Liquid-State NMR Quantum Computing

Vandersypen, L. M. K.; Yannoni, C. S.; Chuang, Isaac L.

doi:10.1002/9780470034590.emrstm0272.pub2

Cited by 8 publications

(9 citation statements)

References 94 publications

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“…Single nuclear qubit coherence times may be extremely long in the liquid samples, although entanglement between them is required for logical operations that involve swapping of spin between two qubits. The inter-qubit coherence time T 2 is usually much shorter in comparison to T 1 because of the inhomogeneities or fluctuations in the local fields at different nuclei when operating with seven ±½ spin qubits (five 19 F nuclei and two 13 C nuclei), in the molecule C 13 O 2 F 5 H 5 [27], an overall decoherence time as long as 1.3-2 s was recently reported.…”

Section: Figure 11mentioning

confidence: 99%

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Quantum Decoherence in Dense Media: A Few Examples

Karlsson¹

2020

Recent Progress in Materials

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Decoherence is a relatively recent concept in the field of quantum mechanics. Although the pioneers of the field must have understood that loss of phase coherence in quantum superpositions is the reason underlying the appearance of definite outcomes in the quantum measurement problem, the latter was not treated in terms of decoherence until sixty years after the formulation of quantum mechanics as described in a report by Joos and Zeh in 1983 [1]. However, soon after, the theory was developed in further detail, and experiments to measure the actual decoherence rates in various systems commenced. Today, decoherence is the main concern for another reason, i.e., the fact that superposition states must be maintained undisturbed in the quantum communication systems and decoherence presents a strong limitation for their practical application. Decoherence appears in open quantum systems, where the basic system under consideration interacts relatively strongly with an environment. Decoherence times may be as long as seconds for small atomic systems in extreme vacua, although below what is presently measurable (i.e., less than a fraction of a femtosecond) in most liquids and solids, where coupling to the surrounding molecules or atomic arrangements is strong. The relatively slow decoherence in well-isolated particle systems has been described in several

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Section: Figure 11mentioning

confidence: 99%

“…In the example described in detail in ref. [27], the number of qubits was sufficient to compute the product 3 × 5. Furthermore, large losses of signal intensity occur as all the molecules do not experience exactly the same local magnetic fields.…”

Section: Figure 11mentioning

confidence: 99%

Quantum Decoherence in Dense Media: A Few Examples

Karlsson¹

2020

Recent Progress in Materials

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“…We now proceed to experimentally demonstrate, on a nuclear spin quantum computer, some of these elementary image transforms. With established processing techniques [63,64], NMR has been used for many demonstrations of quantum information processing [47,62,65,66].…”

Section: Experimental Demonstrationsmentioning

confidence: 99%

Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

et al. 2017

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digital data processors, but others remain time-consuming. In particular, the rapidly increasing volume of image data as well as increasingly challenging computational tasks have become important driving forces for further improving the efficiency of image processing and analysis.Quantum information processing (QIP), which exploits quantum-mechanical phenomena such as quantum superpositions and quantum entanglement [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], allows one to overcome the limitations of classical computation and reaches higher computational speed for certain problems like factoring large numbers [24,25] , searching an unsorted database [26], boson sampling [27][28][29][30][31][32], quantum simulation [33-40], solving linear systems of equations [41][42][43][44][45], and machine learning [46][47][48]. These unique quantum properties, such as quantum superposition and quantum parallelism, may also be used to speed up signal and data processing [49,50]. For quantum image processing, quantum image representation (QImR) plays a key role, which substantively determines the kinds of processing tasks and how well they can be performed. A number of QImRs [51-54] have been discussed.In this article, we demonstrate the basic framework of quan-arXiv:1801.01465v1 [quant-ph]

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“…Initialization faults were discussed in detail by Kak [54], and addressed experimentally in [55,47]. Because initialization accuracies relate to a machine's ability to perform a task (such as not altering the initial state population in NMR [47]), one can develop a test set to determine if the machine is impacted by any of the considered initialization faults. We model these faults using Def.…”

Section: Initialization Faultsmentioning

confidence: 99%

“…The building blocks needed to implement any quantum algorithm with NMR can be based on single spin rotations and CN gates [47]. CN gates are realized using a scheme illustrated in Fig.…”

Section: Faded Control Faultsmentioning

confidence: 99%

Fault Models for Quantum Mechanical Switching Networks

2010

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The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.Comment: (almost) Forgotten rewrite from 200

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Liquid-State NMR Quantum Computing

Cited by 8 publications

References 94 publications

Quantum Decoherence in Dense Media: A Few Examples

Quantum Decoherence in Dense Media: A Few Examples

Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

Fault Models for Quantum Mechanical Switching Networks

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