105 research outputs found

    Prospects and Limitations of Algorithmic Cooling

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    Heat-bath algorithmic cooling (AC) of spins is a theoretically powerful effective cooling approach, that (ideally) cools spins with low polarization exponentially better than cooling by reversible entropy manipulations alone. Here, we investigate the limitations and prospects of AC. For non-ideal and semioptimal AC, we study the impact of finite relaxation times of reset and computation spins on the achievable effective cooling. We derive, via simulations, the attainable cooling levels for given ratios of relaxation times using two semioptimal practicable algorithms. We expect this analysis to be valuable for the planning of future experiments. For ideal and optimal AC, we make use of lower bounds on the number of required reset steps, based on entropy considerations, to present important consequences of using AC as a tool for improving signal-to-noise ratio in liquid-state magnetic resonance spectroscopy. We discuss the potential use of AC for noninvasive clinical diagnosis and drug monitoring, where it may have significantly lower specific absorption rate (SAR) with respect to currently used methods.Comment: 12 pages, 5 figure

    Novel Heat-Bath Algorithmic Cooling methods

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    The field of quantum information has inspired new methods for cooling physical systems at the quantum scale by manipulating entropy in an algorithmic way, such as heat-bath algorithmic cooling (HBAC). These methods not only provide fundamental insight into quantum thermodynamics, but they are also at the core of practical applications in quantum science and quantum technologies. Arguably, the most promising practical applications are in quantum computing, for the preparation of pure states. The ability to prepare highly pure states is required both for initializing qubits in most quantum algorithms and for supplying reliable low-noise ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction (achieving the high levels of purity required represents one of the major challenges not only for ensemble implementations but also for technologies with strong but not perfect projective measurements). The heat bath algorithmic cooling protocols have inspired the work within this thesis, which examines and proposes powerful new techniques that significantly enhance cooling by taking advantage of classical and quantum correlations. These new methods go beyond the limits of conventional cooling techniques, providing a novel way to cool that allows a generalized interaction of the system with the environment, which has not been taken into account in previous work. Concretely, I have contributed to elucidating our understanding of these algorithmic cooling mechanisms by using techniques from quantum information theory and quantum thermodynamics. First, I found the analytical solution of the maximum achievable cooling of these algorithmic cooling methods, which had been a longstanding problem that remained open for almost 15 years. Then, I showed how to circumvent the cooling limits of the conventional algorithmic cooling – which were widely believed to be optimal –, creating novel methods that show how correlations can be used to significantly improve cooling. On the one hand, we fundamentally changed the way previous methods considered the interactions between the system and environment and showed how correlated relaxation processes can be essential for enhancing cooling. On the other hand, we demonstrated that correlations present in the initial state due to internal interactions can be exploited to improve cooling. Finally, we showed how, by using ideas and concepts from resource theory, it is possible to find the optimal entropy compression required for HBAC by studying the n-to-1 distillation of athermality of two level systems

    Optimal Entropy Compression and Purification in Quantum Bits

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    Global unitary transformations that optimally increase the bias of any mixed computation qubit in a quantum system, represented by a diagonal density matrix, towards a particular state of the computational basis which, in effect, increases its purity are presented. Quantum circuits that achieve this by implementing the above data compression technique, a generalization of the 3B-Comp [Fernandez, Lloyd, Mor, Roychowdhury (2004); arXiv: quant-ph/0401135] used before, are described. These circuits enable purity increment in the computation qubit by maximally transferring part of its von Neumann or Shannon entropy to any number of surrounding qubits and are valid for the complete range of initial biases. Using the optswaps, a practicable new method that algorithmically achieves hierarchy-dependent cooling of qubits to their respective limits in an engineered quantum register opened to the heat-bath is delineated. In addition to multi-qubit purification and satisfying two of DiVincenzo's criteria for quantum computation in some architectures, the implications of this work for quantum data compression and quantum thermodynamics are discussed.Comment: 26 pages, 12 + 1 (external) figures; v3: revised manuscrip

    The role of quantum information in thermodynamics --- a topical review

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    This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.Comment: published version. 34 pages, 6 figure

