This is the first companion paper to the Relative Field Localization (RFL) framework (RFL v8.0). It presents a thermal analysis of the RFL localization mechanism, applied to the four principal qubit platforms used in contemporary quantum computing: superconducting, trapped ion, NV center, and photonic. In RFL, the quantum state corresponds to an extended charge distribution, and the classical state to a localized Q-ball. Localization is triggered by any physical interaction with the environment. Thermal photons provide a continuous stream of such interactions. The central result is the thermal localization rate: Γ_loc(T) = Γ_loc^vac [1 + n(ω_C, T)] where n(ω_C, T) is the Bose-Einstein occupation number at the Q-ball frequency ω_C. The condition for coherent quantum computation is k_B T ≪ ħ ω_C. A confinement factor η_conf ≪ 1 is introduced to account for the geometric and material suppression of the environmental coupling. This factor explains why some qubit platforms can operate at much higher temperatures than the naive criterion would suggest — for instance, why NV centers retain coherence at room temperature, while superconducting qubits require millikelvin temperatures. The analysis covers the characteristic Q-ball frequency, the Bose-Einstein distribution, the two limiting regimes of deep cooling and high temperature, the cooling criterion, and the application to the four qubit platforms. A physical interpretation of the confinement factor and its origin is also provided. This paper is the first in a series of three companion papers. The other two are:• RFL Applications II: Double-Slit Interference• RFL Applications III: Compton Scattering and the Measurement Mechanism
This is the first companion paper to the Relative Field Localization (RFL) framework (RFL v8.0). It presents a thermal analysis of the RFL localization mechanism, applied to the four principal qubit platforms used in contemporary quantum computing: superconducting, trapped ion, NV center, and photonic. In RFL, the quantum state corresponds to an extended charge distribution, and the classical state to a localized Q-ball. Localization is triggered by any physical interaction with the environment. Thermal photons provide a continuous stream of such interactions. The central result is the thermal localization rate: Γ_loc(T) = Γ_loc^vac [1 + n(ω_C, T)] where n(ω_C, T) is the Bose-Einstein occupation number at the Q-ball frequency ω_C. The condition for coherent quantum computation is k_B T ≪ ħ ω_C. A confinement factor η_conf ≪ 1 is introduced to account for the geometric and material suppression of the environmental coupling. This factor explains why some qubit platforms can operate at much higher temperatures than the naive criterion would suggest — for instance, why NV centers retain coherence at room temperature, while superconducting qubits require millikelvin temperatures. The analysis covers the characteristic Q-ball frequency, the Bose-Einstein distribution, the two limiting regimes of deep cooling and high temperature, the cooling criterion, and the application to the four qubit platforms. A physical interpretation of the confinement factor and its origin is also provided. This paper is the first in a series of three companion papers. The other two are:• RFL Applications II: Double-Slit Interference• RFL Applications III: Compton Scattering and the Measurement Mechanism
Quantum thermometry plays a critical role in the development of low-temperature sensors and quantum information platforms. In this work, we propose and theoretically analyze a hybrid circuit quantum electrodynamics architecture in which a superconducting qubit is dispersively coupled to two distinct bosonic modes: one initialized in a weak coherent state and the other coupled to a thermal environment. We show that the qubit serves as a sensitive readout of the probe mode, mapping the interference between thermal and coherent photon-number fluctuations onto measurable dephasing. This mechanism enables enhanced sensitivity to sub-millikelvin thermal energy fluctuations through Ramsey interferometry. We derive analytic expressions for the qubit coherence envelope, compute the quantum Fisher information for temperature estimation, and demonstrate numerically that the presence of a coherent reference amplifies the qubit's sensitivity to small changes in thermal photon occupancy. Our results establish a new paradigm for quantum-enhanced thermometry and provide a scalable platform for future calorimetric sensing in high-energy physics and quantum metrology.
Trapped-ion qubits are one approach among many for achieving scalable quantum computers. An ion trap has to be operated with several dc and radio frequency (rf) signals to trap and control its qubits. Many ion trap setups are operated at cryogenic temperatures to reduce thermal influences, to reach very high vacuum, and to achieve high fidelity for quantum operations. A resonance circuit, consisting of a coil and the capacitance of the trap electrodes, is used to step-up a low power rf signal to high amplitudes in close proximity to the ion trap. These ac fields are used to confine ions70μmabove a surface ion trap chip. An increased quality factor (Q-factor) of the resonance circuit leads to a higher voltage gain, but the experiment also benefits from a better attenuation of parasitic frequency components in the confining electric field. The Q-factor is inversely proportional to the trap capacitance. Since ion traps are growing in size due to a larger number of qubits, the capacitance is increasing. Therefore, the development of a coil with low losses becomes even more important. In this work, we present the setup of a superconducting coil for a high-Q resonator, measurements of the Q-factor, and its temperature dependency. The coil is made of a niobium-titanium (NbTi) wire wound on a threaded bobbin made of ceramics and equipped with further thermalization structures. The superconducting resonator is a very promising approach to satisfy the needs for future trapped-ion quantum computing setups.
