A Multi-Qubit Quantum Gate Using the Zeno Effect

Philippe Lewalle1,2, Leigh S. Martin1,3, Emmanuel Flurin1,3, Song Zhang2, Eliya Blumenthal4, Shay Hacohen-Gourgy4, Daniel Burgarth5, and K. Birgitta Whaley1,2

1Berkeley Center for Quantum Information and Computation, Berkeley, California 94720 USA
2Department of Chemistry, University of California, Berkeley, California 94720 USA
3Department of Physics, University of California, Berkeley, California 94720 USA
4Department of Physics, Technion - Israel Institute of Technology, Haifa 32000 Israel
5Center for Engineered Quantum Systems, Macquarie University, 2109 NSW, Australia

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The Zeno effect, in which repeated observation freezes the dynamics of a quantum system, stands as an iconic oddity of quantum mechanics. When a measurement is unable to distinguish between states in a subspace, the dynamics within that subspace can be profoundly altered, leading to non-trivial behavior. Here we show that such a measurement can turn a non-interacting system with only single-qubit control into a two- or multi-qubit entangling gate, which we call a Zeno gate. The gate works by imparting a geometric phase on the system, conditioned on it lying within a particular nonlocal subspace. We derive simple closed-form expressions for the gate fidelity under a number of non-idealities and show that the gate is viable for implementation in circuit and cavity QED systems. More specifically, we illustrate the functioning of the gate via dispersive readout in both the Markovian and non-Markovian readout regimes, and derive conditions for longitudinal readout to ideally realize the gate.

In gate-based quantum computation, algorithms are assembled from sequences of discrete single- and multi-qubit operations. Quantum systems are, by definition, so isolated from external influences that quantum measurements are necessarily an invasive process that alters the physics. The Quantum Zeno Effect refers to a particular manifestation of this principle: Repeated strong quantum measurements will tend to freeze a quantum system in a particular state, inhibiting the dynamics that the system would have undergone unobserved. While quantum gates are most often engineered using the unitary (isolated) dynamics, we here propose a method to realize multi-qubit quantum gates using (open system) Zeno dynamics instead.

In particular, we here propose a family of “Zeno gates'' that realize the dynamics of a conditional phase gate across multiple qubits. Our scheme relies on a local unitary operation using an auxiliary level of one system (one qutrit). The non-local (entangling) aspect of the gate is however realized via the Zeno effect: By engineering a measurement that Zeno blocks transition to the highest joint excitation level of the multi-qubit system, we transform the simple unitary into a multi-qubit gate that could become a building block for computations. Our analysis characterizes the gate performance under increasingly less ideal / more realistic conditions, eventually emphasizing a realization based on two superconducting qudits. Our results here generalize and expand on a recent proof-of-principle experiment [Blumenthal et al., npj Quantum Information 8, 88 (2022)], and suggest several pathways towards improvement of our Zeno gate under realistic conditions.

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