Abstract
Quantum simulation promises to have wide applications in many fields where problems are hard to model with classical computers. Various quantum devices of different platforms have been built to tackle the problems in, say, quantum chemistry, condensed matter physics, and high-energy physics. Here, we report an experiment towards the simulation of quantum gravity by simulating the holographic entanglement entropy. On a six-qubit nuclear magnetic resonance quantum simulator, we demonstrate a key result of Anti-de Sitter/conformal field theory (AdS/CFT) correspondence—the Ryu-Takayanagi formula is demonstrated by measuring the relevant entanglement entropies on the perfect tensor state. The fidelity of our experimentally prepared the six-qubit state is 85.0% via full state tomography and reaches 93.7% if the signal-decay due to decoherence is taken into account. Our experiment serves as the basic module of simulating more complex tensor network states that exploring AdS/CFT correspondence. As the initial experimental attempt to study AdS/CFT via quantum information processing, our work opens up new avenues exploring quantum gravity phenomena on quantum simulators.
Highlights
The study of quantum systems requires an exponential amount of resources on conventional computers due to the exponentially growing dimensionality of Hilbert spaces, which makes it impossible to model even with supercomputers
We make first steps toward to the simulation of quantum gravity on a 6-qubit nuclear magnetic resonance (NMR) quantum processor, where rank-6 perfect tensor that forms the building block of complex tensor networks (TN) is realized with high accuracy
We demonstrate the emergent gravity program in Anti-de Sitter/conformal field theory (AdS/CFT) for the first time in a six-qubit NMR quantum corresponding to the dangling legs, and these boundary ones are simulator, by creating the rank-6 PT in Fig. 1c and measuring the physical qubits, indicating that |Ψ〉 is a state on the relevant entanglement entropies
Summary
The study of quantum systems requires an exponential amount of resources on conventional computers due to the exponentially growing dimensionality of Hilbert spaces, which makes it impossible to model even with supercomputers. There exists a significant field—quantum gravity—that has never been explored by experimental quantum simulation. Many important ideas such as holographic principle and Anti-de Sitter/conformal field theory (ADS/CFT) correspondence remained unrevealed in experiment. Recent development of a discrete version of AdS/CFT correspondence in terms of tensor networks (TN) motivates us to studying AdS/CFT correspondence on quantum simulators. We make first steps toward to the simulation of quantum gravity on a 6-qubit nuclear magnetic resonance (NMR) quantum processor, where rank-6 perfect tensor that forms the building block of complex TN is realized with high accuracy
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