Microsoft Technology Licensing, LLC

David B Wecker

Matthew Benjamin Hastings

Burton Jordan Smith

Richard I Brass

Chris Demetrios Karkanias

Jeongwan Haah

Matthias Troyer

Stuart M Bowers

David Poulin

Douglas Christopher Burger

Charlton E Lui

Dan W Altman

Vinay Krishnaswamy

Timothy David Sharpe

David Bradley Probert, Jr

Abhishek Kumar Singh

Michael P Calligaro

Randal James Ramig

Michael S Cooper

Steven Bourne

Cameron Ali Etezadi

Bela Bauer

Bryan Clark

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. Embodiments of the protocol rely on the construction of weakly self-dual Calderbank-Shor-Steane codes ('CSS codes') with many logical qubits and large distance, allowing one to implement control-Swaps on multiple qubits. This code is referred to herein as the 'inner code'. The control-Swaps are then used to measure properties of the magic state and detect errors, using another code that is referred to as the &#x201c;outer code&#x201d;. Alternatively, one can use weakly-self dual CSS codes which implement controlled Hadamards for the inner code, reducing circuit depth. Several specific small examples of this protocol are disclosed herein.

Magic state distillation with low space overhead and asymptotic input count

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 hare applied first, followed by two body terms of the form h.

Classical simulation constants and ordering for quantum chemistry simulation

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. Embodiments of the protocol rely on the construction of weakly self-dual Calderbank-Shor-Steane codes ('CSS codes') with many logical qubits and large distance, allowing one to implement control-Swaps on multiple qubits. This code is referred to herein as the 'inner code'. The control-Swaps are then used to measure properties of the magic state and detect errors, using another code that is referred to as the 'outer code'. Alternatively, one can use weakly-self dual CSS codes which implement controlled Hadamards for the inner code, reducing circuit depth. Several specific small examples of this protocol are disclosed herein.

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. Embodiments of the disclosed technology can be used, for example, for near-term quantum computers with limited coherence times.

Training a quantum optimizer

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.

Quantum circuit for chemistry simulation

Operators such as unitary operators common in quantum mechanical applications may be approximated by a Trotter-like approximation. An operator may be decomposed and terms of the operator may be grouped, or assigned into levels. The levels may be scaled and applied at unique intervals of calculational steps. A quantum device may have circuitry for applying levels of the operator at the unique intervals.

Optimized trotterization via multi-resolution analysis

Systems and methods for language integration via function redirection are disclosed herein in connection with simulation of quantum computations on classical computers. A base class that all of the functions of a group will instantiate in their context may be defined. The functions may take arguments that may be passed to a member of the base class for dispatch. A dispatcher may be provided to analyze the current context. The dispatcher may perform any of a number of operations as a result, including, but not limited to, passing the arguments to the class instance for execution, returning the class instance directly or via a context holder, returning a new representation of the function for future execution via a context holder, or any other return type that may be desired.

Language integration via function redirection

A quantum annealer simulator approximates unitary quantum dynamics of a quantum annealer on a non-quantum computing device such as a conventional computing device. The quantum annealer simulator may utilize algorithms that may efficiently approximate unitary time evolution of a quantum system, where the quantum system corresponds to a problem for which an optimized solution is sought.

Quantum annealing simulator

Disclosed are systems and methods for improving quantum computation simulation execution time by 'growing' sets of small quantum gates into larger ones. Two approaches are described. In the first approach, sub-strings may be replaced by a single representative that may be used multiple times throughout the quantum circuit. In the second approach, nearby gates may be coalesced in an iterative fashion, to thereby build larger and larger gates. Results may be cached for re-use. Both of these approaches have proven effective and have gained typical simulation speed-ups of 1-2 orders of magnitude.

Quantum gate optimizations

A state (i.e., ket) of a set of qubits may be simulated via a classical computer. Ordering characteristics of the ket (i.e., the 'current' permutation associated with the state) may be determined. An operator (which may be associated with a certain operation to perform on the ket) may be defined and simulated. Ordering characteristics of the operator (i.e., the 'current' permutation associated with operator) may be determined. If the current permutations of the state and operator match, then the operation may be performed to generate a new ket. Alternatively, the operator may be permuted to match the permutation of the current state. Or the state may be permuted to match the current operator permutation. The operation may then be performed, and the state and permutation remembered for the next operation. The process may be repeated for each operation in the series.

Optimizing quantum simulations by intelligent permutation

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.

Personal communications server

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.

Resource management in computing scenarios

Described is a technology comprising a query processing pipeline in which a SPARQL query is processed into an intermediate LINQ query, which is then processed by a LINQ provider. The LINQ provider decides which instructions correspond to flat database queries, and routes those instructions a database engine (e.g., SQL server) for querying a database. Other instructions are provided to a reasoning engine for processing, e.g., by performing a graph traversal and/or database queries. The pipeline may include a parser that parses the query into an abstract syntax tree, and an optimizer that processes the abstract syntax tree into a LINQ query, including by reordering LINQ instructions and/or associating a flag with each of the instructions that indicates whether to query the database or provide the instruction to a reasoning engine.

Query submission pipeline using LINQ

A semantic query may refer to a logical rule, where the rule is defined in terms of constituent expressions. In order to execute the semantic query efficiently, occurrences of the rule may be expanded by replacing the rule with its constituent expressions. Expansion may be performed repeatedly, until only grounded expressions remain. Expressions are grounded when they refer to tables or views that are represented in an underlying database. Once the rule has been reduced to grounded expressions, the semantic query processor may formulate a relational query in terms of the grounded expressions. If the relational query takes into account the various grounded expressions to which the rule reduces, then the portion of the semantic query that refers to the rule may be processed without an excessive number of round trips to the relational database.

Execution of semantic queries using rule expansion

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).

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Bothell, WA, United States of America

David B Wecker