Hybrid quantum computing with ancillas

Abstract

In the quest to build a practical quantum computer, it is important to use efficient schemes for enacting the elementary quantum operations from which quantum computer programs are constructed. The opposing requirements of well-protected quantum data and fast quantum operations must be balanced to maintain the integrity of the quantum information throughout the computation. One important approach to quantum operations is to use an extra quantum system – an ancilla – to interact with the quantum data register. Ancillas can mediate interactions between separated quantum registers, and by using fresh ancillas for each quantum operation, data integrity can be preserved for longer. This review provides an overview of the basic concepts of the gate model quantum computer architecture, including the different possible forms of information encodings – from base two up to continuous variables – and a more detailed description of how the main types of ancilla-mediated quantum operations provide efficient quantum gates.

Keywords:

• Quantum computer
• quantum bus
• ancilla
• hybrid
• qudit
• continuous variable

Acknowledgements

Discussions with many colleagues helped to develop our ideas in this review, but special thanks go to Erika Andersson for introducing us to the topic of ancilla-mediated quantum gates, and to Joschka Roffe for assistance with Section 4, and thoroughly checking the manuscript and references.

Notes

No potential conflict of interest was reported by the authors.

1 Balanced ternary uses the values $-1$, 0 and 1 (as opposed to 0, 1 and 2) and is hence naturally suited to representing negative numbers amongst other advantages.

2 Any wavefunction for which its modulus squared integrates to a constant can be normalised, these are called the square-integrable functions and they are the physically allowed states.

3 The displacement operator is given by $\mathcal{D}(\mathit{\alpha })\equiv e^{iq{q}^{\prime }/2}Z(q^{\prime })X(q)$ with $\mathit{\alpha }=(q+i{q}^{\prime })/\sqrt{2}$ a complex parameter. It is also possible to define displacement operators for a qudit in a similar manner [24].

4 In general, the error gate is $R(2m\mathit{\pi }/d)$, where d is the dimension of the ancilla.

Additional information

Funding

This work was partially supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/L022303/1. TJP is funded by a University of Leeds Scholarship.