Microsoft Technology Licensing, LLC

Socpra Sciences Et Genie S.e.c.

David Poulin

David B Wecker

Matthew Benjamin Hastings

Jeongwan Haah

Matthias Troyer

Jessica Lemieux

Andrew J Ferris

Bettina Heim

Example circuit implementations of Szegedy's quantization of the Metropolis-Hastings walk are presented. In certain disclosed embodiments, a quantum walk procedure of a Markov chain Monte Carlo simulation is implemented in which a quantum move register is reset at every step in the quantum walk. In further embodiments, a quantum walk procedure of a Markov chain Monte Carlo simulation is implemented in which an underlying classical walk is obtained using a Metropolis-Hastings rotation or a Glauber dynamics rotation. In some embodiments, a quantum walk procedure is performed in the quantum computing device to implement a Markov Chain Monte Carlo method; during the quantum walk procedure, an intermediate measurement is obtained; and a rewinding procedure of one or more but not all steps of the quantum walk procedure is performed if the intermediate measurement produces an incorrect outcome.

Quantum-walk-based algorithm for classical optimization problems

A method for determining the n best positions of frozen bits in a channel decoder for a noisy communication channel. A decoding method and decoding processing unit for implementing the channel having frozen bits at the n worst positions. A method and system that iteratively, for each bit i from the n bits, determines a probability vector for the bit i by traversing a logical graph using contraction identities simplified to specific values, indexes the specific values from the contraction identities newly computed during the determination of the probability vector for subsequent reference during a following iteration based on corresponding contraction identities, fixes the bit i from the probability vector and moving to bit i+1 until all n bits are fixed.

Generalized polar codes

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

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.

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Sherbrooke, Canada

David Poulin