Periodic Reporting for period 1 - QUDITS (Quantum Information Processing in High-Dimensional Ion Trap Systems)
Reporting period: 2023-01-01 to 2025-06-30
Quantum computing has revolutionized the way we think about information and information processing. By building on the laws of quantum physics and phenomena such as superposition and entanglement, these devices promise to surpass the capabilities of our best classical computers. Yet, despite impressive recent developments, today's quantum processors still only use a small fraction of their true potential. Quantum computing hardware is almost exclusively built following the decades-old classical paradigm of binary information processing. The underlying physical systems that carry the quantum information, however, are almost always inherently multilevel systems. Similarly, many of the problems targeted by quantum computers also do not neatly fit into a binary paradigm. Hence, there is a twofold loss of computational efficiency: first in the use of only a fraction of the available information capacity, and second in inefficient rewriting of computational tasks into a language that is less suitable than the original formulation. This artificial restriction of quantum computers to just two levels per particle thus greatly limits the computational power of current and future quantum devices.
The goal of this project is to develop, implement, and demonstrate a quantum processor based on multi-level qudits encoded in trapped Ca40 ions. Using up to 8 levels per ion results in a vastly increased computational capacity compared to operating the same hardware with just two levels. In the first stage, this project will demonstrate universal control of multi-qudit registers for quantum computation with competitive performance. In the second stage, this new device will be used to demonstrate the utility of qudit-based quantum computing and simulation by showing how the qudit approach outperforms qubits in several key applications. Examples include qudit-enhanced tasks, such as optimal measurements, gate decompositions, or noise suppression, as well as native qudit tasks, such as quantum simulations of condensed matter and high-energy physics models with naturally exhibit a multi-level structure.
The goal of this project is to develop, implement, and demonstrate a quantum processor based on multi-level qudits encoded in trapped Ca40 ions. Using up to 8 levels per ion results in a vastly increased computational capacity compared to operating the same hardware with just two levels. In the first stage, this project will demonstrate universal control of multi-qudit registers for quantum computation with competitive performance. In the second stage, this new device will be used to demonstrate the utility of qudit-based quantum computing and simulation by showing how the qudit approach outperforms qubits in several key applications. Examples include qudit-enhanced tasks, such as optimal measurements, gate decompositions, or noise suppression, as well as native qudit tasks, such as quantum simulations of condensed matter and high-energy physics models with naturally exhibit a multi-level structure.
Within the project a trapped-ion quantum processor with universal control over 8-dimensional qudits encoded in trapped Ca40+ ions was developed. A universal gate set generally consists of a set of local rotations, combined with a single entangling operation. In the developed platform, arbitrary local rotations are realized by decomposition into native two-level couplings between the electronic states of an ion. It was shown that the quality of these local operations does not decrease as the qudit dimension is increased, a critical feat to demonstrate that any additional complications in qudit control and calibration are well under control. Similarly, an entangling operation between qudits was demonstrated with an error rate that is largely independent of the qudit dimension. This gate, which resembles the archetypal controlled-NOT gate used for qubits, embedded in a higher-dimensional Hilbert space is universal for qudit quantum computing. Yet, with the primary goal of qudit-based quantum information processing being efficiency, it becomes apparent that one entangling gate, although universal, is not sufficient. Hence, over the course of the project several more types of entangling gates were developed. Each of these gates serves a different purpose, such as entangling qubit subspaces, generating full qudit entanglement, or flexibly entangling mixed-dimensional systems, such as registers consisting of qubits and qudits. The resulting platform not only delivers state-of-the-art error rates, but features one of the most extensive gate sets, giving it the ability to efficiently implement a wide range of applications.
Applications studied to date include the native quantum simulation of the seminal Haldane model of a topological phase of matter. This model exhibits a striking difference between qubit and qudit behaviour, where three-dimensional systems show non-classical topological effects, while two-dimensional systems do not. The use of our qudit quantum processor enabled the direct study of a chain of spin-1 particles within the Haldane phase of matter.
Another area where a qudit approach is particularly suitable in the study of lattice gauge theories in high energy physics. Specifically, we consider quantum electrodynamics, which describes the interaction between charged particles and electromagnetic fields on the quantum scale. Here, the force fields are described by so-called gauge fields, which are high-dimensional objects that are most naturally represented by qudits in a quantum processor. Through a combined qubit-qudit approach, we studied both the static as well as dynamic behaviour of quantum electrodynamics in 2D. We observe not only magnetic field effects that do not exist in 1D, but also the interplay between particle pair creation and dynamical fields. Moreover, by encoding the gauge fields directly into qudits, we are able to seamlessly adjust the truncation and computational accuracy of the simulation. All the developed techniques generalize directly to large-scale simulations of quantum electrodynamics in 3D, paving the way towards quantum simulating Nature.
Another area where a qudit approach is particularly suitable in the study of lattice gauge theories in high energy physics. Specifically, we consider quantum electrodynamics, which describes the interaction between charged particles and electromagnetic fields on the quantum scale. Here, the force fields are described by so-called gauge fields, which are high-dimensional objects that are most naturally represented by qudits in a quantum processor. Through a combined qubit-qudit approach, we studied both the static as well as dynamic behaviour of quantum electrodynamics in 2D. We observe not only magnetic field effects that do not exist in 1D, but also the interplay between particle pair creation and dynamical fields. Moreover, by encoding the gauge fields directly into qudits, we are able to seamlessly adjust the truncation and computational accuracy of the simulation. All the developed techniques generalize directly to large-scale simulations of quantum electrodynamics in 3D, paving the way towards quantum simulating Nature.