Ancilla-driven Quantum Computation Research Articles

Ancilla-driven quantum computation for qudits and continuous variables

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-feedforward 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.

Minimal ancilla mediated quantum computation

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.

Unlearning quantum information

Quantum dynamics can be driven by measurement. By constructing measurements that gain no information, effective unitary evolution can be induced on a quantum system, for example in ancilla driven quantum computation. In the non-ideal case where a measurement does reveal some information about the system, it may be possible to "unlearn" this information and restore unitary evolution through subsequent measurements. Here we analyse two methods of quantum "unlearning" and present a simplified proof of the bound on the probability of successfully applying the required correction operators. We find that the probability of successful recovery is inversely related to the ability of the initial measurement to exclude the possibility of a state.

DUMMY TITLE FOR ALIASING 10.1186/epjqt13

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.

Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction

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.

Ancilla-driven quantum computation with twisted graph states

We introduce a new paradigm for quantum computing called Ancilla-Driven Quantum Computation (ADQC) which combines aspects of the quantum circuit (Deutsch, 1989 [1]) and the one-way model (Raussendorf and Briegel, 2001 [2]) to overcome some of the challenging issues in building large-scale quantum computers. Instead of directly manipulating each qubit to perform universal quantum logic gates or measurements, ADQC uses a fixed two-qubit interaction to couple the memory register of a quantum computer to an ancilla qubit. By measuring the ancilla, the measurement-induced back-action on the system performs the desired logical operations.We characterise all two-qubit interactions which couple any ancilla qubit with any memory qubit, while satisfying certain desirable conditions. We require these interactions to implement unitary, stepwise deterministic and universal evolution. Moreover, it should be possible to standardise the computation, that is, applying all global operations at the beginning. We prove there are only two such classes of interactions characterised in terms of the non-local part of the interaction operator. This leads to the definition of a new entanglement resource called twisted graph states generated from non-commuting operators. The ADQC model is formalised in an algebraic framework similar to the Measurement Calculus (Danos et al., 2007 [8]). Furthermore, we present the notion of causal flow for twisted graph states, based on the stabiliser formalism, to characterise the determinism. Finally we demonstrate a compositional embedding between ADQC and both the one-way and circuit models which will allow us to transfer recently developed theory and toolkits of measurement-based quantum computing directly into ADQC.

A FRAMEWORK FOR REPRESENTING AND PRODUCING MOVIES ON QUANTUM COMPUTERS

Adopting a generalization of the DiVincenzo criteria for the physical realization of quantum devices, a standalone component each, is proposed to prepare, manipulate, and measure the various content required to represent and produce movies on quantum computers. The quantum CD encodes, prepares, and initializes the broad content or key frames conveying the movie script. The quantum player uses the simple motion operations to manipulate the contents of the key frames in order to interpolate the missing viewing frames required to effectively depict the shots and scenes of the movie. The movie reader combines the projective measurement technique and the ancilla-driven quantum computation to retrieve the classical movie sequence comprising of both the key and viewing frames for each shot. At appropriate frame transition rates, this sequence creates the impression of continuity in order to depict the various movements and actions in the movie. Two well-thought-out examples demonstrate the feasibility of the proposed framework. Concatenated, these components together facilitate the proposed framework for quantum movie representation and production, thus, opening the door towards manipulating quantum circuits aimed at applications for information representation and processing.

Entanglement-fidelity relations for inaccurate ancilla-driven quantum computation

It was shown by T. Morimae [Phys. Rev. A 81, 060307(R) (2010)] that the gate fidelity of an inaccurate one-way quantum computation is upper bounded by a decreasing function of the amount of entanglement in the register. This means that a strong entanglement causes the low gate fidelity in the one-way quantum computation with inaccurate measurements. In this paper, we derive similar entanglement-fidelity relations for the inaccurate ancilla-driven quantum computation. These relations again imply that a strong entanglement in the register causes the low gate fidelity in the ancilla-driven quantum computation if the measurements on the ancilla are inaccurate.

Twisted Graph States for Ancilla-driven Universal Quantum Computation

We introduce a new paradigm for quantum computing called Ancilla-Driven Quantum Computation (ADQC) which combines aspects both of the quantum circuit [D. Deutsch. Quantum computational networks. Proc. Roy. Soc. Lond A, 425, 1989] and the one-way model [R. Raussendorf and H. J. Briegel. A one-way quantum computer. Physical Review Letters, 86, 2001] to overcome challenging issues in building large-scale quantum computers. Instead of directly manipulating each qubit to perform universal quantum logic gates or measurements, ADQC uses a fixed two-qubit interaction to couple the memory register of a quantum computer to an ancilla qubit. By measuring the ancilla, the measurement-induced back-action on the system performs the desired logical operations. The underlying mathematical model is based on a new entanglement resource called twisted graph states generated from non-commuting operators, leading to a surprisingly powerful structure for parallel computation compared to graph states obtained from commuting generators. [M. Hein, J. Eisert, and H.J. Briegel. Multi-party entanglement in graph states. Physical Review A, 69, 2004. quant-ph/0307130]. The ADQC model is formalised in an algebraic framework similar to the Measurement Calculus [V. Danos, E. Kashefi, and P. Panangaden. The measurement calculus. Journal of ACM, 2007]. Furthermore, we present the notion of causal flow for twisted graph states, based on the stabiliser formalism, to characterise the determinism. Finally we demonstrate compositional embedding between ADQC and both the one-way and circuit models which will allow us to transfer recently developed theory and toolkits of measurement-based quantum computing and quantum circuit models directly into ADQC.