This dissertation addresses the issue of noise in quantum information processing devices. It is common knowledge that quantum states are particularly fragile to the effects of noise. In order to perform scalable quantum computation, it is necessary to suppress effective noise to levels which depend on the size of the computation. Various theoretical proposals have discussed how this can be achieved, under various assumptions about properties of the noise and the availability of qubits. We discuss new approaches to the suppression of noise, and propose experimental protocols characterizing the noise. \n \nIn the first part of the dissertation, we discuss a number of applications of teleportation to fault-tolerant quantum computation. We demonstrate how measurement-based quantum computation can be made inherently fault-tolerant by exploiting its relationship to teleportation. We also demonstrate how continuous variable quantum systems can be used as ancillas for computation with qubits, and how information can be reliably teleported between these different systems. Building on these ideas, we discuss how the necessary resource states for teleportation can be prepared by allowing quantum particles to be scattered by qubits, and investigate the feasibility of an implementation using superconducting circuits. \n \nIn the second part of the dissertation, we propose scalable experimental protocols for extracting information about the noise. We concentrate on information which has direct practical relevance to methods of noise suppression. In particular, we demonstrate how standard assumptions about properties of the noise can be tested in a scalable manner. The experimental protocols we propose rely on symmetrizing the noise by random application of unitary operations. Depending on the symmetry group use, different information about the noise can be extracted. We demonstrate, in particular, how to estimate the probability of a small number of qubits being corrupted, as well as how to test for a necessary condition for noise correlations. We conclude by demonstrating how, without relying on assumptions about the noise, the information obtained by symmetrization can also be used to construct protective encodings for quantum states.
This dissertation addresses the issue of noise in quantum information processing devices. It is common knowledge that quantum states are particularly fragile to the effects of noise. In order to perform scalable quantum computation, it is necessary to suppress effective noise to levels which depend on the size of the computation. Various theoretical proposals have discussed how this can be achieved, under various assumptions about properties of the noise and the availability of qubits. We discuss new approaches to the suppression of noise, and propose experimental protocols characterizing the noise. \n \nIn the first part of the dissertation, we discuss a number of applications of teleportation to fault-tolerant quantum computation. We demonstrate how measurement-based quantum computation can be made inherently fault-tolerant by exploiting its relationship to teleportation. We also demonstrate how continuous variable quantum systems can be used as ancillas for computation with qubits, and how information can be reliably teleported between these different systems. Building on these ideas, we discuss how the necessary resource states for teleportation can be prepared by allowing quantum particles to be scattered by qubits, and investigate the feasibility of an implementation using superconducting circuits. \n \nIn the second part of the dissertation, we propose scalable experimental protocols for extracting information about the noise. We concentrate on information which has direct practical relevance to methods of noise suppression. In particular, we demonstrate how standard assumptions about properties of the noise can be tested in a scalable manner. The experimental protocols we propose rely on symmetrizing the noise by random application of unitary operations. Depending on the symmetry group use, different information about the noise can be extracted. We demonstrate, in particular, how to estimate the probability of a small number of qubits being corrupted, as well as how to test for a necessary condition for noise correlations. We conclude by demonstrating how, without relying on assumptions about the noise, the information obtained by symmetrization can also be used to construct protective encodings for quantum states.
The characterization of noisy quantum circuits is an important step in the development of large-scale quantum computers. As experimental quantum architectures approach the threshold for fault-tolerant quantum computing, obtaining a benchmark of process fidelities is needed to verify the integrity of the system and ensure functionality. Additionally, the ability to successfully implement a quantum code of choice may depend on the type of noise that is present in the system. It is therefore necessary to characterize not only the fidelity of the process, but also the structure of the noise. \n \nRandomized benchmarking is a characterization protocol which extracts partial information from a noisy quantum process. This thesis gives a detailed review of the randomized benchmarking protocol, and presents the results of three collaborative projects which use techniques similar to randomized benchmarking to obtain previously hidden information. The first protocol is designed to obtain a benchmark on loss errors. This protocol also provides information on the detector efficiency and an additional constraint on estimated parameters from randomized benchmarking. The second protocol is an extension of the first, under the special case of coherent leakage errors, for which we obtain an estimate of the leakage rate. The third protocol provides a method of testing for spatial correlations in noisy processes. This test may be used to determine the correlation structure of errors, and the error correcting codes needed for successful experiments in a particular architecture. All protocols presented in this thesis are scalable, platform-independent and insensitive to state preparation and measurement errors. We also provide results of numerical tests of these protocols for simulated noise, which show their accuracy and robustness.
