Scaling trapped-ion processors by adding ions remains challenging. A complementary route exploits the multilevel internal structure of each ion to increase the computational Hilbert space per ion. We introduce a hardware-native hybrid qudit-oscillator instruction set for a general d-level internal register coupled to bosonic modes and prove that three of its native operation families suffice for universality of one qudit coupled to several modes. Adding an entangling operation between ions extends universality to a connected register of several qudits. The architecture natively supports both phase-space and sideband instruction sets and is implemented in the open-source framework HybridLane. As a representative application, we reproduce the dissipative vibronic dynamics of a three-chromophore complex previously simulated on a hybrid qubit-oscillator superconducting platform. Moving from a one-qubit-per-state register to a single qudit stores the entire electronic manifold in one ion, so every electronic coupling becomes a local intra-ion transition and the lab-frame Hamiltonian compiles directly into the ISA. Under the stated sequential timing model from a 40Ca+ qudit processor, one Trotter step is projected to run about ten times faster on the qudit, with an average RMSE of approximately 1.1 percent against the published reference.
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27 pages, 10 figures, 10 tables. Submitted to ACM Transactions on Quantum Computing
Scaling trapped-ion processors by adding ions remains challenging. A complementary route exploits the multilevel internal structure of each ion to increase the computational Hilbert space per ion. We introduce a hardware-native hybrid qudit-oscillator instruction set for a general d-level internal register coupled to bosonic modes and prove that three of its native operation families suffice for universality of one qudit coupled to several modes. Adding an entangling operation between ions extends universality to a connected register of several qudits. The architecture natively supports both phase-space and sideband instruction sets and is implemented in the open-source framework HybridLane. As a representative application, we reproduce the dissipative vibronic dynamics of a three-chromophore complex previously simulated on a hybrid qubit-oscillator superconducting platform. Moving from a one-qubit-per-state register to a single qudit stores the entire electronic manifold in one ion, so every electronic coupling becomes a local intra-ion transition and the lab-frame Hamiltonian compiles directly into the ISA. Under the stated sequential timing model from a 40Ca+ qudit processor, one Trotter step is projected to run about ten times faster on the qudit, with an average RMSE of approximately 1.1 percent against the published reference.
This tutorial offers a pedagogical guide to hybrid quantum processors that integrate discrete-variable (DV) qubits and continuous-variable (CV) oscillators. Aimed at computer scientists, engineers, and physicists, it provides an overview of the experimental, algorithmic, and architectural aspects of this novel and rapidly developing hardware model. Experimental realizations of this model include superconducting, trapped-ion, and neutral-atom platforms. By combining DV and CV components, hybrid oscillator-qubit processors enable a powerful new paradigm that offers complementary strengths for quantum control, error correction, computation, and simulation. Working toward the goal of a full-stack system connecting applications to CV-DV hardware, we define and formulate abstract machine models and instruction set architectures. These essential abstractions enable codesign of hardware and software, and resource estimation for exploring the potential of current and future hardware for computational and simulation tasks. Using these abstractions, we present both new and existing examples that illustrate the benefits of hybrid CV-DV processors relative to traditional DV-only hardware in computation as well as quantum simulation of physical models. Examples include algorithms for transferring states between DV and CV systems, performing the quantum Fourier transform, and simulation of lattice gauge theories. Relative to qubit-only hardware, the bosonic degrees of freedom natively available in hybrid architectures can substantially reduce the circuit complexity of simulations for physical models containing bosons. A key technique is the extension of quantum signal processing ideas to CV-DV systems. This work is intended to serve as a timely and comprehensive guide to this relatively unexplored yet promising approach to quantum computation and to provide a road map to guide future development.
Shuttling-based trapped-ion quantum computers (QCCD) rank among the most mature hardware platforms. Existing and envisaged devices exhibit architectural differences in terms of register layout and connectivity. Platform-specific compilers are required to translate quantum circuits into resource-optimized hardware-level command chains. Hardware platforms and compiler software stacks are mostly developed independently of one another by different research communities. This work aims to bridge these communities by abstracting QCCD architectures and native operations, enabling computer scientists to address compilation problems using generic methods without requiring a deep background in the physical operating principles of the platform. The resulting design space is organized into a small set of architectural archetypes, each posing its own compilation problem. We then select and apply compilation methods to one- and two-dimensional QCCD architectures, finding that the routing overhead scales approximately cubically with the number of qubits for the one-dimensional architecture and approximately quadratically for the two-dimensional one. Extending this to compilation with a quantum error-correction layer reveals additional differences and similarities between the physical and logical levels. We conclude that co-design is a requirement rather than an option, and this work provides the vocabulary, archetypes, and compilation abstraction it needs.
Universal digital quantum computers are able to approximate any Hamiltonian evolution as a digital quantum circuit consisting of discrete time steps. Strongly interacting physics models, for example in high-energy physics or materials science, make this a challenging task for near-term devices as they place a high demand on the quantum resources required [1]. One alternative is analog quantum simulation where the native evolution of a quantum system can be tailored to mimic that of the model of interest. While more efficient at specific problems, there are limits on the types of evolution available and on the observables that can be measured. In this conference paper we present first results towards unifying these two concepts in a trapped-ion experiment. Trapped atomic ions are one of the most advanced experimental platforms for both analog quantum simulation and digital quantum computing. Typically, the internal spin degrees of freedom are used qubits or for the simulation of spin models. The harmonic oscillator modes given by the motion of the ions in the trap are only employed transiently to create quantum gates or spin-spin interactions. However, these motional modes constitute a large Hilbert space themselves and present a bosonic degree of freedom, which is costly to model with qubits. Many systems of interest, for example Lattice gauge theories, require both spin and boson degrees of freedom. It was recently shown that they can be encoded more efficiently using the harmonic oscillator modes directly [2].
Abstract Quantum simulation on noisy intermediate-scale quantum (NISQ) hardware is limited by short coherence time and gate errors. We present a universal variational compilation optimization method (VCOM) that directly leverages the native gate set of trapped-ion processors, namely single-qubit rotations and global Ising-type XX interactions, to construct shallow circuits for simulating molecular Hamiltonians. Specifically, VCOM employs a hybrid optimization strategy combining genetic algorithms with gradient-based refinement to compile Pauli string evolution operators e −i Pt , thereby substantially reducing circuit depth and multi-qubit gate overhead in Hamiltonian simulation. Applied to hydrogen chains, the compiled circuits achieve fidelities comparable to standard decompositions while reducing the proportion of two-qubit operations to only 1.9%–4.6% of the total native gates, a significant improvement over the standard second-order Trotter–Suzuki product formula. Under experimentally motivated laser-intensity and phase-noise models, the proposed scheme maintains high fidelity and exhibits significantly slower degradation than direct native gate decompositions of conventional circuits. These results establish native-gate-based variational compilation as a scalable and practical approach for digital quantum simulation on trapped-ion platforms, with potential extensions to strongly correlated systems and non-equilibrium dynamics.
We report on the implementation of arbitrary circuits on a universal two-qubit register that can act as the computational module in a trapped-ion quantum computer based on the quantum charge-coupled device architecture. A universal set of quantum gates is implemented on a two-ion Coulomb crystal of Be + 9 ions using only chip-integrated microwave addressing. Individual-ion addressing is implemented using microwave micromotion sideband transitions; we obtain upper limits on addressing crosstalk in the register. Arbitrary two-qubit operations are characterized using the cycle benchmarking protocol. Published by the American Physical Society 2024
Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.