Quantum Information Processing with Trapped Ion Qudits

Project Information

QIPID

Grant agreement ID: 840450

DOI

10.3030/840450

Project closed

EC signature date 11 April 2019

Start date 1 September 2020

End date 31 August 2022

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 186 167,04

EU contribution

€ 186 167,04

Coordinated by

UNIVERSITAET INNSBRUCK
Austria

Periodic Reporting for period 1 - QIPID (Quantum Information Processing with Trapped Ion Qudits)

Reporting period: 2020-09-01 to 2022-08-31

Summary of the context and overall objectives of the project

Today's quantum devices are almost exclusively built with binary information processing in mind. While this has been highly successful for classical computers, quantum systems do not naturally fit into this binary paradigm. Instead, virtually all quantum systems underpinning today's quantum technologies are naturally multilevel systems and must be artificially constrained to be operated in a binary fashion. As a result, today's quantum hardware is not used to its full potential, which could be achieved by using the full Hilbert space for computation.

Quantum computers and simulators hold the promise to vastly speed up certain information processing tasks, including in fields such as physics, chemistry, material science, optimization, and finance. The breadth of these applications translates means that such devices are expected to have a wide impact on technology and society. Any improvements in the efficiency of quantum computers or the computational power of a given number of quantum particles will be critical for enabling these technologies to deliver results beyond the capabilities of classical devices sooner.

The objective of this project is to develop the tools for and demonstrate in a proof-of-principle experiment that trapped-ion quantum computers can be operated in a way that makes use of the full Hilbert space by encoding information into so-called qudits (quantum digits), rather than qubits (quantum bits). This approach has the potential to significantly boost the performance of existing quantum computers and enable them to perform more complex tasks with fewer resources.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Within this project, we developed a universal toolbox for qudit quantum information processing with trapped ions. This includes arbitrary pairwise addressed two-level entangling operations in a standardized form that is flexibly embedded in qudit Hilbert spaces of arbitrary (also mixed) dimension. We benchmarked the performance of this toolbox to confirm that it does not notably degrade with dimension, beyond what would be expected due to the higher number of laser pulses required compared to operating the same device as a standard qubit quantum processor. Further enhancing this toolbox, we developed and demonstrated a genuine qudit entangling operation, which enables the direct creation of entanglement over the whole qudit Hilbert space in one gate application. This gate mechanism comes with less control overhead, independent of the qudit dimension, increased performance, and higher entangling power than standard embedded two-level couplings. Together these gates form a powerful toolbox for qudit quantum information processing in trapped ions.

Using the developed methods, we performed a quantum simulation of a topological quantum spin system, where neighboring spins were encoded in distinct subspaces of the qudit Hilbert space. This resulted in almost complete suppression of cross-talk errors, enabling us to perform the simulation in a trapping regime that would not have otherwise been possible and significantly boosting the performance of the quantum processor.
We further exploited the newly developed capabilities to achieve single-setting quantum state characterization by implementing symmetric informationally-complete (SIC) positive operator-valued measures (POVM). The four-outcome SIC POVM is known to be the optimal local measurement for a qubit, yet being non-projective it cannot be realized directly in practice. We demonstrate, how to embed a qubit locally into a four-level system in a way that this measurement turns projective. As a result, the complete characterization of a multi-qubit system, which typically requires an exponential number of measurement settings becomes possible with just a single fixed measurement setting, regardless of the system size, and with virtually no experimental overhead. In addition, we developed a SIC POVM extension of the classical shadow framework, enabling highly efficient data processing for SIC POVMs. Together, these techniques enable, as we demonstrated, the characterization of linear and nonlinear properties of multi-qubit quantum systems in an online fashion.

In summary, we developed and demonstrated a complete toolkit for qudit quantum information processing. As a first application, we already demonstrated how this platform enables a paradigm shift in the way qubit systems can be characterized, and we made first steps towards using it for quantum simulation applications. Over the course of the project, the fellow co-authored 12 publications (4 published, 8 currently under review) and presented the project results at 8 international conferences and workshops (5 invited). The fellow also initiated fruitful and ongoing collaborations with several European and international research groups and made several contributions to outreach events, including as a finalist in Falling Walls Emerging Talents.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Current quantum devices almost exclusively operate with artificial two-level systems. Within this project, we lay the groundwork for a paradigm shift towards using the full multilevel structure of available quantum information carriers. We fully characterized the developed tools using standardized benchmarks to enable a fair comparison against the state-of-the-art. We further demonstrated a genuine qudit entangling gate in trapped ions, which scales seamlessly with the dimension of the system.

Putting the newly developed capabilities to work, we demonstrate, how locally embedding qubits into qudits enables optimal quantum state characterization by means of symmetric informationally-complete (SIC) positive operator-valued measures (POVM) with negligible experimental overhead. This enables the complete characterization of multi-qubit systems with a single measurement setting, rather than an exponential number of measurement settings using state-of-the-art methods. This not only greatly reduces the experimental overhead for one of the most central tasks in quantum information processing but also drastically reduces the classical processing overhead by combining SIC POVM measurements with a newly developed extension of the classical shadow formalism. As a consequence, it becomes possible to characterize linear and nonlinear properties of multi-qubit quantum states in an online fashion, where the classical processing remains faster than the experimental data acquisition for up to tens of qubits. This significantly simplifies the measurement and characterization of quantum systems compared to the state of the art.

We exemplify the potential of the qudit platform for quantum information processing by performing a quantum simulation of a spin system where each neighboring spin is encoded in a different part of the qudit Hilbert space. This technique almost completely eliminates crosstalk errors, which are particularly detrimental in quantum processors. Consequentially, it enabled us to study the phases of quantum matter in a larger system than would have been possible with state-of-the-art qubit methods in the same device. We thus expect this technique to find wider use in crosstalk suppression in trapped ion systems.

(c) Harald Ritsch