Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power

Abstract

We present a new framework for assessing the power of measurement-based quantum computation (MBQC) on short-range entangled symmetric resource states, in spatial dimension one. It requires fewer assumptions than previously known. The formalism can handle finitely extended systems (as opposed to the thermodynamic limit), and does not require translation-invariance. Further, we strengthen the connection between MBQC computational power and string order. Namely, we establish that whenever a suitable set of string order parameters is non-zero, a corresponding set of unitary gates can be realized with fidelity arbitrarily close to unity.

48 pages

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• Counter-intuitive yet efficient regimes for measurement based quantum computation on symmetry protected spin chains
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Scaling of Computational Order Parameters in Rydberg Atom Graph States
• Sub-Riemannian geometry of measurement based quantum computation
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications