The current approach to building quantum computers relies on a strategy of brute force intervention. Engineers attempt to force fragile quantum states to survive by constantly correcting their errors with external machinery. This method treats the quantum bit, or qubit, as an inherently unstable object that must be propped up. It assumes that if we simply build faster control loops, we can outrun the natural decay of the system. However, this perspective ignores the fundamental cost of fighting nature. Every time we correct an error, we are fighting against the natural tendency of the universe to increase disorder. This fight requires energy, and that energy must go somewhere. The reliance on active error correction creates a vicious cycle of energy consumption. As we add more qubits to the system, the number of errors increases. To fix these errors, we need more control hardware and more processing power. This additional hardware generates heat, which disturbs the sensitive quantum states even more. The more we try to fix the system, the more we disturb it. It is like trying to calm a pool of water by slapping the waves flat. The very act of intervention creates new ripples that require further correction. This scaling problem is not just a matter of engineering difficulty; it is a matter of physics. There is a limit to how fast and how efficiently we can extract entropy, or disorder, from a system. Current architectures are approaching this limit rapidly. We are building systems that require massive cooling infrastructure just to keep the control electronics from melting the qubits. This is not a sustainable path to a useful computer. We need a fundamentally different approach. The brute force method also introduces a complexity bottleneck. The software required to track and correct errors in real-time is becoming impossibly complex. We are trying to simulate a perfect machine using imperfect parts, and the overhead is crushing. The ratio of physical qubits needed to build one logical qubit is skyrocketing. We are spending all our resources on error correction, leaving little for actual computation. This is the definition of a diminishing return. We must recognize that the “active” paradigm is a trap. It lures us in with the promise of total control, but it hides the thermodynamic bill. That bill is coming due, and it is higher than we can pay. We cannot simply scale our way out of this problem with more power. We need to stop fighting the environment and start designing systems that are naturally stable. We need to move from active correction to passive protection.
The current approach to building quantum computers relies on a strategy of brute force intervention. Engineers attempt to force fragile quantum states to survive by constantly correcting their errors with external machinery. This method treats the quantum bit, or qubit, as an inherently unstable object that must be propped up. It assumes that if we simply build faster control loops, we can outrun the natural decay of the system. However, this perspective ignores the fundamental cost of fighting nature. Every time we correct an error, we are fighting against the natural tendency of the universe to increase disorder. This fight requires energy, and that energy must go somewhere. The reliance on active error correction creates a vicious cycle of energy consumption. As we add more qubits to the system, the number of errors increases. To fix these errors, we need more control hardware and more processing power. This additional hardware generates heat, which disturbs the sensitive quantum states even more. The more we try to fix the system, the more we disturb it. It is like trying to calm a pool of water by slapping the waves flat. The very act of intervention creates new ripples that require further correction. This scaling problem is not just a matter of engineering difficulty; it is a matter of physics. There is a limit to how fast and how efficiently we can extract entropy, or disorder, from a system. Current architectures are approaching this limit rapidly. We are building systems that require massive cooling infrastructure just to keep the control electronics from melting the qubits. This is not a sustainable path to a useful computer. We need a fundamentally different approach. The brute force method also introduces a complexity bottleneck. The software required to track and correct errors in real-time is becoming impossibly complex. We are trying to simulate a perfect machine using imperfect parts, and the overhead is crushing. The ratio of physical qubits needed to build one logical qubit is skyrocketing. We are spending all our resources on error correction, leaving little for actual computation. This is the definition of a diminishing return. We must recognize that the “active” paradigm is a trap. It lures us in with the promise of total control, but it hides the thermodynamic bill. That bill is coming due, and it is higher than we can pay. We cannot simply scale our way out of this problem with more power. We need to stop fighting the environment and start designing systems that are naturally stable. We need to move from active correction to passive protection.
The persistent challenges in scaling conventional quantum computers suggest a potential misalignment in foundational assumptions. Assuming that physical reality is continuous at the lowest quantum levels forces engineers to fight against natural thermodynamic tendencies. The continuous error model demands an active correction paradigm that may be fundamentally unsustainable for large-scale computation. Alternative mathematical frameworks offer different geometric properties that could naturally suppress error accumulation. Exploring non-Archimedean geometries provides a pathway to bypass the limitations inherent in continuous state spaces. These alternative structures possess discrete topological features that fundamentally alter how errors propagate through a system. Shifting the mathematical foundation could resolve the scaling bottlenecks currently hindering quantum technology development.
Quantum computation is not an imminent achievement . We will not wake up tomorrow and find quantum computers on our desks. At the time of this writing, IBM has just unveiled the Condor – a chip containing 1,121 superconducting qubits. This number will likely increase (perhaps spectacularly) in the near future. However, the qubits have a relatively large error rate and, in the absence of a breakthrough advance that significantly lowers this rate, one would need hundreds of physical qubits to realize an error-corrected logical qubit. Predicting how long it will take to achieve the controlled manipulation of thousands of (logical) qubits (i.e., a number of qubits consistent with the “useful” implementation of known quantum algorithms) is probably not a rational undertaking, at least for a scientist. The most pessimistic experts regard the lively research activity in quantum computation as a waste of time and resources. But the pervading mood in this field is one of cautious optimism, particularly considering the possibility of achieving useful tasks (e.g., simulating quantum systems) with a sufficiently large number of “imperfect” qubits. Expediency may be responsible for some of this optimism; a good feeling about the prospects for quantum computation certainly helps when it comes to publishing papers and getting funded. Ultimately, however, the responsibility for the wise distribution of resources rests with the funding agencies; scientists, on the other hand, are called to explore every aspect of real and possible worlds that looks fascinating and worthy of their curiosity. From this perspective, quantum computation (defined broadly) offers plenty of opportunities for producing “good science.” The problems brought to the fore by the development of this field range from basic questions regarding the foundations of quantum mechanics and unsolved problems in computational complexity, to the investigation of new phases of matter (e.g., topological quantum phases), the quest for “complete” control over quantum systems, and the critical need for significant advances in materials science and device fabrication (e.g., engineering nanoscale heterostructures with atomic precision). Progress in these areas will naturally open new possibilities for interesting applications. Precisely identifying these applications is premature, but building a (general purpose) quantum computer will not necessarily be among the first of them.
Quantum computers have gained widespread interest as they can potentially solve problems that are intractable even for today’s supercomputers, such as the simulation of quantum systems as initially proposed by Feynman. To achieve such tremendous progress, a quantum computer relies on processing the information stored in quantum bits (qubits), the fundamental units of quantum computation, similar to the bits in a classical (i.e., non-quantum) processor. In general, a quantum processor comprising several qubits is connected through a quantum-to-classical interface consisting of classical electrical circuits for manipulating and reading out their quantum state. The accuracy of an operation on a qubit is characterized using the fidelity, which is 100 % in case of a perfect operation. In practice, a fidelity between 99 % and 99.9 % is typically achieved in today’s experiments with less than 100 qubits, limited by non-idealities in the control signals and by the implementation of the physical qubit itself. Since such qubit fidelities are too low to execute relevant quantum algorithms, quantum error correction schemes have been developed which rely on a much larger number of qubits to correct for possible errors, resulting in the need for quantum processors with thousands or millions of qubits. Solid-state qubits promise the largescale integration required to scale to millions of qubits, as they exploit the lithographic fabrication techniques borrowed from the semiconductor industry. However, state-of-theart solid-state qubits, such as transmons and single-electron spin qubits, must be typically cooled to cryogenic temperatures in a dilution refrigerator to exhibit quantum behavior. Because of the limited number of qubits (< 100) in state-of-theart solid-state quantum processors, the classical controller is currently implemented by general-purpose instruments or by tailor-made controllers operating at room temperature connected via several wires to the qubits in the cryogenic chamber. However, these systems must scale to support millions of qubits. While scaling up the underlying quantum processor is already exceptionally challenging, building the electronics required to interface such a large-scale processor is just as relevant and arduous.
The development of quantum computing systems has been a staple of academic research since the mid-1990s when the first proposal for physical platforms were proposed using Nuclear Magnetic Resonance and Ion-Trap hardware. These first proposals were very basic, essentially consisting of identifying a physical qubit (two-level quantum system) that could be isolated and controlled to achieve universal quantum computation. Over the past thirty years, the nature of quantum architecture design has changed significantly and the scale of investment, groups and companies involved in building quantum computers has increased exponentially. Architectural design for quantum computers examines systems at scale: fully error-corrected machines, potentially consisting of millions if not billions of physical qubits. These designs increasingly act as blueprints for academic groups and companies and are becoming increasingly more detailed, taking into account both the nature and operation of the physical qubits themselves and also peripheral environmental and control infrastructure that is required for each physical system. In this paper, several architectural structures that I have worked on will be reviewed, each of which has been adopted by either a national quantum computing program or a quantum startup.
