By using an ancilla qubit as a mediator, two distant qubits can undergo a non-local entangling unitary operation. This is desirable for when attempting to scale up or distribute quantum computation by combining fixed static local sets of qubits with ballistic mediators. Using a model driven by measurements on the ancilla, it is possible to generate a maximally entangling CZ gate while only having access to a less entangling gate between the pair qubits and the ancilla. However this results in a stochastic process of generating control phase rotation gates where the expected time for success does not correlate with the entangling power of the connection gate. We explore how one can use feedback into the preparation and measurement parameters of the ancilla to speed up the expected time to generate a CZ gate between a pair of separated qubits and to leverage stronger coupling strengths for faster times. Surprisingly, by choosing an appropriate strategy, control of a binary discrete parameter achieves comparable speed up to full continuous control of all degrees of freedom of the ancilla.
By using an ancilla qubit as a mediator, two distant qubits can undergo a non-local entangling unitary operation. This is desirable for when attempting to scale up or distribute quantum computation by combining fixed static local sets of qubits with ballistic mediators. Using a model driven by measurements on the ancilla, it is possible to generate a maximally entangling CZ gate while only having access to a less entangling gate between the pair qubits and the ancilla. However this results in a stochastic process of generating control phase rotation gates where the expected time for success does not correlate with the entangling power of the connection gate. We explore how one can use feedback into the preparation and measurement parameters of the ancilla to speed up the expected time to generate a CZ gate between a pair of separated qubits and to leverage stronger coupling strengths for faster times. Surprisingly, by choosing an appropriate strategy, control of a binary discrete parameter achieves comparable speed up to full continuous control of all degrees of freedom of the ancilla.
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.
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.
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.
Efficient generation of cluster states is crucial for engineering large-scale measurement-based quantum computers. Hybrid matter-optical systems offer a robust, scalable path to this goal. Such systems have an ancilla which acts as a bus connecting the qubits. Ancilla-driven schemes are important for chip-based quantum computing architectures, where the flying ancilla mediates between static qubits. Hybrid architectures form a natural substrate for measurement-based quantum computing (MBQC) [1], one type of which (the topological model) has the best error threshold for quantum computing [2]. In this type of processing a highly-entangled cluster state is generated, and then computation performed by sequential qubit measurements. The quantum processing task is to generate the cluster state, after which it becomes a matter of measurement and classical communication. In physically-realizable implementations the cluster is prepared dynamically, a few layers at a time. As the cluster state is the fundamental quantum resource of a measurement-based computation, it becomes extremely important to make it as error-free as possible. Errors in constructing the cluster can propagate rapidly through a computation because of the highly-entangled nature of the state, leading to failure of the computation. Hybrid systems are susceptible to specific error types that other systems are not, because of the use of the mediating ancilla. In cases where the ancilla is not destroyed after each gate there is a nonzero probability of errors propagating through ancilla reuse. FIG. 1: A cluster of 4 bricks of length b = 5 qubits, each made using a different bus. We present the optimal scheme for dynamic fault-tolerant 2-D cluster state generation in hybrid systems where the mediating system can be used for more than a single gate operation without being reset. We divide the cluster state into “Lego bricks”, each of which uses a single bus. We give the optimal method for constructing the bricks, reducing the number of system-bus entanglements. We then show how to determine the block size based on the error threshold of the system being used. We find that, even when the probability of error in the system is high, this scheme can still deliver significant efficiency savings through bus reuse, enabling a larger cluster to be generated. By reducing the time required to prepare sections of the cluster, bus reuse more than doubles the size of the computational workspace that can be used before decoherence effects dominate [3]. A simple example of the bricks is shown in figure 1. They are always the same height (m direction), but have length b (n direction) determined by [3] 1 ¡1 − exp[−(6b + 4)γτ − 16bηβ2]¢ ≤ ε. (1) 2 For a given set of experimental parameters γ, τ, η and β, and desired dephasing limit to ε, this determines b. If we use one bus per CPhase gate to generate a brick, we have 1 ¡1 − exp[−16bγτ − 4ηβ2]¢ ≤ ε. (2) 2 Comparing equations (1) and (2), we find our Lego scheme produces less qubit dephasing than using one bus per CPhase gate provided ηβ2 < ∼ γτ/2. Compared with 8mn − 4(m + n) bus operations with no bus reuse, for large clusters, the Lego scheme uses less than half for b > 2. And even for b = 1, the reduction is O(5mn) compared to O(8mn), equivalent to the method of [4] for five qubits per bus. This will thus be the method of choice for any ancilla-based cluster generation that allows bus reuse. Our results are directly applicable to bus-based experimental production of cluster states, enabling the same FIG. 2: Dynamic generation using multiple ancillas. resources to produce dynamically-generated cluster states of twice the size compared to single-gate bus use, see fig. 2. For multi-bus dynamic schemes, fully scalable operation can be achieved with half the coherence time compared to single-gate buses, needing as few as 20 CPhase gates per bus. We thank Aram Harrow, Ashley Stephens and Simon Devitt for useful discussions. CH was supported by EU project QAP and the Bristol Centre for Nanoscience and Quantum Information. KLB is supported by a UK Engineering and Physical Sciences Research Council industrial CASE studentship from Hewlett-Packard, VMK is supported by a UK Royal Society University Research Fellowship and WJM acknowledges partial support from the EU project HIP and MEXT in Japan.
The formation of multipartite quantum entanglement by repeated operation of one- and two-qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one-dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a nonlocal geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single-qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the nonlocal geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and nonlocal interactions between the qubits.