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Quantum Information and Measurement (QIM)

Coherent Quantum Fourier Transform Using 3-Qubit Conditional Gates and Ultrasensitive Magnetometry with RF-Driven Trapped Ions.

I. Baumgart, Jianming Cai, Svetoslav S. Ivanov, Ch. Piltz, Martin Bodo Plenio, Alex Retzker, Theeraphot Sriarunothai, Sabine Wölk, Ch. Wunderlich

Published Jan 1, 2017• 0 citations
Publisher

Abstract

Using long-range magnetic gradient induced coupling between three effective spins, a coherent QFT is efficiently realized with trapped Yb+ ions. With a single Yb+ ion, RF magnetic fields are measured close to the quantum limit.
DOI
10.1364/qim.2017.qw6a.5

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We propose a simplified mathematical construction of the quantum Fourier transform which is suited for systems described by Ising-type Hamiltonians. By contrast to the standard Cooley-Tuckey scheme, which prescribes sequences of CPHASE gates, our implementation is based on one-qubit gates and a free evolution process. We also show how to obtain a quadratic speed-up by applying the conditional interactions simultaneously. Thus rather than O(N2N^2N2) our implementation time scales as O(NNN). Finally, we show a realization of our method with homogeneous microwave driven ion traps in a magnetic field with gradient.
Using trapped atomic ions, we demonstrate a tailored and versatile effective spin system suitable for quantum simulations and universal quantum computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system and, thus, can serve as a quantum memory, while simultaneously, other coupled spins perform conditional quantum dynamics. Also, microwave pulses can change the sign of spin-spin couplings, as well as their effective strength, even during the course of a quantum algorithm. Taking advantage of the simultaneous long-range coupling between three spins, a coherent quantum Fourier transform-an essential building block for many quantum algorithms-is efficiently realized. This approach, which is based on microwave-driven trapped ions and is complementary to laser-based methods, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer.
We present a new method for coherent control of trapped ion qubits in separate interaction regions of a multizone trap by simultaneously applying an electric field and a spin-dependent gradient. Both the phase and amplitude of the effective single-qubit rotation depend on the electric field, which can be localized to each zone. We demonstrate this interaction on a single ion using both laser-based and magnetic-field gradients in a surface-electrode ion trap, and measure the localization of the electric field.
Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio-frequency radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the Hamiltonian describing this coupling in the presence of a resonant dynamic gradient, is identical, in a dressed state basis, to the Hamiltonian in the case of a static gradient. The coupling strength is in both cases described by the same effective Lamb-Dicke parameter. This insight can be used to overcome demanding experimental requirements when using a dynamic gradient field for state-of-the-art experiments with trapped ions, for example, in quantum information science. At the same time, this insight opens new experimental perspectives by way of using a single resonant or detuned dynamic gradient field, inducing long-range coupling, for conditional multi-qubit dynamics.