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arXiv:1106.0270 · Physical Review A

Scalable uniform construction of highly conditional quantum gates

Svetoslav S. Ivanov, Nikolay V. Vitanov

Published Aug 16, 2011• 14 citations
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Abstract

We present a scalable uniform technique for the construction of highly conditional multiply-controlled-not quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.

DOI
10.1103/physreva.84.022319

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We present a scalable uniform technique for the construction of highly conditional multiply-controlled-not quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.
We present a scalable uniform technique for construction of highly conditional Cn^nn-NOT quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.
We show that, under certain conditions, the two-qubit controlled-NOT logic operations can be realized exactly using one laser pulse. The target qubit and the control qubit are encoded by the internal and external degrees of freedom of a single trapped ion. The multiquantum process of the interaction between the internal and external degrees of freedom of the ion is considered. This scheme neither requires the cooled ion in its vibrational ground state nor necessitates performance of the Lamb-Dicke approximation.
Conditional multiqubit gates are a key component for elaborate quantum algorithms. In a recent work, Rasmussen et al. [Phys. Rev. A 101, 022308 (2020)] proposed an efficient single-step method for a prototypical multiqubit gate, a Toffoli gate, based on a combination of Ising interactions between control qubits and an appropriate driving field on a target qubit. Trapped ions are a natural platform to implement this method, since Ising interactions mediated by phonons have been demonstrated in increasingly large ion crystals. However, the simultaneous application of these interactions and the driving field required for the gate results in undesired entanglement between the qubits and the motion of the ions, reducing the gate fidelity. In this work, we propose a solution based on adiabatic switching of these phonon-mediated Ising interactions. We study the effects of imperfect ground-state cooling and use spin-echo techniques to undo unwanted phase accumulation in the achievable fidelities. For gates coupling to all axial modes of a linear crystal, we calculate high-fidelity (>99(>99%)(>99 NNN-qubit rotations with N=3−−7N=3--7N=3−−7 ions cooled to their ground state of motion and a gate time below 1 ms. Finally, we study the effect of laser intensity fluctuations and find that the proposed gate requires intensity stabilization with subpercentage noise levels. The high fidelities obtained also for large crystals could make the gate competitive with gate-decomposed, multistep variants of the NNN-qubit Toffoli gate, at the expense of requiring ground-state cooling of the ion crystal.
We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique is fairly robust to parameter fluctuations and operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions; thus the implementation complexity grows only linearly with the size of the system. The approach does not require individual addressing of the ions in the trap and can be applied both inside and outside the Lamb–Dicke regime.
Abstract We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors. The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and, unlike the state of the art, requires neither weak-coupling Lamb–Dicke approximation nor perturbation treatment. With the application of gradient-based optimal control, it enables finding amplitude- and phase-modulated laser control protocols that work without the Lamb–Dicke approximation, promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies. Also, robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections. Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation, and thus can find applications in near-future experiments.
We introduce two types of two-qubit controlled-phase gates, which operate with trapped ions in a linear Paul trap. Each ion is addressed individually with two sequential bichromatic laser pulses, the two frequency components of which are tuned on exact resonance with the first blue and red vibrational sidebands of the qubit transition frequency. For suitably chosen pulse areas and relative laser phases the dependence on the phonon number vanishes and the net effect is a controlled-phase gate between the electronic qubit states. In contrast to earlier gates, in which the pulses addressing the two ions are separated in time, we use partly overlapping pulses, which make the present gates faster, e.g., by about 26% for rectangular and over 50% for sinusoidal pulses.