Computational Power and Correlation in Quantum Computational Tensor Network

Abstract

We investigate relations between computational power and correlation in resource states for quantum computational tensor network, which is a general framework for measurement-based quantum computation. We find that if the size of resource states is finite, not all resource states allow correct projective measurements in the correlation space, which is related to non-vanishing two-point correlations in the resource states. On the other hand, for infinite-size resource states, we can always implement correct projective measurements if the resource state can simulate arbitrary single-qubit rotations, since such a resource state exhibits exponentially-decaying two-point correlations. This implies that a many-body state whose two-point correlation cannot be upperbounded by an exponentially-decaying function cannot simulate arbitrary single-qubit rotations.

10 pages, 1 figure; v2: Revised version; v3 General proof is added; v4 minor changes; v5 published version

References in corpus (13)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Fault-tolerant quantum computation with high threshold in two dimensions
• Resource-efficient linear optical quantum computation
• Topological fault-tolerance in cluster state quantum computation
• Valence Bond Solids for Quantum Computation
• Novel schemes for measurement-based quantum computation
• Universal resources for measurement-based quantum computation
• Measurement-based quantum computation beyond the one-way model
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates
• Graph states as ground states of many-body spin-1/2 Hamiltonians
• Quantum computation in correlation space and extremal entanglement
• Topologically protected measurement-based quantum computation on the thermal state of a nearest-neighbor two-body Hamiltonian with spin-3/2 particles

Cited by in corpus (7)

• Blind quantum computation protocol in which Alice only makes measurements
• Lecture Notes of Tensor Network Contractions
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Ancilla-Driven Universal Blind Quantum Computation
• Graph states as ground states of two-body frustration-free Hamiltonians
• Functional Tensor Network Solving Many-body Schrödinger Equation
• Quantum computational tensor network on string-net condensate