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arXiv:1706.09660 · New Journal of Physics

Deterministic nonlinear phase gates induced by a single qubit

Ki-min Park B, Petr Marek, Radim Filip

Published Apr 4, 2018• 21 citations
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Abstract

We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.

DOI
10.1088/1367-2630/aabb86

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We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.
Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since strong highly nonlinear operations are often unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, it is possible to resolve these issues and implement a nonlinear operation both nearly deterministically and nearly perfectly. We explicitly demonstrate the approach by constructing self-Kerr and cross-Kerr couplings in a realistic situation, which require a feasible dispersive coupling between the two-level system and the oscillator.
Abstract Continuous-variable (CV) quantum information processing harnesses versatile experimental tools that leverage the power of infinite-dimensional oscillators controlled by a single qubit. Increasingly available elementary Rabi gates have been proposed as a resource for implementing universal CV gates, but the requirement of many weak, non-commuting gates is a bottleneck in scaling up such an approach. In this study, we propose a resource-efficient technique using Fourier expansion to implement arbitrary non-linear phase gates in a single oscillator. This method reduces the number of sequentially required gates exponentially. These gates represented by cubic, quartic, and other arbitrary nonlinear potentials have applications in CV quantum information processing with infinite-dimensional oscillators controlled by a single qubit. Our method outperforms previous approaches and enables the experimental realization of a wide range of applications, including the development of bosonic quantum sensors, simulations, and computation using trapped ions and superconducting circuits.
Nonlinear phase gates are essential to achieve the universality of continuous-variable quantum processing and its applications. We present a deterministic protocol for generating nonlinear phase gates in trapped ion systems using simultaneous two-tone sideband drives beyond the Lamb-Dicke regime. Our approach harnesses higher-order interaction terms typically neglected or suppressed to construct nonlinear phase gates. This methodology enables high-fidelity gate engineering with a near three-fold reduction in control pulses compared to state-of-the-art theoretical proposals.
Non-Gaussian gates remain a key bottleneck for universal continuous-variable (CV) quantum computation because the nonlinearities they require are difficult to engineer. To address this challenge, we develop an efficient qubit-oscillator Rabi synthesis scheme for polynomial phase gates, with a total interaction time that scales polylogarithmically with the inverse target error ε\varepsilonε. Specifically, for a class of readily preparable initial states, we show that a degree-RRR phase gate can be approximated by an analytically constructed Rabi sequence with total time O(log⁡(R−1)/2+o(1)(1/ε))O(\log^{(R-1)/2+o(1)}(1/\varepsilon))O(log(R−1)/2+o(1)(1/ε)). This construction requires no numerical optimization and therefore extends naturally to arbitrarily large multimode systems. We further establish a total-time lower bound of Ω(log⁡(R−1)/2(1/ε))Ω(\log^{(R-1)/2}(1/\varepsilon))Ω(log(R−1)/2(1/ε)), showing that the synthesis is near optimal. As applications, we use this scheme to simulate representative CV quantum dynamics and implement a CV quantum algorithm for solving linear partial differential equations. These results establish qubit-oscillator Rabi control as an efficient, analytically compilable, and near-optimal primitive for CV quantum information processing.
We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.
The motional modes of trapped ions are promising candidates for continuous-variable (CV) quantum computation and simulation. However, to achieve a universal gate set for CV quantum computation, anharmonic nonlinear unitaries are required. Here, we experimentally demonstrate a protocol that allows us to approximate the cubic phase gate. By numerically optimizing the phase angles and amplitudes of a set of state-dependent force pulses, we demonstrate the cubic phase gate for both vacuum and low-ααα coherent state inputs and verify its performance. Our protocol can also be extended to approximate other nonlinear unitaries.