[Background] Quantum processors offer a new paradigm for computing which can more accurately model –simulate– the intrinsic quantum nature of microscopic phenomena, can more efficiently compute algorithms with a quantum formulation versus that of their classical formulation, and has been shown to have a higher energy efficiency than classical processors when solving the same problem. Yet, the practical physical implementation of quantum processors is inherently transient, stochastic, and prone to perturbations, which makes the best-performing quantum processor to date to sink in errors before it can get past the 25th circuit gate layer of computation with its 25 quantum bits. A quantum processor promises us benefits, but only if built within a utility-scale size, currently estimated to be of about O(10^6) quantum bits x O(10^9) gate layers, and if we manage to overcome its errors by engineering it fault-tolerantly. After about 30 years in the pursuit of building this machine, we are several orders of magnitude away from usefulness. The challenge is such that this machine potentially boils down to be the largest-scale and most-challenging engineering project that human kind pursues to build during the 21st century. Accordingly, this challenge must be approached with a pragmatic engineering mindset. [Objective] Therefore, this work takes an engineering approach to define a system-level control paradigm for quantum processors, which enables scalability, reliability, usefulness, efficiency, sustainability, and resilience, within the case study of trapped ions. [Methods] In this work, I apply engineering methods, namely, systems and control engineering for the development of a machine. The first step is to clearly understand and describe the problem and what is at stake along the expectations of a current worldwide quantum investment in the US$ O(10^9). To that end, I examine existing prior art through a systematic literature review and conduct numerous interviews of European physicists in order to comprehend the status quo of quantum computing. Second, I use a top-down system-level methodology for the conception of the control system of quantum processors. Finally, I realize a proof of concept for one constituent machine compliant to the system-level proposal. [Results] In light of examining the status quo strategy for quantum computing, I must challenge it and advocate to redirect our efforts towards building this machine as a closed-loop locked-algorithm control system in order to ultimately enable its resilience. First, I propose the top-level ASQP machine and the DiQuNET architecture as novel paradigm for the control of quantum processors. Second, I develop a proof of concept of the first DiQuIC: the ITIC, which is a constituent machine of the DiQuNET system that implements a particular functional task in a trapped-ion quantum processor. [Conclusion] The ASQP is a novel system-level use-case proposal for a quantum processor. The DiQuNET paradigm is a novel system-level proposal for the physical control implementation of the quantum Turing machine. Overall, the control paradigm endows a quantum processor with scalability, reliability, usefulness, sustainability, efficiency, and resilience features. It is a proposal that opens the door to the standardization, the industrial realization, and the human-resources distributed and collaborative development of the control system of quantum processors. Cite this thesis as: S. Castillo, “The DiQuNET Paradigm for the Control of Quantum Processors: The case for Trapped Ions,” Doctoral Thesis, University of Innsbruck, Dept. Mechatron., Innsbruck, Austria, 2026. doi: https://doi.org/10.5281/zenodo.23236620 Thesis information: Grade: 1 (excellent)ISCED-11 Level 8 * Advisors: Prof. T. Northup (UIBK, AT) and Prof. E. Charbon (EPFL, CH)* Evaluator: Prof. R. van Meter (Keio Uni, JP & Editor-in-Chief of IEEE TQE)* Tech-transfer Mentor: Jamie Urquhart (Founder of ARM. Ltd., UK) Revision history: 2026-03-27: First release v1.02026-09-29: Release v2.0: updated intro, chap. 1, and biography.
Quantum computing exists at the intersection of mathematics, physics, chemistry, and engineering; the main goal of quantum computing is the creation of devices and algorithms which use the properties of quantum mechanics to store, manipulate and measure information. There exist many families of algorithms, which, using non-classical logical operations, can outperform traditional, classical algorithms in terms of memory and processing requirements. In addition, quantum computing devices are fundamentally smaller than classical processors and memory elements; since the physical models governing their performance are applicable on all scales, as opposed to classical logic elements, whose underlying principles rely on the macroscopic nature of the device in question. \n \nQuantum algorithms, for the most part, are predicated on a theory of resources. It is often assumed that quantum computers can be placed in a precise fiducial state prior to computation, and that logical operations are perfect, inducing no error on the system which they affect. These assumptions greatly simplify algorithmic design, but are fundamentally unrealistic. In order to justify their use, it is necessary to develop a framework for using a large number of imperfect devices to simulate the action of a perfect device, with some acceptable probability of failure. This is the study of fault-tolerant quantum computing. In order to pursue this study effectively, it is necessary to understand the fundamental nature of generic quantum states and operations, as well as the means by which one can correct quantum errors. Additionally, it is important to attempt to minimize the use of computational resources in achieving error reduction and fault-tolerant computing. \n \nThis thesis is concerned with three projects related to the use of error-prone quantum systems to transmit and manipulate information. The first of these is concerned with the use of imperfectly-prepared states in error-correction routines. Using optimal quantum error correction, we are able to deduce a method of partially protecting encoded quantum information against preparation errors prior to encoding, using no additional qubits. The second of these projects details the search for entangled states which can be used to transmit classical information over quantum channels at a rate superior to classical states. The third of these projects concerns the transcoding of data from one quantum code into another using few ancillary resources. The descriptions of these projects are preceded by a brief introduction to representations of quantum states and channels, for completeness. \n \nThree techniques of general interest are presented in appendices. The first is an introduction to, and a minor advance in the development of optimal error correction codes. The second is a more efficient means of calculating the action of a quantum channel on a given state, given that the channel acts non-trivially only on a subsystem, rather than the entire system. Finally, we include documentation on a software package developed to aid the search for quantum transcoding operations.