Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states

Abstract

Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents stabilizer states. In this work, we integrate these two approaches to present a generalization of the tableau formalism used for Clifford circuit simulation. We explicitly prove how to update our formalism with Clifford gates, non-Clifford gates, and measurements, enabling universal circuit simulation. We also discuss how the framework allows for efficient simulation of more states, raising some interesting questions on the representation power of tensor networks and the quantum properties of resources such as entanglement and magic, and support our claims with simulations.

13 pages (4 pages main text), 4 figures, v2

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Cited by in corpus (26)

• Magic spreading in random quantum circuits
• Magic Resources of the Heisenberg Picture
• Clifford Dressed Time-Dependent Variational Principle
• Tensor networks for quantum computing
• Stabilizer disentangling of conformal field theories
• Doped stabilizer states in many-body physics and where to find them
• Stabilizer Tensor Networks with Magic State Injection
• Disentangling critical quantum spin chains with Clifford circuits
• Nonstabilizerness dynamics in many-body localized systems
• Bridging Entanglement and Magic Resources within Operator Space
• A nonstabilizerness monotone from stabilizerness asymmetry
• Simulation of Quantum Computers: Review and Acceleration Opportunities
• Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications
• Fermionic Magic Resources of Quantum Many-Body Systems
• Disentangling magic states with classically simulable quantum circuits
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Unveiling clean two-dimensional discrete time crystals on a digital quantum computer
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• Certifying nonstabilizerness in quantum processors
• Clifford-Dressed Variational Principles for Precise Loschmidt Echoes
• Analyzing the free states of one quantum resource theory as resource states of another
• Efficient simulation of logical magic state preparation protocols
• Limits of Clifford Disentangling in Tensor Network States
• A streamlined demonstration that stabilizer circuits simulation reduces to Boolean linear algebra
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• High-expressibility Quantum Neural Networks using only classical resources