Microsoft Technology Licensing, LLC

Alexei V Bocharov

Krysta Marie Svore

David Earl Heckerman

David Maxwell Chickering

Martin Henri Roetteler

Robert L Rounthwaite

Zhaohui Tang

Vadym Kliuchnikov

Scott Conrad Oveson

Parsa Hassan Bonderson

Roman Bela Bauer

Alan D Tran

Joshua T Goodman

Xingshan Cui

Bryan T Starbuck

Michael Hartley Freedman

Nathan O Wiebe

Yuri Gurevich

Matthias Troyer

Ojiakonobi Udezue

Zhenghan Wang

Paul Smolensky

Jon Yard

Stephen Lardieri

Sebastian Schoennenbeck

Manish M Anand

Jonathan Welch

Eshan Kemp

A computing system is provided, including a processor configured to identify a plurality of measurement sequences that implement a logic gate. Each measurement sequence may include a plurality of measurements of a quantum state of a topological quantum computing device. The processor may be further configured to determine a respective estimated total resource cost of each measurement sequence of the plurality of measurement sequences. The processor may be further configured to determine a first measurement sequence that has a lowest estimated total resource cost of the plurality of measurement sequences. The topological quantum computing device may be configured to implement the logic gate by applying the first measurement sequence to the quantum state.

Measurement sequence determination for quantum computing device

A quantum prediction AI system includes a quantum prediction circuit adapted to receive an input vector representing a subset of a time-sequential sequence; encode the input vector as a corresponding qubit register; apply a trained quantum circuit to the qubit register; and measure one or more qubits output from the quantum prediction circuit to infer a next data point in the series following the subset represented by the input vector.

Quantum bit prediction

A method of training a quantum computer employs quantum algorithms. The method comprises loading, into the quantum computer, a description of a quantum Boltzmann machine, and training the quantum Boltzmann machine according to a protocol, wherein a classification error is used as a metric for the protocol.

Quantum algorithms for supervised training of quantum boltzmann machines

This application concerns methods, apparatus, and systems for performing quantum circuit synthesis and/or for implementing the synthesis results in a quantum computer system. In certain example embodiments: a universal gate set, a target unitary described by a target angle, and target precision is received (input); a corresponding quaternion approximation of the target unitary is determined; and a quantum circuit corresponding to the quaternion approximation is synthesized, the quantum circuit being over a single qubit gate set, the single qubit gate set being realizable by the given universal gate set for the target quantum computer architecture.

Method and system for approximate quantum circuit synthesis using quaternion algebra

A Probabilistic Quantum Circuit with Fallback (PQFs) is composed as a series of circuit stages that are selected to implement a target unitary. A final stage is conditioned on unsuccessful results of all the preceding stages as indicated by measurement of one or more ancillary qubits. This final stage executes a fallback circuit that enforces deterministic execution of the target unitary at a relatively high cost (mitigated by very low probability of the fallback). Specific instances of general PQF synthesis method and are disclosed with reference to the specific Clifford+T, Clifford+V and Clifford+&#x3c0;/12 bases. The resulting circuits have expected cost in log(1/&#x3b5;)+O(log(log(1/&#x3b5;)))+const wherein b is specific to each basis. The three specific instances of the synthesis have polynomial compilation time guarantees.

Efficient synthesis of probabilistic quantum circuits with fallback

Certain ensembles of metapletic anyons allow for topologically protected encoding and processing of quantum information. Such processing is done by sequences of gates (circuits) drawn from a certain basis of unitary metaplectic gates. A subject unitary operator required for the desired processing can be approximated to any desired precision by a circuit that has to be effectively and efficiently synthesized on a classical computer. Synthesis methods use unitary reflection operators that can be represented either exactly or by ancilla-assisted approximation over the basis of metaplectic gates based on cost-optimizing determinations made by the synthesis algorithm.

Efficient topological compilation for metaplectic anyon model

Ripple-carry and carry look-ahead adders for ternary addition and other operations include circuits that produce carry values or carry status indicators that can be stored on qutrit registers associated with input values to be processed. Inverse carry circuits are situated to reverse operations associated with the production of carry values or carry status indicators, and restored values are summed with corresponding carry values to produce ternary sums.

Method and system for efficient quantum ternary arithmetic

Methods are provided for exact synthesis of unitaries for qudit and multi-qubit systems. In addition, state preparation methods are provided. The syntheses produce circuits that have lowest cost for a given cost function.

Exact quantum circuits and circuit syntheses for qudit and multiple qubit circuits

Quantum circuits and circuit designs are based on factorizations of diagonal unitaries using a phase context. The cost/complexity of phase sparse/phase dense approximations is compared, and a suitable implementation is selected. For phase sparse implementations in the Clifford+T basis, required entangling circuits are defined based on a number of occurrences of a phase in the phase context in a factor of the diagonal unitary.

Method for efficient implementation of diagonal operators over clifford+T basis

Repeat-Until-Success (RUS) circuits are compiled in a Clifford+T basis by selecting a suitable cyclotomic integer approximation of a target rotation so that the rotation is approximated within a predetermined precision. The cyclotomic integer approximation is randomly modified until a modified value can be expanded into a single-qubit unitary matrix by solving one or more norm equations. The matrix is then expanded into a two-qubit unitary matrix of special form, which is then decomposed into an optimal two-qubit Clifford+T circuit. A two-qubit RUS circuit using a primary qubit and an ancillary qubit is then obtained based on the latter decomposition. An alternate embodiment is disclosed that keeps the total T-depth of the derived circuit small using at most 3 additional ancilla qubits. Arbitrary unitary matrices defined over the cyclotomic field of 8th roots of unity are implemented with RUS circuits.

Efficient synthesis of repeat-until-success circuits in clifford + T basis

Methods and systems transform a given single-qubit quantum circuit expressed in a first quantum-gate basis into a quantum-circuit expressed in a second, discrete, quantum-gate basis. The discrete quantum-gate basis comprises standard, implementable quantum gates. The given single-qubit quantum circuit is expressed as a normal representation. The normal representation is generally compressed, in length, with respect to equivalent non-normalized representations. The method and systems additionally can map normal representations to canonical-form representations, which are generally further compressed, in length, with respect to normal representations.

Method and system for decomposing single-qubit quantum circuits into a discrete basis

Methods for compiling single-qubit quantum gates into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model are based on a probabilistically polynomial algorithm that, given a single-qubit unitary gate and a desired target precision, outputs a braid pattern that approximates the unitary to desired precision and has a length that is asymptotically optimal (for a circuit with such property). Single-qubit unitaries that can be implemented exactly by a Fibonacci anyon braid pattern are classified, and associated braid patterns are obtained using an iterative procedure. Target unitary gates that are not exactly representable as braid patterns are first approximated to a desired precision by a unitary that is exactly representable, then a braid pattern associated with the latter is obtained.

Method and system for efficient decomposition of single-qubit quantum gates into Fibonacci anyon braid circuits

A target quantum circuit expressed in a first quantum gate basis may be transformed into a corresponding quantum circuit expressed in a second quantum gate basis, which may be a universal set of gates such as a V gate basis set. The target quantum circuit may be expressed as a linear combination of quantum gates. The linear combination of quantum gates may be mapped to a quaternion. The quaternion may be factorized, based at least in part on an amount of precision between the target quantum circuit and the corresponding quantum circuit expressed in the second quantum gate basis, into a sequence of quaternion factors. The sequence of quaternion factors may be mapped into a sequence of quantum gates of the second quantum gate basis, where the sequence of sequence of quantum gates is the corresponding quantum circuit.

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Redmond, WA, United States of America

Alexei V Bocharov