After years of effort by quantum scientists, decoherence due to thermal effects still remains a huge hindrance to the upscaling of quantum computers. This thesis presents the temperature scaling of decoherence in a trapped-ion qubit. Microscopic quantum noise simulations are carried out. The resulting numerical scaling laws of coherence times, T1 and T2, are presented. The results enable experimentalists to determine, as a function of temperature, an upper bound for the time over which a quantum computer can be operated without a disastrous loss of quantum coherence, and the duration over which a memory qubit retains its information. Given the tradeoff between the enormous resource overhead demanded by quantum error correction protocols and the adverse effects of decoherence, the results provide guidance for the implementation and optimization of practical error suppression methods in the current era of quantum computers.
After years of effort by quantum scientists, decoherence due to thermal effects still remains a huge hindrance to the upscaling of quantum computers. This thesis presents the temperature scaling of decoherence in a trapped-ion qubit. Microscopic quantum noise simulations are carried out. The resulting numerical scaling laws of coherence times, T1 and T2, are presented. The results enable experimentalists to determine, as a function of temperature, an upper bound for the time over which a quantum computer can be operated without a disastrous loss of quantum coherence, and the duration over which a memory qubit retains its information. Given the tradeoff between the enormous resource overhead demanded by quantum error correction protocols and the adverse effects of decoherence, the results provide guidance for the implementation and optimization of practical error suppression methods in the current era of quantum computers.
Quantum computing holds the promise of solving problems that are intractable for classical computers, with applications ranging from optimization and materials simulation to cryptography. It achieves this by leveraging the exponentially scaling dimensionality of the space encoding quantum information and by executing algorithms on quantum registers in superposition states – a feature often referred to as quantum parallelism. However, while encoding information in computational units capable of exploring a continuous set of quantum states enables exponential scaling of computational power with system size, quantum systems are also more susceptible to errors than their classical counterparts. These errors take the form of both control errors, where miscalibration of the control pulses causes coherent errors on the qubit states, as well as incoherent errors due to energy relaxation and dephasing. Scaling quantum systems to run useful algorithms involving hundreds or thousands of logical qubits will require quantum error correction. In this approach, quantum information is redundantly encoded across an entangled state of many physical qubits. This has enabled experimental demonstrations across various platforms – including ion traps, superconducting circuits, and neutral atoms – showing that encoded quantum states can be preserved beyond the coherence times of the constituting physical qubits. However, quantum state preservation is only one component needed for scalable quantum computing. To execute algorithms, it is also necessary to implement quantum gates on and between encoded qubits, in a way that maintains fault tolerance by preserving the ability to correct errors as they occur during the computation. In the first part of this thesis, we demonstrate the implementation of an error-corrected quantum operation that entangles two logical qubits. This is achieved by performing lattice surgery on a distance-three surface code qubit, resulting in a logical Bell state encoded in distance-three repetition codes, which enable the correction of single bit-flip errors. We further introduce techniques to benchmark and characterize the performance of logical operations, including applying the protocol to arbitrary logical input states and performing logical quantum process tomography. Together, these results constitute one of the first realizations of error-corrected lattice surgery in superconducting circuits. While quantum error correction can correct errors provided they occur with sufficiently low frequency, it may fail when many qubits experience errors simultaneously. In the second part of this thesis, we therefore shift focus to a specific error mechanism known to cause correlated errors in superconducting circuits – quasiparticle-induced decoherence. In this case, various forms of energy deposition on the quantum device can break Cooper pairs into quasiparticles, which may subsequently diffuse to the tunnel junction and interact with the qubit state, thereby causing decoherence. In this thesis, we investigate the impact of quasiparticle tunneling on qubit performance, with a focus on infrared-induced quasiparticles. We compare the sensitivity of niobium-based qubits to those made from tantalum – a material that has gained interest in recent years following demonstrations of qubits with improved coherence times based on this material. Using a thermal radiator source, we show that the performance of tantalum qubits may be limited by infrared-induced quasiparticles in typical superconducting circuit experimental setups. By employing both ambient and in-line infrared filters, we investigate the effectiveness of different filtering strategies and develop best practices for engineering cryogenic environments for superconducting quantum processors. The results presented in this thesis contribute to the advancement of quantum computing based on superconducting circuits by implementing and characterizing quantum error-corrected operations, and by investigating quasiparticles as a source of decoherence, along with strategies to improve infrared filtering and signal conditioning in cryogenic environments for future fault-tolerant quantum computing.
