Thesis
Expanding adiabatic horizons : computing counterdiabatic driving in new models
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2026
- Thesis identifier
- T17660
- Person Identifier (Local)
- 202157397
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- There any many technologies we use on a daily basis that make use of quantum mechanics, such as the electronic device this thesis is likely being read on, that have drastically shaped the way we live over the last hundred years. However, we have barely scratched the surface of potential applications, with many phenomena being secluded to laboratory experiments or sometimes still only theoretical. There are many steps on the path between explaining the underlying theory, and applying it to the everyday world. Even at the time of writing, some 350 years after Newton wrote down the laws of classical mechanics, engineers and physicists still find new applications of his theory. Whilst there are surely many more years of development ahead, we wish to highlight some of the most successful quantum applications up to the time of writing. Firstly there is the field of semiconductor physics, which has played a fundamental role in our advancement of electronics, allowing for smaller and more dense computing units [1–3]. Another quantum technology that has had numerous applications are lasers, which have been used for studying quantum optics [4, 5], applications in communication networks [6, 7], and even in medical procedures [8, 9]. Applications of quantum phenomena in measurement devices lead to the field of quantum sensing [10, 11], with resulting technologies such as atomic clocks [12, 13] and magnetometers [14, 15]. The field of quantum communication [16], has explored the use of quantum cryptography to protect our data [17, 18], and quantum entanglement to transfer information across large distances [19]. Currently, one of the most sought after technologies is that of quantum computers [20, 21], with the ability to overcome the exponential scaling of quantum problems, either universally with digital quantum computers [22, 23], or more specifically with analogue quantum computers [24, 25]. This lists a few of the key applications so far of quantum mechanics, but what steps need to be taken to further the number of quantum applications? Of course, there are many answers to this question, with many different interesting and useful areas of quantum physics, but we shall look at one step in particular, namely the control over a quantum system [26, 27]. In almost all experiments, some parameter will need to be varied, whether to prepare a state [28–30], or to look at out of equilibrium phenomena [31, 32]. However many losses occur into unwanted states during these processes, for example arising from coupling to a external environment [33, 34], or from diabatic excitations [35, 36]. To combat environmental coupling, protocols can be developed to avoid states with high loss such as with STIRAP [37–39], or feedback can be used to return the lost information [40, 41], alongside other methods [42–44]. However, even for a closed or near to closed system, diabatic excitations still need to be accounted for by designing a pulse to use the excitations productively [45, 46], adding an extra feedback step to address the populations of unwanted states [47, 48], or driving the pulse adiabatically to reduce the effect of the excitations [49–51]. Narrowing down the topic of this thesis again, we will look at adiabatic driving and how to increase driving speed whilst retaining the adiabatic following. This field of speeding up adiabatic pulse are known as shortcuts to adiabaticity [52, 53], and can range in application in many forms. Some example include using invariants and scaling [54, 55], or fast-forward techniques [56, 57]. We in particular are interested in counterdiabatic driving [58, 59], where an extra operator is added to the Hamiltonian to counteract any diabatic excitations. Counterdiabatic driving first appeared as an idea in quantum chemistry by Demirplak and Rice [60], but was also independently formulated under the name ‘transitionless driving’ at the same time by Berry [61]. The operator that provides the counterdiabatic driving is referred to as the Adiabatic Gauge Potential (AGP) [36, 58]. The AGP can provide significant insights into the dynamics of a Hamiltonian [36], which is still an ongoing area of research, with current examples including the strength of diabatic losses [62], or a measure for quantum chaos [63–65]. As such the AGP is a very valuable operator to compute, however it is often not straightforward to do so, as its dimension is near the size of the full Hilbert space for most non trivial cases. In addition, whilst in principle it is always possible to apply a counterdiabatic drive, in practise the AGP can be difficult to implement [59]. This has led to approximate forms being developed, for example using only local operators [58], generating relevant operators form nested commutators [66], or Krylov methods [67, 68]. Whilst these methods do not have the ability to perfectly remain in a given eigenstate of a Hamiltonian, they can still greatly improve adiabatic procedures [69], or be used in conjugation with other control methods to help simplify the optimisation procedure [70, 71]. A large focus in AGP research has been targeted towards quantum information [62, 71–73], as improving quantum gate fidelity allows more accurate results, and shortening pulse sequence prevents losses in current quantum hardware from decoherence [74–76]. This has been one reason why the majority of AGP research has been focused on spin-1/2 models, such that qubits in quantum computers can be addressed. However there any many models beyond spin-1/2 that are of interest to physicists, with some implementations of quantum information using larger spins such as with qutrits [77, 78], or including the environment in the equations for a true open systems description [34, 79]. As such to be able to describe other quantum systems such as bosonic or fermionic physics, it is important to expand the current scope of AGP physics beyond spin-1/2 models, developing methods that work across many different types of systems. This is a key theme of this thesis, expanding the current scope of physical models the AGP has been applied to, and providing methodology within these new bases. [See thesis text for bibliographical references]
- Advisor / supervisor
- Kirton, Peter
- Daley, Andrew
- Resource Type
- DOI
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