Quantum simulations of a qubit of space
arXiv:2003.13124 · doi:10.1103/PhysRevD.103.046001
Abstract
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simulated on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers, giving satisfactory fidelities. The circuits provide building blocks for quantum simulations of complex spin networks in the future. Furthermore, a class of maximally entangled states of spin networks is introduced. As an example of application, attempts to determine transition amplitudes for a monopole and a dipole spin networks with the use of superconducting quantum processor are made.
arXiv comment17 pages. Matches the version published in PRD
References in corpus (40)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- The Large N Limit of Superconformal Field Theories and Supergravity
- Elementary gates for quantum computation
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- The World as a Hologram
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Background Independent Quantum Gravity: A Status Report
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Discreteness of area and volume in quantum gravity
- Quantum Geometry and Black Hole Entropy
- Entanglement Renormalization and Holography
- Real Ashtekar Variables for Lorentzian Signature Space-times
- Black hole entropy in Loop Quantum Gravity
- Loop Quantum Gravity
- Characterizing Quantum Gates via Randomized Benchmarking
- Renormalization and tensor product states in spin chains and lattices
- Local subsystems in gauge theory and gravity
- Quantum Gravity and Regge Calculus
- Quantum Gravity, Torsion, Parity Violation and all that
- Physical effects of the Immirzi parameter
- Classical and quantum communication without a shared reference frame
- Towards Spinfoam Cosmology
- Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
- Detailed black hole state counting in loop quantum gravity
- Quantum Black Holes: Entropy and Entanglement on the Horizon
- Stepping out of Homogeneity in Loop Quantum Cosmology
- Entanglement Entropy in Loop Quantum Gravity
- Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
- Gluing polyhedra with entanglement in loop quantum gravity
- Dynamics for a 2-vertex Quantum Gravity Model
- A Modular Sewing Kit for Entanglement Wedges
- Intertwiner Entanglement on Spin Networks
- Quantum Spacetime on a Quantum Simulator
- Ising Spin Network States for Loop Quantum Gravity: a Toy Model for Phase Transitions
- Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
- Efficient Simulation of Loop Quantum Gravity -- A Scalable Linear-Optical Approach
- Quantum Surface and Intertwiner Dynamics in Loop Quantum Gravity
- Entanglement entropy and correlations in loop quantum gravity
- Gauge fields and quantum entanglement
- Measuring Holographic Entanglement Entropy on a Quantum Simulator
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- Stabilizer entropy of quantum tetrahedra
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- All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks
- Curvature from multipartite entanglement in quantum gravity states
- Quantum speed limit and stability of coherent states in quantum gravity
- The Ponzano-Regge cylinder and Propagator for 3d quantum gravity
- Magic of discrete lattice gauge theories
- Observation of Two-Vertex Four-Dimensional Spin Foam Amplitudes with a 10-qubit Superconducting Quantum Processor