Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
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abstract
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories.
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Digital quantum simulations of string dynamics in a (2+1)D U(1) quantum link model on IBM hardware with up to 112 qubits agree with tensor networks at short times and thermal averages at long times.
For diagonal quadratic evolutions, qubit encodings are asymptotically cheaper than qudit encodings in both Trotter and LCU settings, but small-dimension qudits can win under favorable synthesis or code-switching assumptions.
A quantum simulation framework is developed and demonstrated for energy loss and hadronization of a heavy quark in 1+1D SU(2) lattice gauge theory on 18 qubits of IBM hardware, with results matching classical simulations.
Collider scattering processes such as electron-positron annihilation to muon pairs can be represented as quantum circuits with unitary and non-unitary components.
A minimal implementation of SU(N) pure Yang-Mills theory on digital quantum computers is presented with simplified Hamiltonians, improved infinite-mass convergence, and SU(2) embedding into R^4, benchmarked by Monte Carlo simulations.
The talk summarizes the quantum simulation program for lattice gauge theories, covering target problems in dense matter, algorithmic strategies, recent progress, and remaining challenges.
citing papers explorer
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Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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String dynamics of a (2+1)D U(1) quantum link model on a digital quantum computer
Digital quantum simulations of string dynamics in a (2+1)D U(1) quantum link model on IBM hardware with up to 112 qubits agree with tensor networks at short times and thermal averages at long times.
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
For diagonal quadratic evolutions, qubit encodings are asymptotically cheaper than qudit encodings in both Trotter and LCU settings, but small-dimension qudits can win under favorable synthesis or code-switching assumptions.
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A Framework for Quantum Simulations of Energy-Loss and Hadronization in Non-Abelian Gauge Theories: SU(2) Lattice Gauge Theory in 1+1D
A quantum simulation framework is developed and demonstrated for energy loss and hadronization of a heavy quark in 1+1D SU(2) lattice gauge theory on 18 qubits of IBM hardware, with results matching classical simulations.
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A collider as a quantum computer
Collider scattering processes such as electron-positron annihilation to muon pairs can be represented as quantum circuits with unitary and non-unitary components.
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A minimal implementation of Yang-Mills theory on a digital quantum computer
A minimal implementation of SU(N) pure Yang-Mills theory on digital quantum computers is presented with simplified Hamiltonians, improved infinite-mass convergence, and SU(2) embedding into R^4, benchmarked by Monte Carlo simulations.
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Quantum Simulation of Gauge Theories for Particle and Nuclear Physics
The talk summarizes the quantum simulation program for lattice gauge theories, covering target problems in dense matter, algorithmic strategies, recent progress, and remaining challenges.