Ancilla-driven quantum computation for qudits and continuous variables

Abstract

(2017) 'Ancilla-driven quantum computation for qudits and continuous variables. ', Physical review A., 95 (5). 052317.Further information on publisher's website:https://doi.org/10.1103/PhysRevA.95.052317Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 95, 052317 c (2017) 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. Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher-dimensional qudits or quantum continuous variables (QCVs). In this paper, we use a general "quantum variable" formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated "quantum memory" register and which may be applied to the setting of qubits, qudits (for d > 2), or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical feed forward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. Finally, we discuss settings in which these models may be of practical interest.

Relative resilience to noise of standard and sequential approaches to measurement-based quantum computation

“…This, along with the effects of imperfect measurements [34], will be topics of further investigations that we plan to perform in the future. Also, we plan to conduct similar investigations using continuous-variable systems as opposed to qubits [31,35], to clarify whether the choice of the dimensionality of the physical system supporting the computation has an impact on the relative resilience of computational models.…”

“…More general approaches to computation similar in spirit to MBQC -in the sense that they also rely on adaptable measurements to drive the computation -have been considered in the literature, and are usually referred to as quantum computation via ancillae [27][28][29][30][31]. In particular, Anders et al [32] have introduced a setting -dubbed ancilla-driven quantum computation (ADQC) -in which the quantum systems involved in the computation are classified in two sets that mutually interact (see also Refs.…”

Universal quantum computation via quantum controlled classical operations

“…with a unitary device), or one can implement it indirectly by performing transformations and measurements on an ancillary control system. The latter method has been extensively studied in the context of quantum steering [9], measurement based quantum computing [10][11][12], fusion-based quantum computing [13,14] and ancilla driven quantum computation (ADQC) [15][16][17][18]. Motivated by the aforementioned results obtained by Shi and Aharonov, we may now ask the following question: can one achieve universal quantum computation by supplementing classical operations with a quantum control?…”

Realizing quantum linear regression with auxiliary qumodes

“…A typical example is an light-atom interacting system, which demonstrates how discrete energy levels and continuous light fields evolve quantum mechanically. Notably, a hybrid scenario of information processing using both discrete and continuous variables has been proposed before [1][2][3][4][5], such as hybrid quantum computing [3][4][5]. The relevant advantages have been indicated in tasks like quantum float computing [6] and quantum phase estimation(QPE) [3,7], in which infinite dimensions of continuous variables are exploited [7][8][9][10], making the proposals promising.…”