Quantum Circuits Assisted by Local Operations and Classical Communication: Transformations and Phases of Matter

2021/03/31 by Lorenzo Piroli, Georgios Styliaris, J. Ignacio Cirac · 3 citations
Computer Science · Physics and Astronomy · #Electronic circuit #Quantum #Quantum Computing Algorithms and Architecture #Quantum algorithm #Quantum circuit #Quantum many-body systems #Quantum network #Quantum state #Set (abstract data type) #Topological Materials and Phenomena #Topology (electrical circuits) #Unitary state #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.127.220503

published as Phys. Rev. Lett. 127, 220503 (2021) · 6+5 pages, no figures; v4: minor revision, references added

arxiv created 2021/11/11 · openalex publication_date 2021/11/23 · arxiv updated 2021/11/24 · openalex created_date 2021/12/06 · openalex updated_date 2026/08/06

Abstract

We introduce deterministic state-transformation protocols between many-body quantum states that can be implemented by low-depth quantum circuits followed by local operations and classical communication. We show that this gives rise to a classification of phases in which topologically ordered states or other paradigmatic entangled states become trivial. We also investigate how the set of unitary operations is enhanced by local operations and classical communication in this scenario, allowing one to perform certain large-depth quantum circuits in terms of low-depth ones.

Citations

• Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
• Classifying quantum phases with the Kirby torus trick
• Classification of topological quantum matter with symmetries
• Colloquium: Area laws for the entanglement entropy
• Theory of fault-tolerant quantum computation
• Three qubits can be entangled in two inequivalent ways
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
• Unitarity plus causality implies localizability
• Valence-bond states for quantum computation
• Simulating adiabatic evolution of gapped spin systems
• Fault-tolerant quantum computation by anyons
• Quantum computing, postselection, and probabilistic polynomial-time
• Quantum Computing in the NISQ era and beyond
• Dynamical Purification Phase Transition Induced by Quantum Measurements
• Quantum entanglement

Cited by

• Demonstrating advantages of dynamic quantum circuits on a hybrid superconducting qubit-cavity processor
• Anomalous matrix product operator symmetries and 1D mixed-state phases
• Layered KIK quantum error mitigation for dynamic circuits and error correction