Radio frequency (RF) radiation is a powerful tool in computing, communication, and sensing due to the ability to engineer strong electrical interactions. Within cryogenic systems, in particular, microwave (MW) frequency superconducting qubits have demonstrated promise as a platform for quantum computing, and MW and millimeter-wave (mmW) systems have been valuable tools in sensing. However, owing to their low energy, the weak, single-photon level signals employed by these systems suffer high sensitivity to thermal noise when they exit the thermal bath, as well as short attenuation lengths due to absorption and scattering in cables. Telecommunication frequency optical photons, meanwhile, have long propagation lengths and can be supported by low-loss optical fibers. The high photon energy makes signals insensitive to thermal noise, and the high frequency can allow many RF signals to be multiplexed onto a single optical carrier. Interfacing RF and optical radiation to leverage both strong interactions with macroscopic systems characteristic of electrical interactions and low-loss propagation characteristic of optical photons has been critical to realizing our global communication system. Leveraging the infrastructure developed to support this industry, such as single photon detectors, is attractive for scaling cryogenic RF systems. Coherent conversion processes, especially, can benefit a wide range of applications, especially in computing and sensing, by preserving quantum states, and retaining phase information necessary for quantum gates, and enable the use of measurement techniques that can increase detection sensitivity. This dissertation focuses on using the electro-optic effect in thin-film lithium niobate to form an efficient, coherent interface between radio- and telecommunication-frequency photons. Lithium niobate is an attractive platform due to its high electro-optic coefficient (approx. 30 pm/V), wide transparency window (DC to 400 THz), and ability to support low-loss optical waveguides (.2 dB/m), all of which deviate little from room temperature down to near-zero Kelvin environments. First, I explore the development of low-loss lithium niobate optical cavities and operation of lithium niobate waveguides at low temperatures. While lithium niobate is an electro-optic material with a DC response, using the electro-optic response at room temperature for stable biasing and low-frequency operation has remained a challenge. A temperature- and frequency-dependent study is conducted to identify lithium charge migration as a potential screening mechanism suppressed at low temperatures. Next, I explore the use of RF-cavity enhanced, triply resonant photonic molecules (created from two coupled low-loss optical cavities) for forming efficient electro-optic interfaces with microwave (3-10 GHz) and millimeter wave (100 GHz) radiation. In the microwave regime, I explore microwave-optical transduction for forming optical interfaces with microwave qubits, specifically focusing on superconducting qubits. The characterization of one such transducer is demonstrated, and the device is used to optically synthesize microwave signals at low temperatures, bypassing the need for input microwave control lines. Outlook for other interfaces, including optical photon mediated quantum information transfer, is discussed. At mmW frequencies, the triply resonant photonic molecule is explored for low-power ( mW) optical-frequency shifting.
When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize despite strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium with respect to the Hamiltonian. Using experimental and numerical methods we observe the essential signatures of MBL: initial state memory retention, Poissonian distributed many-body energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where detailed modeling of MBL becomes impossible.
This is the third companion paper to the Relative Field Localization (RFL) framework (RFL v8.0). It presents a physical account of Compton scattering in which the photon is absorbed by the extended charge distribution, the electron gains the photon energy, the charge localizes into a Q-ball at the peak of j^0, and a new photon is re-emitted from the peak. This mechanism provides a direct physical explanation for:• Why the scattered photon loses energy• Why it emerges from a definite spatial location• How energy loss is tied to the localization process The account proceeds in four stages:1. Absorption: The incoming photon is fully absorbed by the extended charge.2. Excitation: The electron gains the photon energy (ΔE_e = E_γ).3. Localization: The gained energy drives the charge to localize into a Q-ball at the peak x_α.4. Re-emission: A new photon is emitted from the peak, carrying the remaining energy E_γ'. Energy conservation is exact:E_γ = E_γ' + E_Q-ball + E_kin In the simplest case, the energy loss is set by the characteristic Q-ball scale:ΔE_γ ~ ħ ω_C The treatment follows the RFL localization law τ_loc = S_RL · L³ · m² and is consistent with the standard Compton result in the appropriate limit. The finite time delay between absorption and re-emission is of order τ_loc. This paper is the third in a series of three companion papers. The other two are:• RFL Applications I: Thermal Effects in Quantum Computing• RFL Applications II: Double-Slit Interference
The rate at which external random thermal fluctuations drive transitions between, and cause decoherence of, the near ground vibrational (harmonic oscillator) quantum states of trapped cold ions is of crucial importance in relation to quantum computing. Presented here is an estimate of these rates, for a single trapped ion, based on a quantum perturbation approach where an external thermal energy reservoir is electrically coupled to the ion. The results are for a general system, and it is shown that the relevant parameter in the interpretation of experimentally observed heating rates is the correlation time of the fluctuations. The rates due to the fluctuating electric field associated with blackbody radiation are also considered and shown to be negligible.