Anyon Condensation Constructs Fixed-Point Tensor Networks for Mixed Quantum States

The quest to understand complex states of matter extends beyond traditional, pure quantum systems, and now includes intrinsically mixed states which exhibit unique properties not found in their pure counterparts. Bader Aldossari, Sergey Blinov, and Zhu-Xi Luo, all from the Georgia Institute of Technology, present a new method for representing these challenging mixed states using tensor networks, a powerful tool for modelling quantum systems. Their approach leverages the principles of anyon condensation within specifically constructed quantum states, offering a way to describe phases arising from both pure quantum systems and those affected by significant disorder or decoherence. This work expands the scope of tensor network representations, enabling the study of previously inaccessible phases of matter and providing insights into the behaviour of quantum systems in realistic, noisy environments.

Researchers present a general protocol to construct fixed-point tensor network representations for intrinsically mixed-state topological phases, which exhibit nontrivial topological phenomena and do not have pure-state counterparts. The method exploits the power of anyon condensation in Choi states and is applicable to cases where the target states arise from pure-state topological phases subject to strong decoherence or disorders in the Abelian sectors. This approach successfully models decoherence in several well-known topological phases, including the toric code and more complex systems, and extends to chiral topological order which cannot be described by conventional models.

Topological Phases, Tensor Networks, Quantum Computation References

This collection of references reflects the vibrant and rapidly evolving field of topological phases of matter and their applications to quantum computation. It’s a valuable resource for researchers and students interested in this exciting area of physics, highlighting the ongoing efforts to understand and harness the unique properties of these states of matter.

Tensor Networks Map Disordered Quantum States

Researchers have developed a powerful new method for representing and understanding intrinsically disordered quantum states, known as mixed states, using tensor networks. These networks provide an efficient way to describe complex systems that don’t conform to the simpler rules governing pure quantum states, opening doors to exploring phenomena not previously accessible through conventional methods. The approach leverages the concept of anyon condensation within a mathematical framework called Choi states, allowing researchers to represent the state’s properties in a computationally manageable way, even when dealing with substantial levels of noise or disruption.

Mixed-State Topological Phases via Tensor Networks

The significance of this work lies in extending the powerful tensor network approach to encompass mixed-state systems, which are more realistic representations of physical systems subject to noise and disorder. By providing a means to efficiently represent and study these states, the research opens avenues for understanding the stability of topological phases and exploring novel topological phenomena unique to mixed states. The authors acknowledge that the current method focuses on specific types of decoherence and does not address all possible noise models, suggesting future research could explore wider applications and three-dimensional renormalization group procedures.