GCAMPS: A Scalable Classical Simulator for Qudit Systems

Abstract

Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently introduced Clifford Augmented Matrix Product State (CAMPS) method offer scalability and efficiency by combining both tensor network and stabilizer simulation techniques and leveraging their complementary advantages. This hybrid simulation method has indeed demonstrated significant improvements in simulation performance for qubit circuits. Our work generalises the CAMPS method to higher quantum degrees of freedom -- qudit simulation, resulting in a generalised CAMPS (GCAMPS). Benchmarking this extended simulator on quantum systems with three degrees of freedom, i.e. qutrits, we show that similar to the case of qubits, qutrit systems also benefit from a comparable speedup using these techniques. Indeed, we see a greater improvement with qutrit simulation compared to qubit simulation on the same $T$-doped random Clifford benchmarking circuit as a result of the increased difficulty of conventional qutrit simulation using tensor networks. This extension allows for the classical simulation of problems that were previously intractable without access to a quantum device and will open new avenues to study complex many-body physics and to develop efficient methods for quantum information processing.

9 pages, 7 figures

References in corpus (25)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Improved Simulation of Stabilizer Circuits
• Tensor networks for complex quantum systems
• Qudits and high-dimensional quantum computing
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Simulation of quantum circuits by low-rank stabilizer decompositions
• A positive tensor network approach for simulating open quantum many-body systems
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Lecture Notes of Tensor Network Contractions
• Augmenting Density Matrix Renormalization Group with Clifford Circuits
• Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states
• Fast estimation of outcome probabilities for quantum circuits
• Calibrating the role of entanglement in variational quantum circuits
• Tensor Networks Can Resolve Fermi Surfaces
• Clifford Dressed Time-Dependent Variational Principle
• Stabilizer Tensor Networks with Magic State Injection
• A Herculean task: Classical simulation of quantum computers
• Disentangling critical quantum spin chains with Clifford circuits
• Quantum Complexity and Chaos in Many-Qudit Doped Clifford Circuits
• Quantum magic dynamics in random circuits
• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
• A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
• Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement