Abstract: A method to build a lookup decoder for mapping error syndromes based on quantum-stabilizer code to corresponding error corrections comprises (A) enumerating a subset of error syndromes up to a maximum error weight based on the quantum-stabilizer code; (B) iterating through the subset of error syndromes to compute an error state of highest probability for each error syndrome of the subset, where the error state defines error in a qubit register of a quantum computer; and (C) for each error syndrome of the subset of error syndromes, storing in classical computer memory an error correction based on the error state of highest probability and mapped to that error syndrome.

Abstract: A method for performing long-range multi-qubit measurements in a quantum circuit utilizes a graph that maps qubits of the quantum circuit to nodes that are connected to one another by edges. The method provides for identifying sets of the nodes on the graph corresponding to sets of qubits targeted by multi-qubit operations in a quantum algorithm and for defining a group of edge-disjoint paths connecting the nodes of each set. The group of edge-disjoint paths is defined such that no two of the paths in the group share an edge. The method further provides for performing a set of operations to entangle the qubits corresponding to the to the identified set of nodes that are included in each path in the group and for performing the set of multi-qubit operations on the entangled sets of the qubits.

Abstract: A method for performing long-range multi-qubit measurements in a quantum circuit utilizes a graph that maps qubits of the quantum circuit to nodes that are connected to one another by edges. The method provides for identifying sets of the nodes on the graph corresponding to sets of qubits targeted by multi-qubit operations in a quantum algorithm and for defining a group of edge-disjoint paths connecting the nodes of each set. The group of edge-disjoint paths is defined such that no two of the paths in the group share an edge. The method further provides for performing a set of operations to entangle the qubits corresponding to the to the identified set of nodes that are included in each path in the group and for performing the set of multi-qubit operations on the entangled sets of the qubits.

Abstract: One aspect of this disclosure relates to a method for operating a quantum computing device. A request to execute a first n-qubit gate on a set of n target qubits is received. The first n-qubit gate is representable as an m-qubit diagonal gate conjugated by a Clifford gate, where m?n. A set of m interface qubits on which to perform the m-qubit diagonal gate are identified. A Clifford operation is executed on each interface qubit and its corresponding target qubits. The m-qubit diagonal gate is executed on the set of m interface qubits.

Abstract: One aspect of this disclosure relates to a method for operating a quantum computing device. A request to execute a first n-qubit gate on a set of n target qubits is received at the quantum computing device. The receiving a request to execute a first n-qubit gate on a set of n target qubits, the n-qubit gate including one or both of a diagonal gate and a diagonal gate conjugated by a multi-qubit Clifford gate. A set of n interface qubits on which to perform the first n-qubit gate is identified, the set of n interface qubits located remotely from the set of n target qubits. A joint Z-Z measurement is executed on each target qubit and its corresponding interface qubit via a pre-established entanglement. The first n-qubit gate is executed on the set of n interface qubits.

Abstract: Disclosed herein are example layouts and layout generation techniques for fault-tolerant quantum computers. Example embodiments comprise methods for performing a layout reduction technique for fault-tolerant quantum computing. In certain embodiments, a layout of an arbitrary quantum circuit is reduced to a layout of exponents of a multiple qubit Pauli matrix and measurements of a multiple qubit Pauli matrix. In certain embodiments, qubits are marked as one of a data, interface, or ancilla qubit for a 2D nearest neighbor graph of qubit connectivity, and an ancilla-path is provided from a respective data qubit to a respective interface qubit.

Abstract: The present invention extends to methods, systems, computer program products, and data structures for efficiently storing and accessing electronic messages representing fax transmissions. The messages are extended according to a fax schema that defines formats for adding fax protocol specific and/or or fax application specific data fields to an electronic message. According to the fax schema, the messages have relationships with other data fields stored using other schemas that define the accounting services, message content, and message participants associated with the fax transmission. The fax schema promotes efficient storage and access of electronic messages representing fax transmissions, while also facilitating integrating messages received by fax transmission with other types of existing message protocols and message applications.

Abstract: In an Item-based system, Images (e.g., JPEG, TIFF, bitmap, and so on) are treated as core platform objects (“Image Items” or, more simply, “Images”) and exist in an “Image Schema” that provides an extensible representation of an Image in the system—that is, the characteristics of an Image and how that Image relates to other Items (including but not limited to other Images) in the system. To this end, the Image Schema defines the properties, behaviors, and relationships for Images in the system, and the Schema also enforces rules about Images, for example, what data specific Images must contain, what data specific Images may optionally contain, how specific Images can be extended, and so on and so forth.

Abstract: Architecture that facilitates the calculation of the final margins and positions of all objects in one formatting pass, without the need to reformat an object in the margin neighborhood. Clearance objects, float objects, and empty objects are taken into account. The one-pass algorithm computes the positions of objects on the document due to collapsing margins, determines the sizes of the resulting collapsed margins, and correctly places empty objects, floats, and clearance objects in the document. Clearances due to objects that belong to the neighborhood are processed as well as clearances due to objects outside of the neighborhood.

