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Softwareq Inc.

Priyanka Mukhopadhyay

Michele Mosca

Vlad Gheorghiu

The present application recognizes the problem of reducing the CNOT-count in Clifford+T circuits on connectivity constrained architectures. Here, one can 'slice' the circuit at the position of Hadamard (H) gates and “build” the intermediate portions. Two kinds of partitioning are evaluated, namely: (i) a simple method of partitioning the gates of the input circuit based on the locality of H gates, and (ii) a second method of partitioning the phase polynomial of the input circuit. The intermediate {CNOT, T} sub-circuits can be synthesized using Steiner trees, similar to the work of Nash, Gheorghiu, Mosca [NGM20] and Kissinger, de Griend [KdG19]. The following algorithms have certain procedural differences that also help to further reduce the CNOT-count. The performances of the algorithms are compared while mapping different benchmark circuits as well as random circuits to some popular architectures like 9-qubit square grid, 16-qubit square grid, Rigetti 16qubit Aspen, 16-qubit IBM QX5, 20-qubit IBM Tokyo.

System and method for reducing CNOT count in Clifford+T circuits on connectivity constrained architectures

A method is provided for synthesizing quantum circuits while reducing the T-count, comprising, for a plurality of qubits: determining a target unitary and executing a set of candidate operations W with a single T gate and computing a specific function f of U Wkeeping the values of W that correspond to specific multiplicities such that after the first collection of W operators is selected a collection of unitaries U Wis determined to consider in the next round to build a tree. A method of synthesizing quantum circuits while reducing the T-depth is also provided, comprising, for a plurality of qubits: determining a target unitary and execute a set of candidate operations W with T depth of one and computing a specific function f of U W, keeping the values of W that correspond to specific multiplicities such that after the first collection of W operators is selected a collection of unitaries U Wis determined to consider in the next round to build a tree. A method of re-synthesizing quantum circuits while reducing T-depth is also provided, comprising, for a plurality of qubits considering all cluster sizes up to a maximum sized cluster, and continuing recursively.

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Waterloo, Canada

Priyanka Mukhopadhyay