phase space of the qudit [23,24]. These models have been shown to require a lower number of operations to implement certain gate sequences than a direct implementation of the circuit model [19,22,25]. However, neither of these models can implement a universal gate set on the register using only this ancilla-register interaction and so, although no interactions between register qubits are required, some further direct access is needed to the register qubits to implement some basis-changing single-qubit unitary [22,26].…”