The theoretical concepts of quantum computation in the idealized and undisturbed case are well understood. However, in practice, all quantum computation devices do suffer from decoherence effects as well as from operational imprecisions.\nThis work assesses the power of error-prone quantum computation devices using largescale\nnumerical simulations on parallel supercomputers. We present the Juelich Massively Parallel Ideal Quantum Computer Simulator (JUMPIQCS), that simulates a generic quantum computer on gate level. It comprises an error model for decoherence and operational errors. The robustness of various algorithms in the presence of noise has been analyzed.\nThe simulation results show that for large system sizes and long computations it is imperative to actively correct errors by means of quantum error correction. We implemented the 5-, 7-, and 9-qubit quantum error correction codes. Our simulations confirm that using error-prone correction circuits with non-fault-tolerant quantum error correction will always fail, because more errors are introduced than being corrected. Fault-tolerant methods can\novercome this problem, provided that the single qubit error rate is below a certain threshold.\nWe incorporated fault-tolerant quantum error correction techniques into JUMPIQCS using\nSteane’s 7-qubit code and determined this threshold numerically. Using the depolarizing\nchannel as the source of decoherence, we find a threshold error rate of (5.2 ± 0.2) · 10−6.\nFor Gaussian distributed operational over-rotations the threshold lies at a standard deviation of 0.0431±0.0002. We can conclude that quantum error correction is especially well suited for the correction of operational imprecisions and systematic over-rotations.\nFor realistic simulations of specific quantum computation devices we need to extend the generic model to dynamic simulations, i.e. time-dependent Hamiltonian simulations of realistic hardware models. We focus on today’s most advanced technology, i.e. ion trap quantum computation. We developed the Dynamic Quantum Computer Simulator for Ion Traps (DyQCSI). Starting from a microscopic Hamiltonian, it does not rely on approximations that are usually necessary for an analytical approach. We show that the effects due to these\napproximations are significant. We present several ways for the visualization of the state of the system during its time evolution and demonstrated the benefit of the simulation approach for parameter optimizations.
Quantum computers promise to solve models of important physical processes, optimize complex cost functions, and challenge cryptography in ways that are intractable using current computers. In order to achieve these promises, quantum computers must both increase in size and decrease error rates. To increase the system size, we report on the design, construction, and operation of an integrated trapped ion quantum computer consisting of a chain of 15 171Yb+ ions with all-to-all connectivity and high-fidelity gate operations. In the process, we identify a physical mechanism that adversely affects gate fidelity in long ion chains. Residual heating of the ions from noisy electric fields creates decoherence due to the weak confinement of the ions transverse to a focused addressing laser. We demonstrate this effect in chains of up to 25 ions and present a model that accurately describes the observed decoherence. To mitigate this noise source, we first propose a new sympathetic cooling scheme to periodically re-cool the ions throughout a quantum circuit, and then demonstrate its capability in a proof-of-concept experiment. One path to suppress error rates in quantum computers is through quantum error correction schemes that combine multiple physical qubits into logical qubits that robustly store information within an entangled state. These extra degrees of freedom enable the detection and correction of errors. Fault-tolerant circuits contain the spread of errors while operating the logical qubit and are essential for realizing error suppression in practice. We demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a distance-3 Bacon-Shor logical qubit in our quantum computer. The result is an encoded logical qubit with error rates lower than the error of the entangling operations required to operate it.
Numerical optimal control (GRAPE) can in principle discover pulse shapes that suppress all coherent gate error to machine precision. But when does that capability actually matter? We present a systematic comparison of Gaussian, DRAG, and GRAPE pulses for single-qubit gates on a three-level transmon model parameterized by IQM Garnet hardware (T1=37μs, T2=9.6μs,α/2π=−200 MHz), with the explicit goal of identifying the regimes where numerical optimization provides genuine practical advantage over analytical methods.