Abstract: Architecture of one or more algorithms for autofitting objects with non-trivial geometries in documents. The algorithms autofit rectangular objects (such as floaters), when the objects contain both left and right aligned objects, autofit tables, determine correct sizes of a parent object and its child object when the width of the parent object is unknown (referred to as an auto-width), and the width of the parent's child object is expressed in percentages of the parent object width. A two-pass algorithm determines the best (or optimal) sizes of margins, borders, and paddings of objects where any combination thereof can have fixed width, auto width, and/or percentage-expressed width. Additionally, the algorithms can recursively calculate the optimal widths of objects inside other objects, where the outer object width is undefined. The algorithms can process an unlimited number of nesting levels.

Abstract: A programming interface for a computer platform can include various functionality. In certain embodiments, the programming interface includes one or more of the following groups of types or functions: those related to core file system concepts, those related to entities that a human being can contact, those related to documents, those common to multiple kinds of media, those specific to audio media, those specific to video media, those specific to image media, those specific to electronic mail messages, and those related to identifying particular locations.

Abstract: Embodiments relate to systems and methods for formatting a set of expressions in a document. In embodiments, the systems and methods provide the ability to format a set of expressions by aligning expressions or parts of expressions to each other or to the margins of the document, while also supporting breaking of one or more expressions into multiple parts to be placed on different lines. Breaking can include breaking in places requested by a user or breaking in places that are automatically determined to fit the expressions between the margins of a document.

Abstract: A Relational Schema Definition (RSD) language that uses metadata of the relational database to generate an implementation-neutral or implementation-specific format that represents the precise database structure and data. The RSD language is a declarative description language such that an RSD file can then be used offline in a disconnected environment to reconstruct and use the database.

Abstract: A system and method for presenting images and related items to a user. A digital image from a data store is assessed, and a portion of the image is defined as a region of interest. Properties are associated with this defined region, and these properties are utilized to infer relationships between the region of interest and related items in the data store. Optionally, a user input indicating a desire to view related content may be received and such content may be presented to the user.

Abstract: A data mapping architecture for mapping between two or more data sources without modifying the metadata or structure of the data sources themselves. Data mapping also supports updates. The architecture also supports at least the case where data sources that are being mapped, are given, their schemas predefined, and cannot be changed. The architecture includes a mapping component that receives respective metadata from at least two arbitrary data models, and maps expressions between the data models.

Abstract: Architecture of one or more algorithms for autofitting objects with non-trivial geometries in documents. The algorithms autofit rectangular objects (such as floaters), when the objects contain both left and right aligned objects, autofit tables, determine correct sizes of a parent object and its child object when the width of the parent object is unknown (referred to as an auto-width), and the width of the parent's child object is expressed in percentages of the parent object width. A two-pass algorithm determines the best (or optimal) sizes of margins, borders, and paddings of objects where any combination thereof can have fixed width, auto width, and/or percentage-expressed width. Additionally, the algorithms can recursively calculate the optimal widths of objects inside other objects, where the outer object width is undefined. The algorithms can process an unlimited number of nesting levels.

Abstract: Architecture that facilitates the calculation of the final margins and positions of all objects in one formatting pass, without the need to reformat an object in the margin neighborhood. Clearance objects, float objects, and empty objects are taken into account. The one-pass algorithm computes the positions of objects on the document due to collapsing margins, determines the sizes of the resulting collapsed margins, and correctly places empty objects, floats, and clearance objects in the document. Clearances due to objects that belong to the neighborhood are processed as well as clearances due to objects outside of the neighborhood.

Abstract: A Relational Schema Definition (RSD) language that uses metadata of the relational database to generate an implementation-neutral or implementation-specific format that represents the precise database structure and data. The RSD language is a declarative description language such that an RSD file can then be used offline in a disconnected environment to reconstruct and use the database.

Abstract: A method and system are provided in which data may be multityped using a schematized data model. A standardized schema in a schematized data model includes at least one base construct for representing data that is common across multiple types of an object that the model represents. An extension to the standardized schema is at least one extension construct for representing data that is specific to a single type of the multiple types of the object. Instances of the extension construct are directly or indirectly associated with exactly one instance of the base construct without impacting the behavior and functionality of the base construct. Multiple extensions may be used to represent data that is specific to each of the corresponding multiple types of the object.

Abstract: A Relational Schema Definition (RSD) language that uses metadata of the relational database to generate an implementation-neutral or implementation-specific format that represents the precise database structure and data. The RSD language is a declarative description language such that an RSD file can then be used offline in a disconnected environment to reconstruct and use the database.