Abstract: Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance.

Abstract: Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance.

Abstract: Quantum computations based on second quantization are performed by applying one body and two body terms in a selected order. Typically, terms associated with operators that commute are applied prior to application of other terms. In a particular example, one body terms of the form hpp are applied first, followed by two body terms of the form hprrp.

Abstract: Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance.

Abstract: Among the embodiments disclosed herein are variants of the quantum approximate optimization algorithm with different parametrization. In particular embodiments, a different objective is used: rather than looking for a state which approximately solves an optimization problem, embodiments of the disclosed technology find a quantum algorithm that will produce a state with high overlap with the optimal state (given an instance, for example, of MAX-2-SAT). In certain embodiments, a machine learning approach is used in which a “training set” of problems is selected and the parameters optimized to produce large overlap for this training set. The problem was then tested on a larger problem set. When tested on the full set, the parameters that were found produced significantly larger overlap than optimized annealing times. Testing on other random instances (e.g., from 20 to 28 bits) continued to show improvement over annealing, with the improvement being most notable on the hardest problems.

Abstract: Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance.

Abstract: Among the embodiments disclosed herein are variants of the quantum approximate optimization algorithm with different parametrization. In particular embodiments, a different objective is used: rather than looking for a state which approximately solves an optimization problem, embodiments of the disclosed technology find a quantum algorithm that will produce a state with high overlap with the optimal state (given an instance, for example, of MAX-2-SAT). In certain embodiments, a machine learning approach is used in which a “training set” of problems is selected and the parameters optimized to produce large overlap for this training set. The problem was then tested on a larger problem set. When tested on the full set, the parameters that were found produced significantly larger overlap than optimized annealing times. Testing on other random instances (e.g., from 20 to 28 bits) continued to show improvement over annealing, with the improvement being most notable on the hardest problems.

Abstract: Quantum circuits for chemistry simulation are based on second quantization Hamiltonian coefficients for one-body and two-body interactions. Jordan-Wigner series that conserve parity can be defined so that selected CNOT gates are removed from the associated circuits. Basis change gates such as Hadamard or Y-gates can be coupled to some or all qubits of a quantum circuit or cancelled in view of corresponding gates in adjacent circuits. In some examples, CNOT gates can be moved to different circuit locations.

Abstract: Quantum computations based on second quantization are performed by applying one body and two body terms in a selected order. Typically, terms associated with operators that commute are applied prior to application of other terms. In a particular example, one body terms of the form hpp are applied first, followed by two body terms of the form hprrp.

Abstract: Quantum circuits for chemistry simulation are based on second quantization Hamiltonian coefficients for one-body and two-body interactions. Jordan-Wigner series that conserve parity can be defined so that selected CNOT gates are removed from the associated circuits. Basis change gates such as Hadamard or Y-gates can be coupled to some or all qubits of a quantum circuit or cancelled in view of corresponding gates in adjacent circuits. In some examples, CNOT gates can be moved to different circuit locations.

Abstract: This patent application pertains to urgency-based resource management in computing scenarios. One implementation can identify processes competing for resources on a system. The implementation can evaluate an urgency of individual competing processes. The implementation can also objectively allocate the resources among the competing processes in a manner that reduces a total of the urgencies of the competing processes.

Abstract: This patent application pertains to urgency-based resource management in computing scenarios. One implementation can identify processes competing for resources on a system. The implementation can evaluate an urgency of individual competing processes. The implementation can also objectively allocate the resources among the competing processes in a manner that reduces a total of the urgencies of the competing processes.

Abstract: A method of performing a computing transaction is disclosed. In one disclosed embodiment, during performance of a transaction, if an operation in a transaction can currently be performed, then a result for the operation is received from a transaction system. On the other hand, if the operation in the transaction cannot currently be performed, then a message indicating that the operation would fail is received from the transaction system. The transaction ends after receiving for each operation in the transaction a result or a message indicating that the operation would fail.

Abstract: An improved system and method for a personal communications server is provided. The system and method may provide seamless multi-functional wireless communications for different integrated applications desired by a user. To this end, a computing device with a telecommunications interface is provided for coupling to a mobile phone network. The computing device may be without an attached audio input and output device, but may include a network interface for coupling with an external audio input and output device to receive audio from the mobile phone network and/or to send audio to the mobile network. A computer with a network interface may also be coupled with the computing device to receive data from a mobile phone network and/or to send data to the mobile network.

Abstract: A document, publication or a portion of a publication containing collateral information (e.g. advertisements) is delivered in electronic form, preferably appearing electronically as it appears in traditional printed form. Collateral information associated with the document, publication or portion of the publication is dynamically replaced, enabling the user to potentially receive more useful and relevant information and enabling the publisher to potentially generate new revenue from the replaced collateral information.

Abstract: Systems and methods are disclosed for providing feedback corresponding to user input. The disclosed systems and methods may include receiving input from a user manipulatable input device, the input corresponding at least one of the following: symbols and commands. Furthermore, the disclosed systems and methods may include overlaying on a display device a virtual image representative of the user manipulatable input device. In addition, the disclosed systems and methods may include provisioning the virtual image to indicate a user's interaction with the user manipulatable input device.

Abstract: An improved system and method for a personal communications server is provided. The system and method may provide seamless multi-functional wireless communications for different integrated applications desired by a user. To this end, a computing device with a telecommunications interface is provided for coupling to a mobile phone network. The computing device may be without an attached audio input and output device, but may include a network interface for coupling with an external audio input and output device to receive audio from the mobile phone network and/or to send audio to the mobile network. A computer with a network interface may also be coupled with the computing device to receive data from a mobile phone network and/or to send data to the mobile network.

Abstract: Systems, methods, and computer-readable media for processing electronic ink: (a) receive electronic ink input; (b) convert the input to machine-generated objects; and (c) render the objects such that their size substantially corresponds to the input's original size. The input ink may constitute text, and the machine-generated objects may correspond to words, lines, and/or other groupings of text generated by a handwriting recognizer. To enable quick and easy identification of recognizer errors, in at least some systems and methods, a user may select one or more words, which will cause the system to display the original ink corresponding to the selected word(s). Such systems also may display alternative words generated by the recognizer corresponding to the selected original ink and allow the user to select one of the alternatives to make corrections in the recognized text (akin to using a spell-checking or handwriting recognition program).

Abstract: An implementation of a technology, described herein, for wireless signal transmission and/or reception. One of the implementations, described herein, wirelessly couples a wireless device to a non-co-located antenna. This non-co-located antenna receives long-range wireless signals. It converts those signals into a short-range wireless signal and transmits them to the non-co-located wireless device. This abstract itself is not intended to limit the scope of this patent. The scope of the present invention is pointed out in the appending claims.