Abstract
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.
Highlights
The original theoretical setting for quantum computation is the gate model [ ] in which a global unitary that acts on a register of qubits, which computes the solution to some problem, is decomposed into a sequence of fundamental gates that are applied to the register
We show that an interaction of this form, along with ancillas prepared in the computational basis, can implement universal quantum computation on the register if θ is such that CR(θ ) is entangling and {v, v } is a universal set for SU( ) where vi := R(θ i + θa)uR(θ i + θr)
The only control necessary in these models to implement universal quantum computation on a register of qubits is a single fixed-time ancilla-register interaction between one ancilla qubit and one register qubit and ancilla preparation in the computational basis. The first of these models is based on maximally entangling interactions that are locally equivalent to CZ and requires multiple ancilla qubits to mediate two-qubit entangling gates on the register
Summary
The original theoretical setting for quantum computation is the gate model [ ] in which a global unitary that acts on a register of qubits, which computes the solution to some problem, is decomposed into a sequence of fundamental gates that are applied to the register. In this paper we will show that it is possible to develop deterministic models that require only a single fixed ancilla-register interaction and ancilla preparation in the computational basis with no ancilla measurements necessary Such schemes require a minimal level of control of both the ancillary and register systems whilst allowing for universal quantum computation. As we have shown how to implement a two-qubit entangling gate and a universal set for SU( ) on the register this is a minimal control model of ancilla-mediated quantum computation. This Lja gives v = H and v = R(θ )HR(θ ) which we have shown to be a universal set for SU( ) when θ = π/ and so this form for Lja is appropriate for implementing the second minimal control model With this simple interaction Hamiltonian, H(π/ ), local control of the ancilla is required. It would be interesting to consider which physical systems have Hamiltonians that are naturally suited to generating appropriate interactions for the models introduced and we leave a more detailed study of this for future work
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