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IEEE International Magnetic Conference - Short Papers (INTERMAG Short Papers)

Universal Set of Magnon-Mediated Quantum Gates

Cody Trevillian, V. S. Tiberkevich

Published May 1, 2023• 1 citation
Publisher

Abstract

We propose a universal set of magnon-mediated quantum gates applied to a hybrid quantum system of mutually noninteracting qubits coupled to an ancilla magnonic mode. The gates are realized through dynamic manipulation of the frequency of the magnon mode and control of its initial state, without directly changing any qubit parameters. We present protocols for arbitrary single-qubit gates and two-qubit controlled phase gate, which together form a universal set and can be combined to perform any unitary transformation on the qubit subsystem. Our results demonstrate principal possibility of realizing a universal quantum computer controlled solely through manipulation of magnon-qubit interactions.

DOI
10.1109/intermagshortpapers58606.2023.10228694

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We propose a universal set of magnon-mediated quantum gates applied to a hybrid quantum system of mutually noninteracting qubits coupled to an ancilla magnonic mode. The gates are realized through dynamic manipulation of the frequency of the magnon mode and control of its initial state, without directly changing any qubit parameters. We present protocols for arbitrary single-qubit gates and two-qubit controlled phase gate, which together form a universal set and can be combined to perform any unitary transformation on the qubit subsystem. Our results demonstrate principal possibility of realizing a universal quantum computer controlled solely through manipulation of magnon-qubit interactions.
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We propose a hybrid quantum system consisting of a magnetic particle inductively coupled to two superconducting transmon qubits, where qubit-qubit interactions are mediated via magnons. We show that the system can be tuned into three different regimes of effective qubit-qubit interactions, namely, a transverse (XX+YYXX+YYXX+YY), a longitudinal (ZZZZZZ), and a nontrivial ZXZXZX interaction. In addition, we show that an enhanced coupling can be achieved by employing an ellipsoidal magnet, carrying anisotropic magnetic fluctuations. We propose a scheme for realizing two-qubit gates, and simulate their performance under realistic experimental conditions. We find that iswap and cz gates can be performed in this setup with an average fidelity $\ensuremath{\gtrsim}99%$, while an icnot gate can be applied with an average fidelity $\ensuremath{\gtrsim}88%$. Our proposed hybrid circuit architecture offers an alternative platform for realizing two-qubit gates between superconducting qubits and could be employed for constructing qubit networks using magnons as mediators.
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.
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.
We introduce a model of quantum computation intermediate between the gate-based and measurement-based models. A quantum register is manipulated remotely with the help of a single ancilla that ``drives'' the evolution of the register. The fully controlled ancilla qubit is coupled to the computational register only via a fixed unitary two-qubit interaction and then measured in suitable bases, driving both single- and two-qubit operations on the register. Arbitrary single-qubit operations directly on register qubits are not needed. We characterize all interactions EEE that induce a unitary, stepwise deterministic measurement back-action on the register sufficient to implement any quantum channel. Our scheme offers experimental advantages for computation, state preparation, and generalized measurements, since no tunable control of the register is required.
This letter presents a model system for controllable two-magnon interference in the time domain. This two-magnon interference, i.e., a magnonic analog to the photonic Hong-Ou-Mandel effect, is supported by a tunable magnonic beamsplitter operation formed in a hybrid cavity magnonic system comprising a pair of mutually coupled magnon modes. By applying a time-dependent magnetic field, magnons can be excited independently in each mode and subsequently brought into interaction, shifting from independent to collective oscillations, to realize a controllable magnonic beamsplitter. When the beamsplitter operation is applied to an initially unentangled two-magnon state, a maximally entangled magnonic N00NN00NN00N state with tunable phase sensitivity is produced. These findings suggest that two-magnon interference in hybrid cavity magnonic systems may enable novel quantum metrological devices to study fundamental magnon dynamics and contribute to developing hybrid magnonic quantum computing architectures.