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Predicting Noise in a Trapped-ion Quantum Simulator of a Lattice Gauge Theory

Hassan Ugail

Published Oct 5, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-11231107/v1

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Decoherence, Measurement and Quantum Computing in Ion Traps

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This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.

•Jan 1, 2000•0 citations
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.
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 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.
Aharonov–Bohm interference in a Z2{\pmb{\mathbb{Z}}}_{\bf{2}}Z2​ lattice gauge theory on a hybrid qubit–oscillator quantum computer
Abstract Lattice gauge theories, which have both dynamical matter and gauge fields, are strongly coupled problems that lie beyond the reach of classical computation. Quantum simulations may provide a tractable approach for studying lattice gauge theories, but implementing gauge-invariant encodings and real-time evolution remains experimentally challenging. Here we demonstrate a resource-efficient encoding of a Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 lattice gauge theory using a hybrid qubit–oscillator trapped-ion quantum device, with the qubits representing the gauge fields and the vibrational modes of the ions encoding the bosonic matter fields. We use synthetic dimensions to construct higher dimensional lattice geometries, and we combine digital and analogue techniques to prepare the initial states, realize the gauge-invariant real-time evolution and measure the relevant observables. After observing dynamics obeying Gauss’s law in a Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 link, we extend this approach to a loop geometry formed by two qubits and two oscillators. In this quasi-two-dimensional set-up, we observe Aharonov–Bohm interference with dynamical gauge fields encoding the magnetic flux, thereby demonstrating the interplay between charge and flux. Our results establish a path for scalable quantum simulations of lattice gauge theories in higher dimensions.
Abstract In the lattice system, when the synthetic flux reaches a π phase along a closed loop under the synthetic gauge field, destructive interference occurs and gives rise to the localization phenomenon. This is known as the Aharonov–Bohm (AB) caging effect. It provides a powerful tool for the study of quantum transport and dynamical effects. In the system where lattice sites possess internal structure and the underlying gauge field is non-Abelian, localization can also occur, forming the non-Abelian AB caging. Here, we propose an experimental scheme to synthesize non-Abelian gauge fields with a single trapped ion by coupling multiple internal levels and Fock states in its motion via laser fields. In contrast to the Abelian AB caging, we numerically observe that the non-Abelian AB caging occurs either when the interference matrix is nilpotent, or when the initial state is specifically set. Our experimental scheme broadens the study of localization phenomena and provides a novel tool for the study of non-Abelian physics.
We present a quantum simulation of the SU(2) lattice gauge theory in 1+1 dimensions with one flavor of fermions, performed using the trapped-ion Quantinuum System Model H2. This work is based on the loop-string-hadron (LSH) formulation of the gauge theory, and is distinguished by using qubits to represent both bosonic-gauge and fermionic-matter degrees of freedom. Furthermore, we access the j=1j=1j=1 electric-flux sector beyond the jmax⁡=1/2j_{\max}=1/2jmax​=1/2 truncation commonly used in SU(2) quantum simulations. To that end, we digitize an electric-field degree of freedom using a multiqubit register for representing the bosonic quantum number. Our simulation therefore synthesizes several key ingredients relevant to quantum simulations in higher spatial dimensions, in particular explicit local gauge-field degrees of freedom represented here by a multiqubit bosonic register, while relying solely on circuit-construction optimizations that are expected to scale polynomially with lattice size. This work demonstrates that modern quantum hardware is increasingly able to accommodate the features of complicated but physically important lattice gauge theories while successfully reproducing the expected Trotterized dynamics.
This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.