Quantum information processing has been the subject of countless discoveries since the early 1990's. It is believed to be the way of the future for computation: using quantum systems permits one to perform computation exponentially faster than on a regular classical computer. Unfortunately, quantum systems that not isolated do not behave well. They tend to lose their quantum nature due to the presence of the environment. If key information is known about the noise present in the system, methods such as quantum error correction have been developed in order to reduce the errors introduced by the environment during a given quantum computation. In order to harness the quantum world and implement the theoretical ideas of quantum information processing and quantum error correction, it is imperative to understand and quantify the noise present in the quantum processor and benchmark the quality of the control over the qubits. Usual techniques to estimate the noise or the control are based on quantum process tomography (QPT), which, unfortunately, demands an exponential amount of resources. \n \nThis thesis presents work towards the characterization of noisy processes in an efficient manner. The protocols are developed from a purely abstract setting with no system-dependent variables. To circumvent the exponential nature of quantum process tomography, three different efficient protocols are proposed and experimentally verified. The first protocol uses the idea of quantum error correction to extract relevant parameters about a given noise model, namely the correlation between the dephasing of two qubits. Following that is a protocol using randomization and symmetrization to extract the probability that a given number of qubits are simultaneously corrupted in a quantum memory, regardless of the specifics of the error and which qubits are affected. Finally, a last protocol, still using randomization ideas, is developed to estimate the average fidelity per computational gates for single and multi qubit systems. \n \nEven though liquid state NMR is argued to be unsuitable for scalable quantum information processing, it remains the best test-bed system to experimentally implement, verify and develop protocols aimed at increasing the control over general quantum information processors. For this reason, all the protocols described in this thesis have been implemented in liquid state NMR, which then led to further development of control and analysis techniques.
Quantum information processing is the coherent manipulation of a quantum state for the purpose of performing an information processing task. It is known that certain tasks can in principle be performed much more efficiently using quantum information processing rather than ordinary classical processing. Examples include factoring, secure key distribution, and the simulation of quantum systems. However, significant theoretical and technological obstacles stand in the road to achieving these promised benefits. It is exceedingly difficult to construct devices that are able to achieve an extensive level of control of a quantum state while keeping that state well isolated from the effects of noise. Although there is considerable experimental effort underway to build devices that are less noisy and more controllable, there is also a significant theoretical program aimed at finding schemes that make such physical limitations have less effect on the overall reliability of a device. The crowning achievement is the theory of fault-tolerant quantum error-correction, which shows that a noisy quantum device can be efficiently made to behave as though it were noise free, so long as the amount of noise present is below the “noise threshold”. A central result of this thesis is the calculation of the noise threshold for optical cluster-state quantum computing. Optical cluster-state quantum computing is one of the most promising proposals for the physical implementation of a quantum computer (i.e., a generic quantum information processing device). Previous studies of the value of the threshold, that considered other physical implementations, do not apply to optical quantum computing due to the unusual features of the optical proposal such as nondeterministic gates and photon loss. We present the first detailed analysis of the value of the noise threshold for this proposal. Our analysis involves a number of innovations, including a method for error-correction known as telecorrection, whereby repeated error-syndrome measurements are guaranteed to agree due to the use of teleportation during the correction process. This thesis also considers how to overcome limits to the amount of physical control able to be applied to a quantum device. We ask, if a quantum device can only control limited parts of its quantum state, can that device still be used to achieve a useful information processing task? We consider simple networks of interacting quantum spins where only a few of the spins are controllable, and consider the problem of using this system for high-fidelity quantum communication (i.e., using the system as a simple “quantum wire”). Without control, such systems generally yield a very poor communication fidelity. We show that a very simple scheme that involves controlling a small number of the spins can be used to greatly increase the fidelity across the entire network. The scheme is designed using techniques of state encoding. The thesis also considers the problem of engineering the interactions in a quantum device so that the ground state is a quantum error-correcting code. Such a problem is an important part of the proposal for naturally fault-tolerant systems, which have the ability to resist noise whilst using little or no external control. Our results prove that a certain important class of quantum error-correcting codes, the so called nondegenerate codes, cannot be the eigenstate of any physically-plausible quantum system. This result places significant restrictions on the design of naturally fault-tolerant devices, and sheds light on why current proposals for natural fault tolerance use codes that are degenerate.
