Abstract: Classical and quantum computational systems and methods for principal component analysis of multi-dimensional datasets are presented. A dataset is encoded in a tensor of rank p, where p is a positive integer that may be greater than 2. The classical methods are based on linear algebra. The quantum methods achieve a quartic speedup while using exponentially smaller space than the fastest classical algorithm, and a super-polynomial speedup over classical algorithms that use only polynomial space. In particular, an improved threshold for recovery is achieved. The presented classical and quantum methods work for both even and odd ranked tensors. Accordingly, quantum computation may be applied to large-scale inference problems, e.g., machine learning applications or other applications that involve highly-dimensional datasets.

Abstract: In a quantum-computation method, quantum-computer code is received for execution on a quantum computer. The quantum computer includes a plurality of qubits associated with a corresponding plurality of particles, and the plurality of particles define a quantum state. The quantum-computer code is decomposed into a sequence of operations including a total spin-state measurement on particles corresponding to two or more of the qubits. Then the sequence of operations is applied on the plurality of particles to thereby transform the quantum state according to the quantum-computer code initially received.

Abstract: Examples are disclosed that relate to, on a quantum computing device, distilling magic states encoded in a [[n,k,d]] block code comprising an outer code. One example provides a method comprising preparing encoded noisy magic states using data qubits, and measuring Clifford stabilizers on the data qubits, thereby applying an inner code. The method further comprises initializing output qubits and initiating a teleportation of distilled magic states derived from the encoded noisy magic states to the output qubits. The method further comprises measuring X-stabilizers on the data qubits, postselecting based on the outcomes, measuring each data qubit destructively utilizing Z-stabilizers, and applying one or more postselection conditions to the data qubits to complete the teleportation of the distilled magic states to the output qubits.

Abstract: A detection system used to alert an operator of a work machine of humans or objects dangerously close to the machine or a work tool attached to the machine. The detection system uses one or more cameras to capture images of an area surrounding the machine. The captured images are displayed on an interface electronically connected to a processor. Prior to operation, one or more zones surrounding the work tool or work machine are defined and projected on the images displayed on the interface. The processor analyzes the images captured by the cameras and determines if a characteristic of a predetermined object is within one or more of the identified zones. If the processor determines the characteristic of the predetermined object is within one of the zones, the processor will identify the object on the display and trigger a warning system to alert to the operator to take necessary precautions.

Abstract: A detection system used to alert an operator of a work machine of humans or objects dangerously close to the machine or a work tool attached to the machine. The detection system uses one or more cameras to capture images of an area surrounding the machine. The captured images are displayed on an interface electronically connected to a processor. Prior to operation, one or more zones surrounding the work tool or work machine are defined and projected on the images displayed on the interface. The processor analyzes the images captured by the cameras and determines if a characteristic of a predetermined object is within one or more of the identified zones. If the processor determines the characteristic of the predetermined object is within one of the zones, the processor will identify the object on the display and trigger a warning system to alert to the operator to take necessary precautions.

Abstract: Examples are disclosed that relate to, on a quantum computing device, distilling magic states encoded in a [[n,k,d]] block code comprising an outer code. One example provides a method comprising preparing encoded noisy magic states using data qubits, and measuring Clifford stabilizers on the data qubits, thereby applying an inner code. The method further comprises initializing output qubits and initiating a teleportation of distilled magic states derived from the encoded noisy magic states to the output qubits. The method further comprises measuring X-stabilizers on the data qubits, postselecting based on the outcomes, measuring each data qubit destructively utilizing Z-stabilizers, and applying one or more postselection conditions to the data qubits to complete the teleportation of the distilled magic states to the output qubits.

Abstract: Classical and quantum computational systems and methods for principal component analysis of multi-dimensional datasets are presented. A dataset is encoded in a tensor of rank p, where p is a positive integer that may be greater than 2. The classical methods are based on linear algebra. The quantum methods achieve a quartic speedup while using exponentially smaller space than the fastest classical algorithm, and a super-polynomial speedup over classical algorithms that use only polynomial space. In particular, an improved threshold for recovery is achieved. The presented classical and quantum methods work for both even and odd ranked tensors. Accordingly, quantum computation may be applied to large-scale inference problems, e.g., machine learning applications or other applications that involve highly-dimensional datasets.

Abstract: A detection system used to alert an operator of a work machine of humans or objects dangerously close to the machine or a work tool attached to the machine. The detection system uses one or more cameras to capture images of an area surrounding the machine. The captured images are displayed on an interface electronically connected to a processor. Prior to operation, one or more zones surrounding the work tool or work machine are defined and projected on the images displayed on the interface. The processor analyzes the images captured by the cameras and determines if a characteristic of a predetermined object is within one or more of the identified zones. If the processor determines the characteristic of the predetermined object is within one of the zones, the processor will identify the object on the display and trigger a warning system to alert to the operator to take necessary precautions.

Abstract: A detection system used to alert an operator of a work machine of humans or objects dangerously close to the machine or a work tool attached to the machine. The detection system uses one or more cameras to capture images of an area surrounding the machine. The captured images are displayed on an interface electronically connected to a processor. Prior to operation, one or more zones surrounding the work tool or work machine are defined and projected on the images displayed on the interface. The processor analyzes the images captured by the cameras and determines if a characteristic of a predetermined object is within one or more of the identified zones. If the processor determines the characteristic of the predetermined object is within one of the zones, the processor will identify the object on the display and trigger a warning system to alert to the operator to take necessary precautions.

Abstract: A detection system used to alert an operator of a work machine of humans or objects dangerously close to the machine or a work tool attached to the machine. The detection system uses one or more cameras to capture images of an area surrounding the machine. The captured images are displayed on an interface electronically connected to a processor. Prior to operation, one or more zones surrounding the work tool or work machine are defined and projected on the images displayed on the interface. The processor analyzes the images captured by the cameras and determines if a characteristic of a predetermined object is within one or more of the identified zones% If the processor determines the characteristic of the predetermined object is within one of the zones, the processor will identify the object on the display and trigger a warning system to alert to the operator to take necessary precautions.

Abstract: Performance management systems and methods may utilize a plurality of modules. A performance network module may receive a post from a user and cause the post to be displayed on a display, and receive a comment associated with the post from the user and cause the post to be displayed on the display. A report module may generate a report including a question and send the report to the user, and receive an answer to the question in the report from the user and store the answer in a database. A goal module may receive a goal and/or an update to the goal, and update a status associated with the goal. A review module may generate a review including a question and send the review to the user, and receive an answer to the question in the review from the user and store the answer in the database.