Abstract A recent trapped-ion experiment realised a lattice gauge theory with the gauge field in the internal states of the ions and bosonic matter in their vibrations. We showed earlier that its noise damage can be predicted. Here, we show that most of it can be undone. The conservation law of the theory is a parity of each vibrational mode, which heating flips, so a heating event leaves a mark that can be read without disturbing the physics. We keep only the runs in which this mark never changed. With equal heating rates and continuous monitoring, the kept runs reproduce the heating-free dynamics exactly, with a closed-form yield. Reading the mark at finite intervals introduces a small bias linear in the interval, which we derive and bound. At the reported rates, a single final check removes most of the heating and preparation damage while accepting eight runs out of ten.
Abstract A recent trapped-ion experiment realised a lattice gauge theory with the gauge field in the internal states of the ions and bosonic matter in their vibrations. We showed earlier that its noise damage can be predicted. Here, we show that most of it can be undone. The conservation law of the theory is a parity of each vibrational mode, which heating flips, so a heating event leaves a mark that can be read without disturbing the physics. We keep only the runs in which this mark never changed. With equal heating rates and continuous monitoring, the kept runs reproduce the heating-free dynamics exactly, with a closed-form yield. Reading the mark at finite intervals introduces a small bias linear in the interval, which we derive and bound. At the reported rates, a single final check removes most of the heating and preparation damage while accepting eight runs out of ten.
A recent trapped-ion experiment realised a lattice gauge theory in which the internal states of the ions carry the gauge field and their vibrations carry bosonic matter. In that experiment, a charge moving around a loop was frozen in place by Aharonov--Bohm interference. The noise of such a device is usually simulated after the measurements have been made. Here we show that it can be predicted before the machine is run. For each quantity that the experiment measures, we derive, from the reported noise rates alone, a formula for how it decays together with a bound it can never exceed. The results reveal a simple pattern. The local conservation law of the theory is a parity of the vibrational mode, so heating violates it at a rate that grows as the mode warms, and the violation accelerates rather than accumulating steadily. At zero electric field, each of the three noise processes of the device leaves its own fingerprint. Heating affects only the conservation law, motional dephasing only the interference, and qubit errors only the stored flux and the frozen state. Once the electric field is switched on, the frozen state begins to leak, and we write an exact formula and a guaranteed bound for that leak.
Abstract A recent trapped-ion experiment has realised a lattice gauge theory in which the internal states of the ions carry the gauge field and their vibrations carry bosonic matter. Tt observed a charge moving around a loop being frozen in place by Aharonov–Bohm interference. The noise of such a device is usually simulated after the fact. Here we show that it can be predicted in advance. For each quantity the experiment measures we derive, from the reported noise rates alone, a formula for how it decays and a bound that it can never exceed. Because the local conservation law of the theory is a parity of the vibrational mode, heating violates it at a rate that grows as the mode warms, so the violation accelerates rather than accumulating steadily. At zero electric field the three noise processes of the device leave three different fingerprints. Heating affects only the conservation law, motional dephasing affects only the interference, and qubit errors affect only the stored flux and the frozen state. Furthermore, with the field switched on, we provide an exact formula and a guaranteed bound for the escape from the frozen state.
Abstract: Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract:
Gauge theories form the foundation of the Standard Model of particle physics. These theories can exhibit confinement, where charged particles only occur in bound states, connected by flux strings whose energy grows linearly with separation. Simulating the real-time dynamics of such strings, including their breaking, remains a major challenge for classical computations and a promising target for quantum simulations. While recent quantum simulation experiments explored string-breaking dynamics in abelian lattice gauge theories, non-abelian theories are qualitatively distinct because gauge fields themselves carry charge. Here, we report the first quantum simulation of genuine non-abelian string-breaking dynamics in a pure SU(2) lattice gauge theory, where gauge-field self-interactions drive string breaking even in the absence of dynamical matter. Our results are obtained on a trapped-ion quantum computer, using native qudit Hilbert spaces to encode truncated gauge fields on a ladder geometry and implement digital Trotter dynamics. We experimentally study unbreakable and breakable strings generated by fundamental and adjoint static charges, respectively. We locally resolve string oscillations and coherent string breaking through the creation of gluonic excitations driven by non-abelian plaquette interactions. Our work establishes hardware-efficient, problem-tailored qudit simulations as a promising route for accessing non-perturbative dynamics relevant to high-energy physics.
Abstract Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract
Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales only polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle--antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.