A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task.
The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step.
One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.
This work was done by Michail Zak of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Information Sciences category. NPO-30193.
This Brief includes a Technical Support Package (TSP).
Quantum Search in Hilbert Space
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Overview
The document presents a technical support package from NASA's Jet Propulsion Laboratory (JPL) detailing advancements in quantum computing, specifically focusing on a proposed algorithm for searching large databases stored in a Hilbert-space memory structure. The work, conducted by Michail Zak, aims to enhance the efficiency of information retrieval in complex systems, which is particularly relevant for NASA's applications.
The core of the proposed algorithm involves mapping stored information into a unitary operator that acts on a quantum state, representing the information to be retrieved. This approach allows for the simultaneous posing of multiple search queries through quantum parallelism, effectively solving the search problem in a single computational step. The algorithm is designed to handle relational databases where information is represented as complex orthonormal vectors, enabling the dimensionality of the memory space to be exponentially large while utilizing only linear resources.
However, the document notes that the preprocessing required to map the information into a Hilbert space can be exponentially expensive. Therefore, the algorithm is expected to be most beneficial in scenarios where the resources available for preprocessing are significantly greater than those for searching. This makes it particularly suitable for ground-based processing in NASA applications, where memory searches can be performed on remote objects.
Additionally, the document discusses the importance of autonomous diagnosis in complex systems, highlighting a method for detecting and comparing events from control and sensor signals. This method can identify both nominal and faulty operations, providing critical information about fault onset and characteristics. Such capabilities are essential for monitoring system performance and ensuring reliability in aerospace missions.
The technical support package also includes references to further information available online, emphasizing the significance of this research in the context of NASA's ongoing technological advancements. Overall, the document encapsulates a promising approach to leveraging quantum computing for efficient data retrieval and system diagnostics, potentially transforming how complex systems are monitored and managed in aerospace and other fields.
