Describes a decomposition technique to write a qudit unitary as a sequence of SU(2) rotations and outlines a scheme to map decompositions on to other decompositions.
Simulating entangled, many-body quantum systems is notoriously hard, especially in the case of high-dimensional nature of physical underlying objects. In this work, we propose an approach for simulating the Potts model based on the Suzuki-Trotter decomposition that we construct for qudit systems. Specifically, we introduce two qudit-native decomposition schemes: (i) the first utilizes Molmer-Sorensen gate and additional local levels to encode the Potts interactions, while (ii) the second employs an light-shift gate that naturally fits qudit architectures. These decompositions enable a direct and efficient mapping of the Potts model dynamics into hardware-efficient qudit gate sequences for trapped-ion platform. Furthermore, we demonstrate the use of a Suzuki-Trotter approximation with our evolution-into-gates framework, for detecting the dynamical quantum phase transition. Our results establish a pathway toward qudit-based digital quantum simulation of many-body models and provide a new perspective on probing nonanalytic behavior in high-dimensional quantum many-body models.
We present qubit logic on qudits (QLOQ), a compression scheme in which the qubits from a hardware agnostic circuit are divided into groups of various sizes, and each group is mapped to a physical qudit for computation. QLOQ circuits have qubit-logic inputs, outputs, and gates, making them compatible with existing qubit-based algorithms and Hamiltonians. We show that arbitrary qubit-logic unitaries can in principle be implemented with significantly fewer two-level (qubit) physical entangling gates in QLOQ than in qubit encoding. We achieve this advantage in practice for two applications: variational quantum algorithms, and unitary decomposition. The variational quantum eigensolver (VQE) for LiH took 5 hours using QLOQ on one of Quandela's cloud-accessible photonic quantum computers, whereas it would have taken 4.39 years in qubit encoding. We also provide a QLOQ version of the Quantum Shannon Decomposition, which not only outperforms previous qudit-based proposals, but also beats the theoretical lower bound on the CNOT cost of unitary decomposition in qubit encoding.
Recent developments in mapping lattice gauge theories relevant to the Standard Model onto digital quantum computers identify scalable paths with well-defined quantum compilation challenges toward the continuum. As an entry point to these challenges, we address the simulation of SU(2) lattice gauge theory. Using qudit registers to encode the digitized gauge field, we provide quantum resource estimates, in terms of elementary qudit gates, for arbitrarily high local gauge field truncations. We then demonstrate an end-to-end simulation of real-time, qutrit-digitized SU(2) dynamics on a cube. Through optimizing the simulation, we improved circuit decompositions for uniformly controlled qudit rotations, an algorithmic primitive for general applications of quantum computing. The decompositions also apply to mixed-dimensional qudit systems, which we found advantageous for compiling lattice gauge theory simulations. Furthermore, we parallelize the evolution of opposite faces in anticipation of similar opportunities arising in three-dimensional lattice volumes. This work details an ambitious executable for future qudit hardware and attests to the value of codesign strategies between lattice gauge theory simulation and quantum compilation.