Quantum computers have the potential to solve several interesting problems in polynomial \ntime for which no polynomial time classical algorithms have been found. However, \none of the major challenges in building quantum devices is that quantum systems are very \nsensitive to noise arising from undesired interactions with the environment. Noise can lead \nto errors which can corrupt the results of the computation. Quantum error correction is \none way to mitigate the effects of noise arising in quantum devices. \nWith a plethora of quantum error correcting codes that can be used in various settings, \none of the main challenges of quantum error correction is understanding how well various \ncodes perform under more realistic noise models that can be observed in experiments. \nThis thesis proposes a new decoding algorithm which can optimize threshold values of \nerror correcting codes under different noise models. The algorithm can be applied to \nany Markovian noise model. Further, it is shown that for certain noise models, logical \nClifford corrections can further improve a code's threshold value if the code obeys certain \nsymmetries. \n \nSince gates and measurements cannot in general be performed with perfect precision, \nthe operations required to perform quantum error correction can introduce more errors \ninto the system thus negating the benefits of error correction. Fault-tolerant quantum \ncomputing is a way to perform quantum error correction with imperfect operations while \nretaining the ability to suppress errors as long as the noise is below a code's threshold. \nOne of the main challenges in performing fault-tolerant error correction is the high resource \nrequirements that are needed to obtain very low logical noise rates. With the use of \nflag qubits, this thesis develops new fault-tolerant error correction protocols that are applicable \nto arbitrary distance codes. Various code families are shown to satisfy the requirements \nof flag fault-tolerant error correction. We also provide circuits using a constant number of \nqubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewer \nqubits than previous fault-tolerant error correction protocols. \n \nIt is often the case that the noise afflicting a quantum device cannot be fully characterized. \nFurther, even with some knowledge of the noise, it can be very challenging to use \nanalytic decoding methods to improve the performance of a fault-tolerant scheme. This \nthesis presents decoding schemes using several state of the art machine learning techniques \nwith a focus on fault-tolerant quantum error correction in regimes that are relevant to near \nterm experiments. It is shown that even in low noise rate regimes and with no knowledge \nof the noise, noise can be further suppressed for small distance codes. Limitations of machine \nlearning decoders as well as the classical resources required to perform active error \ncorrection are discussed. \n \nIn many cases, gate times can be much shorter than typical measurement times of \nquantum states. Further, classical decoding of the syndrome information used in quantum \nerror correction to compute recovery operators can also be much slower than gate times. \nFor these reasons, schemes where error correction can be implemented in a frame (known \nas the Pauli frame) have been developed to avoid active error correction. In this thesis, we \ngeneralize previous Pauli frame schemes and show how Clifford frame error correction can \nbe implemented with minimal overhead. Clifford frame error correction is necessary if the \nlogical component of recovery operators were chosen from the Clifford group, but could \nalso be used in randomized benchmarking schemes.
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.
For several decades it has been appreciated that quantum computers hold incredible promise to perform calculations intractable to classical computation. However, this promise has be slow to realize. Dozens of quantum systems are currently being investigated for use in quantum information processing - none of which have yet demonstrated algorithms involving more than a handful of qubits and it remains unclear which, if any, of these systems will ultimately compose a scalable, robust quantum information processing architecture. In this thesis we employ analytical, optimal and algebraic control techniques to evaluate various quantum systems for their potential use in quantum information processing. In doing so, we have additionally identified several novel characterization procedures capable of probing both the coherent and incoherent dynamics of quantum systems. The first part of this thesis discusses work motivated by attempts to utilize donor qubits in silicon as quantum bits. We first propose a measurement of the state of a single donor electron spin using two-dimensional electron gas of a field-effect transistor and electrically detected magnetic resonance. We analyze the potential sensitivity of this measurement and show that it is a quantum nondemolition measurement of an electron-encoded state. We then present the first of two novel qubit characterization procedures. We consider the problem of rapidly characterizing a large number of similarly prepared qubits using techniques from optimal experiment design. All qubits are assumed to evolve according to the same physical processes, though the Hamiltonian parameters may vary from device to device - an inevitability in solid state qubits. We use the Cram\\'er-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Though applied to dipole- and exchange-coupled qubits, this technique is widely applicable to other systems. The second part of the thesis discusses the role that control can play in measuring and mitigating noise in qubit systems. Our first result describes a method for quickly simulating the effects of arbitrary markovian noise on qubit systems through the use of a numerically optimized, multi-state Markovian fluctuator. This ability to rapidly simulate the noisy qubit evolution allows us to compute control sequences capable of maximally decoupling the qubit from the noise source. We then introduce the second characterization procedure of the these, showing that a single measurable and controllable qubit may act as a spectrometer of dephasing noise. We show that the formalism of dynamical decoupling can be used to estimate the short-time correlation function of the noise source, while long time correlations may be estimated by a very simple series of free evolution experiments. This technique is applicable to the wide range of physical implementations which suffer from dephasing noise.The final part of this thesis demonstrates that trapped neutral atoms may be utilized for the robust simulation of complex systems exhibiting a topological phase. We present a method to simulate the toric code Hamiltonian stroboscopically, and demonstrate that our technique preserves the ground state degeneracy . Furthermore, we introduce a dissipative mechanism allowing for thermalization of the system to a finite temperature or direct cooling to the ground state manifold.