    Representation, Characterization, and Mitigation of Noise in Quantum Processors

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    Quantum computers have the potential to outperform classical computers on several families of important problems, and have a great potential to revolutionize our understanding of computational models. However, the presence of noise deteriorates the output quality from near-term quantum computers and may even offset their advantage over classical computers. Studies on noise in these near-term quantum devices has thus become an important field of research during the past years. This thesis addresses several topics related to this subject including representing, quantifying, and mitigating noise in quantum processors. To study noise in quantum processors, it is first necessary to ask how noise can be accurately represented. This is the subject of Chapter 2. The conventional way is to use a gate-set, which include mathematical objects assigned to each component of a quantum processor, and compare individual gate-set elements to their ideal images. Here, we present some clarifications on this approach, pointing out that a gauge freedom exists in this representation. We demonstrate with experimentally relevant examples that there exists equally valid descriptions of the same experiment which distribute errors differently among objects in a gate-set, leading to different error rates. This leads us to rethink about the operational meaning to figures of merit for individual gate-set elements. We propose an alternative operational figure of merit for a gate-set, the mean variation error, and develop a protocol for measuring this figure. We performed numerical simulations for the mean variation error, illustrating how it suggests a potential issue with conventional randomized benchmarking approaches. Next, we study the problem of whether there exist sufficient assumptions under which the gauge ambiguity can be removed, allowing one to obtain error rates of individual gate-set elements in a more conventional manner. We focus on the subset of errors including state preparation and measurement (SPAM) errors, both subject to a gauge ambiguity issue. In Chapter 3, we provide a sufficient assumption that allows a separate SPAM error characterization, and propose a protocol that achieves this in the case of ideal quantum gates. In reality where quantum gates are imperfect, we derived bounds on the estimated SPAM error rates, based on gate error measures which can be estimated independently of SPAM processes. We tested the protocol on a publicly available quantum processor and demonstrated its validity by comparing our results with simulations. In Chapter 4, we present another protocol capable of separately characterizing SPAM errors, based on a different principle of algorithmic cooling (AC). We propose an alternative AC method called measurement-based algorithmic cooling (MBAC), which assumes the ability to perform (potentially imperfect) projective measurements on individual qubits and is available on various modern quantum computing platforms. Cooling reduces the error on initial states while keeping the measurement operations untouched, thereby breaking the gauge symmetry between the two. We demonstrate that MBAC can significantly reduce state preparation error under realistic assumptions, with a small overhead that can be upper bounded by measurable quantities. Thus, our results can be a valuable tool not only for benchmarking near-term quantum processors, but also for improving the quality of state preparation processes in an algorithmic manner. The capability of AC for improving initial state quality has inspired us to perform a parallel study on the thermodynamic cost of AC protocols. The motivation is that since cooling a subset of qubits may result in finite energy increase in its environment, applying them in certain platforms that are temperature-sensitive could induce a negative impact on the overall stability. Meanwhile, previous studies on AC have largely focused on subjects like cooling limits, without paying attention to their thermodynamics. Understanding the thermodynamic cost of AC is of both theoretical and practical interest. These results are presented in Chapter 5. After reviewing their procedure, cooling limits, and target state evolution of various AC protocols, we propose two efficiency measures based on the amount of work required, or the amount of heat released. We show how these measures are related to each other and how they can be computed for a given protocol. We then compare the previously studied protocols using both measures, providing suggestions on which ones to use when these protocols are to be carried out experimentally. We also propose improved protocols that are energetically more favorable over the original proposals. Finally, in Chapter 6, we present a study on a different family of methods aiming at reducing effective noise level in near-term hardware called quantum error mitigation (QEM). The principle behind various QEM approaches is to mimic outputs from the ideal circuit one wants to implement using noisy hardware. These methods recently became popular because many near-term hybrid quantum-classical algorithms only involve relatively shallow depth circuits and limited types of local measurements, implying a manageable cost of performing data processing to alleviate the effect of noise. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between quantum error correction (QEC) and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace preserving while the commonly-used Moore-Penrose pseudoinverse may not be. Finally, we study the consequences of having an imperfect knowledge about the noise, and derive conditions when noise can be reduced using QEM
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