A quantum information processor with trapped ions (1308.3096v1)

Abstract: Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of $^{40}$Ca${^+}$ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.

• The paper demonstrates a trapped-ion processor implementing high-fidelity (>99% for single-qubit and 98% for entangling gates) quantum operations.
• Detailed noise characterization reveals dephasing and motional heating as key challenges, mitigated via dynamical decoupling and calibration.
• The processor successfully simulates quantum algorithms, including QFT and order-finding, paving the way for scalable quantum computing.

An Expert Analysis of "A Quantum Information Processor with Trapped Ions"

The paper by Schindler et al. presents the development and implementation of a small-scale quantum information processor using trapped ${}^{40}\mathrm{Ca}^+$ ions in a macroscopic linear Paul trap. The authors provide an account of the operational architecture, noise characterization, and example quantum algorithms, elucidating the potential and limitations of trapped ion-based quantum computing.

Key Contributions and Methodology

The core contribution of this paper lies in demonstrating a quantum information processor that successfully implements a comprehensive set of quantum operations. These operations include single-qubit rotations, entangling gates, and a series of carefully controlled non-coherent operations that enable the simulation of arbitrary Markovian processes. Notably, the architecture uses composite operations, built upon the M{\o}lmer-S{\o}rensen (MS) gate, which is crucial for producing entangled states such as GHZ states.

A distinctive feature of this processor is the direct utilization of non-coherent optical and phase damping processes, expanding the quantum controllability beyond pure unitary transformations. The design acknowledges the critical role of error rates, driven by the dominant noise processes, including dephasing and heating of the motional modes. The paper details thorough characterizations of these error processes, highlighting the various sources of decoherence and possible mitigations via careful experimental calibration.

Strong Numerical Results and Claims

The fidelity of the demonstrated operations is noteworthy, with single-qubit gates achieving over 99% accuracy and entangling gates attaining up to 98% fidelity for two-ion operations under optimal conditions. The paper identifies dephasing due to laser frequency noise as a primary fidelity limiting factor, and uses dynamical decoupling strategies to further extend coherence times.

Implications for Future Developments

This research suggests multiple implications for future advancements in ion trap quantum computing. The ability to handle non-coherent operations suggests utility in open quantum system simulations, potentially broadening applicability in quantum process verifications and noise engineering. Additionally, the realization of the quantum Fourier transform (QFT) and order-finding algorithms lays foundational work for scaling to more complex algorithms like Shor's factorization.

The intricate details of the experimental setup, particularly the advances in AC-Stark and MS gate implementations, provide a roadmap for enhancing qubit numbers while managing crosstalk and addressing errors. Improvements in mitigating motional decoherence and further refinements in ion control will be vital for progressing to larger quantum registers.

Conclusion

In sum, Schindler et al. deliver a substantial contribution to the field of quantum computing with ions, exemplifying how trapped ion processors may evolve into feasible platforms for complex quantum algorithms. While significant challenges remain, particularly regarding error correction and scalability, the insights and methodologies of this paper decidedly advance the state of quantum processing infrastructure. Their work encapsulates a significant milestone demonstrating how coherent and non-coherent operations can be harnessed cohesively for quantum information processing.