Our central finding is that properly calibrated DRAG already operates near the decoherence floor. At 20 ns gate time, GRAPE eliminates all coherent error (1−F<10−15), but DRAG achieves 1−F=4.9×10−4 in coherent error alone,and 8.4×10−4 under full decoherence -- only 1.2× above GRAPE's decoherence-limited performance. More surprisingly,DRAG is \emph{more robust} than GRAPE to qubit frequency detuning (minimum fidelity 0.990 vs.\ 0.931 over ±5 MHz), the dominant calibration uncertainty in charge-noise-limited transmons. GRAPE retains superior amplitude robustness (minimum fidelity 0.994 vs.\ 0.990) and provides the only route to guaranteed zero coherent error, which matters at short gate times (≲15 ns) where perturbative corrections break down.
These results lead to concrete calibration guidance: (1) properly calibrated DRAG is sufficient for gate times ≳20 ns on hardware with T2/T≳500, (2) GRAPE is necessary at short gate times or when targeting error rates well below the decoherence floor, and (3) robust optimal control incorporating frequency uncertainty should be used when detuning is the dominant noise source. We decompose the full error budget (coherent, T1, T2, control noise) and provide the open-source QubitPulseOpt framework for reproducing all results.
This review synthesizes current understanding of decoherence pathways across leading hardware platforms and explains why several experimentally observed noise features—drift, burst events, coherent components, correlated and non-Markovian structure, and leakage—can be disproportionately damaging for QEC. Decoherence remains the dominant impediment to scalable quantum computing because it is not a single error mechanism but a system-level phenomenon arising from materials defects, electromagnetic loss, control electronics, measurement backaction, and the broader environment in which a processor operates. Quantum error correction (QEC) is designed to algorithmically suppress physical noise, yet its practical success depends on how closely real devices satisfy the assumptions under which fault tolerance is proved: approximate locality, weak temporal correlations, sufficiently stochastic error statistics, low leakage, and reliable syndrome extraction. We then evaluate fundamental and engineering challenges that shape the viability of QEC at scale: syndrome measurement fidelity, correlated error suppression, decoding latency and classical co-processing, architectural constraints (connectivity, crosstalk, calibration overhead), and the resource cost of implementing a universal fault-tolerant gate set. Recent demonstrations of below-threshold behaviour and “break-even” regimes show that QEC is transitioning from theory to practice, but also clarify what remains unresolved: maintaining stable noise below fault-tolerance targets over long times, scaling to many logical qubits with low correlated-error rates, and integrating hardware-aware codes and decoders. We conclude with research priorities that treat decoherence and QEC as part of a co-designed stack spanning device physics, control, architecture, and algorithms.
Quantum computing has the potential to transform information technology by offering algorithms for certain tasks, such as quantum simulation, that are vastly more efficient than what is possible with any classical device. But experimentally implementing practical quantum information processing is a very difficult task. Here we study two important, and closely related, aspects of this challenge: architectures for quantum computing, and quantum error correction Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters, but the challenge remains of how to scale these systems to build practical quantum devices. In Part I of this thesis we analyse one approach to building a scalable quantum computer by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. Here we describe a method by which even these error-prone cells can perform quantum error correction. Groups of cells generate and purify shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (10% error rate) we find that our protocol can succeed provided that all intra-cell error rates are below 0.8%. Furthermore, we show that with some adjustments, the protocols we employ can be made robust also against high levels of loss in the network interconnects. We go on to analyse the potential running speed of such a device. Using levels of fidelity that are either already achievable in experimental systems, or will be in the near-future, we find that employing a surface code approach in a highly noisy and lossy network architecture can result in kilohertz computer clock speeds. In Part II we consider the question of quantum error correction beyond the surface code. We consider several families of topological codes, and determine the minimum requirements to demonstrate proof-of-principle error suppression in each type of code. A particularly promising code is the gauge color code, which admits a universal transversal gate set. Furthermore, a recent result of Bombin shows the gauge color code supports an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction. Here, we demonstrate the promise of single-shot error correction by designing a decoder and investigating its performance. We simulate fault-tolerant error correction with the gauge color code, and estimate a sustainable error rate, i.e. the threshold for the long time limit, of ~0.31% for a phenomenological noise model using a simple decoding algorithm.