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arXiv:1402.6674 · Physical Review A

Quantum computation mediated by ancillary qudits and spin coherent states

Timothy J Proctor, Shane Dooley, Viv M. Kendon

Published Jan 8, 2015• 6 citations
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Abstract

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.

DOI
10.1103/physreva.91.012308

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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 ddd-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.
Models of universal quantum computation where the required interactions between computational qubits are mediated by some ancillary system are highly relevant to experimental realisations of a quantum computer. We introduce two such models of quantum computation, the first of which employs a d-level (qudit) ancilla and the second of which is based on the coherent states of n spins. The computation is implemented with geometric phase gates, created via controlled displacement operators defined on a discrete lattice phase space, in the case of a qudit ancilla, and a Bloch sphere, in the case of a spin coherent state ancilla. Both of these models are shown to be different possible generalisations to finite dimensions of the field-mode quantum bus (qubus) computer. We then consider the computational complexity of the qubus architecture and show that although in certain circumstances the model can be used to reduce the number of operations required to implement quantum circuits, contrary to previous claims [New J. Phys. 13, 095007, 2011] this is not the case for the quantum Fourier transform (QFT). Furthermore, using the generalisation of the qubus model to a qudit bus, we show that this reduction in the circuit complexity depends on the dimensionality of the bus.
Schemes of universal quantum computation in which the interactions between the computational elements, in a computational register, are mediated by some ancillary system are of interest due to their relevance to the physical implementation of a quantum computer. Furthermore, reducing the level of control required over both the ancillary and register systems has the potential to simplify any experimental implementation. In this paper we consider how to minimise the control needed to implement universal quantum computation in an ancilla-mediated fashion. Considering computational schemes which require no measurements and hence evolve by unitary dynamics for the global system, we show that when employing an ancilla qubit there are certain fixed-time ancilla-register interactions which, along with ancilla initialisation in the computational basis, are universal for quantum computation with no additional control of either the ancilla or the register. We develop two distinct models based on locally inequivalent interactions and we then discuss the relationship between these unitary models and the measurement-based ancilla-mediated models known as ancilla-driven quantum computation.
We characterize a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [Phys. Rev. A 82, 020301(R) (2010)], but does not require measurements of the ancillas, and in this respect is similar to the original gate-based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to swap combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite, and fault-tolerant gate set for universal quantum computation in this model.
We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010], but does not require measurements of the ancillas, and in this respect is similar to the original gate based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to SWAP combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite and fault tolerant gate set for universal quantum computation in this model.
Schemes of universal quantum computation in which the interactions between the computational elements, in a computational register, are mediated by some ancillary system are of interest due to their relevance to the physical implementation of a quantum computer. Furthermore, reducing the level of control required over both the ancillary and register systems has the potential to simplify any experimental implementation. In this paper we consider how to minimise the control needed to implement universal quantum computation in an ancilla-mediated fashion. Considering computational schemes which require no measurements and hence evolve by unitary dynamics for the global system, we show that when employing an ancilla qubit there are certain fixed-time ancilla-register interactions which, along with ancilla initialisation in the computational basis, are universal for quantum computation with no additional control of either the ancilla or the register. We develop two distinct models based on locally inequivalent interactions and we then discuss the relationship between these unitary models and the measurement-based ancilla-mediated models known as ancilla-driven quantum computation.
A model of universal quantum computation with qudits (ddd-level systems) is presented in which the gates are implemented on a register entirely via fixed-form sequential interactions with ancillary qudits followed by adaptive, variable basis measurements of these ancillas. The model maintains determinism via classical feed-forward of measurement outcomes in a similar fashion to the qudit one-way model. An embedding of the qudit one-way model is given which demonstrates that the hybrid quantum-classical advantages of one-way quantum computation are also inherent in the model presented here, including the ability to implement any Clifford gate in constant depth using multiple ancillas in parallel. A model which requires only fixed basis measurements is then presented, but due to the lack of adaptive controls it can only implement universal quantum computation in a stochastic sense. Interestingly, this scheme may then be altered to recover determinism by replacing ancilla measurements with ancilla preparation. These models provide an intuitive setting for understanding the interplay between the benefits gained from classical controls, measurements and state preparation in the context of multi-valued logic ancilla-based quantum computation.