Quantum-classical simulation of quantum field theory by quantum circuit learning

We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing the Hamiltonian using Pauli spin matrices. To address this challenge, we leverage quantum circuit learning, employing a compact configuration of qubits and low-depth quantum circuits to predict real-time dynamics in quantum field theories. The key advantage of this approach is that a single-qubit measurement can accurately forecast various physical parameters, including fully-connected operators. To demonstrate the effectiveness of our method, we use it to predict quench dynamics, chiral dynamics and jet production in a 1+1-dimensional model of quantum electrodynamics. We find that our predictions closely align with the results of rigorous classical calculations, exhibiting a high degree of accuracy. This hybrid quantum-classical approach illustrates the feasibility of efficiently simulating large-scale QFTs on cutting-edge quantum devices

Quantum Extensive Form Games

We propose a concept of quantum extensive-form games, which is a quantum extension of classical extensive-form games. Extensive-form games is a general concept of games such as Go, Shogi, and chess, which have triggered the recent AI revolution, and is the basis for many important game theoretic models in economics. Quantum transitions allow for pairwise annihilation of paths in the quantum game tree, resulting in a probability distribution that is more likely to produce a particular outcome. This is similar in principle to the mechanism of speed-up by quantum computation represented by Grover's algorithm. A quantum extensive-form game is also a generalization of quantum learning, including Quantum Generative Adversarial Networks. Therefore it will become new theoretic basis of quantum machine learning, as well as a basis for a new game theoretic foundation for microeconomics. We propose the quantum angel problem as a new example of quantum extensive-form games. This is a quantum version of angel problem proposed by Conway in 1996. His original problem has already been solved, but by quantizing it, it becomes a non-trivial problem. In the quantum angel problem, Angel moves on a general graph as a quantum walker. By not only changing the dimensions and geometry of the graph, but also by adding/relaxing restrictions to the quantum resources available to Angel and Devil, the difficulty and complexity of the game is diversified in a way that is not possible in the traditional angel problem.Comment: 12 page

Long-range quantum energy teleportation and distribution on a hyperbolic quantum network

Teleporting energy to remote locations is new challenge for quantum information science and technology. Developing a method for transferring local energy in laboratory systems to remote locations will enable non-trivial energy flows in quantum networks. From the perspective of quantum information engineering, we propose a method for distributing local energy to a large number of remote nodes using hyperbolic geometry. Hyperbolic networks are suitable for energy allocation in large quantum networks since the number of nodes grows exponentially. To realise long-range quantum energy teleportation, we propose a hybrid method of quantum state telepotation and quantum energy teleportation. By transmitting local quantum information through quantum teleportation and performing conditional operations on that information, quantum energy teleportation can theoretically be realized independent of geographical distance. The method we present will provide new insights into new applications of future large-scale quantum networks and potential applications of quantum physics to information engineering

Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware

Teleporting physical quantities to remote locations is a remaining key challenge for quantum information science and technology. Quantum teleportation has enabled the transfer of quantum information, but teleportation of quantum physical quantities has not yet been realized. Here we report the realization and observation of quantum energy teleportation on real superconducting quantum hardware. We achieve this by using several IBM's superconducting quantum computers. The results are consistent with the exact solution of the theory and are improved by the mitigation of measurement error. Quantum energy teleportation requires only local operations and classical communication. Therefore our results provide a realistic benchmark that is fully achievable with current quantum computing and communication technologies.Comment: Code is available https://github.com/IKEDAKAZUKI/Quantum-Energy-Teleportatio

Topological Aspects of Matters and Langlands Program

In the framework of Langlands program, we offer a unified description of the integer and fractional quantum Hall effect as well as the fractal nature of energy spectra of 2d Bloch electrons. We categorify topological invariants on the Brillouin Zone and address the several dualities in a coherent manner where analogs of the classical Fourier transform provide an essential crux of the matter. Based on the Langlands philosophy, we elucidate the duality of topological computation and that of Ising models in the same context

Investigating global and topological order of states by local measurement and classical communication: Study on SPT phase diagrams by quantum energy teleportation

Distinguishing non-local orders, including global and topological orders of states through solely local measurements and classical communications (LOCC) is a highly non-trivial and challenging task since the topology of states is determined by the global characteristics of the many-body system, such as the system's symmetry and the topological space it is based on. Here we report that we reproduced the phase diagram of Ising model and symmetry protected topological (SPT) phases using the quantum energy teleportation protocol, which foresees non-trivial energy transfer between remote observers using the entanglement nature of the ground state and LOCC. The model we use includes the Haldane model, the AKLT model and the Kitaev model. Therefore our method paves a new general experimental framework to determine and quantify phase transitions in various condensed matter physics and statistical mechanics