Sdim: Open-Source Qudit Stabilizer Simulator for High-Dimensional Quantum Computation and Benchmarking

The pursuit of fault-tolerant quantum computing continues to drive innovation in computational techniques, and recent advances have seen experimental groups building quantum hardware based on high-dimensional quantum systems known as qudits. However, a crucial gap has existed in the available computational tools, as no widely accessible simulator could effectively model and analyse these qudit systems. Now, Adeeb Kabir, Steven Nguyen, and Sohan Ghosh, along with colleagues from Rutgers University and the University of California, Davis, address this challenge with the development of Sdim, the first open-source qudit stabilizer simulator. This new simulator not only bridges a critical gap in the field, but also provides essential infrastructure for exploring the potential of qudits, mirroring the impact earlier simulators had on the development of qubit-based quantum computation, and enabling researchers to evaluate and benchmark qudit circuits at realistic scales.

Simulating Qudits Beyond Prime Dimensions

Researchers have developed a new method for simulating qudits, quantum systems extending beyond the standard qubit, with a particular focus on systems where the qudit possesses more than two states. This work addresses the challenges inherent in simulating qudits with dimensions that are not prime numbers, such as 4, 6, or 8. The simulation relies on a “tableau” representation, a numerical method for tracking the state of multiple qudits using arrays to represent the properties that define the quantum state. This approach overcomes limitations encountered when working with non-prime dimensions, which present unique difficulties because the mathematical rules governing these systems become more complex.

To address these complexities, the team introduced “Weyl operators,” a generalization of standard quantum gates, to accurately represent the state of the qudits. They also employed a technique called lifting, which transforms the calculations to a modified dimension, simplifying the mathematical operations. Utilizing the Smith Normal Form, a powerful technique for analyzing the system, allows for determining the outcomes of measurements, although it can be computationally demanding. This new approach provides a crucial tool for understanding and developing qudit-based quantum technologies, opening up new possibilities for quantum computing research.

Qudit Simulation Using Tableau Representation

The creation of a new open-source simulator for qudits represents a significant step forward in fault-tolerant quantum computing. Recognizing the limitations of existing software, researchers engineered a simulator capable of handling qudits of any dimension, allowing for detailed numerical characterization of quantum protocols at realistic scales. The simulator utilizes the “tableau” representation, a method for tracking the state of multiple qudits using numerical arrays to represent the properties that define the quantum state. Quantum gates are applied by modifying the tableau’s properties, effectively evolving the quantum state.

The simulator accurately models noise, implementing errors with adjustable parameters to simulate imperfect quantum systems. Measurements are performed locally, with the ability to simulate different types of measurements by applying transformations before and after the measurement. To demonstrate the simulator’s capabilities, researchers successfully simulated a simple quantum algorithm, verifying its accuracy and performance. This work provides essential computational infrastructure for exploring novel qudit-based algorithms and protocols.

Open-Source Simulator Validates Qudit Circuit Performance

Scientists have developed the first open-source simulator specifically designed for qudits and demonstrated its capabilities in evaluating and sampling complex quantum circuits. This simulator utilizes a technique called Pauli frame sampling to efficiently compute numerous outcomes of a qudit circuit, achieving performance comparable to existing state vector simulations used for qubits. The research team validated the simulator’s performance by simulating a quantum error detection code, successfully validating logical error rates and extending simulations to parameters previously intractable with other tools. Experiments demonstrate the simulator’s ability to accurately model various types of noise, with validation procedures confirming that the empirical distributions align with theoretical expectations. Performance evaluations involved running the simulator on complex circuits of entangled qudits, allowing for a direct comparison of sampling complexity with other simulators. The simulator’s validation suite, available publicly, includes comprehensive tests for both error-free and noisy simulations, ensuring its reliability and accuracy.

Qudit Simulation and Efficient Pauli Sampling

This work presents a new open-source simulator designed to evaluate quantum circuits utilizing qudits, quantum bits with more than two possible states. Unlike existing tools focused on qubits, this simulator supports qudits of any dimension, addressing a significant gap in the field of fault-tolerant quantum computing. The simulator’s accuracy has been thoroughly validated against state vector simulations, and it demonstrates an advantage in efficiently simulating circuits, even with a modest number of qudits. The team also developed an efficient method for sampling Pauli measurements, which streamlines computations and enhances the simulator’s ability to handle large, measurement-intensive systems. This capability is valuable for characterizing hardware designed to implement complex quantum gates, as demonstrated through applications to randomized benchmarking and locally-rotated benchmarking. While acknowledging the simulator currently provides a foundational infrastructure, the researchers emphasize its importance as a crucial step towards enabling practical qudit-based fault-tolerant quantum computing.