A method and system for performing a controlled-unitary gate between qubits

Abstract

There is provided a method of performing a data-data controlled-unitary gate between a first data qubit as control in a first basis (Formula (I)) and a second data qubit as target, and wherein the unitary gate of the controlled-unitary matrix is defined by a unitary matrix U, the method comprising the following operations: (i) providing the first data qubit in the first basis (Formula (I)), the second data qubit, and an ancilla qubit, wherein each data qubit is connected to the ancilla qubit and wherein the first and second data qubits are not directly connected to each other, wherein the first data, second data, and ancilla qubits are all either (A) physical qubits each hosted in a respective physical mode of one or more physical resonators or (B) logical qubits each hosted by a plurality of physical qubits which are configured to perform an error correction code to encode the respective logical qubits; (ii) configuring the ancilla qubit to be able to perform a controlled-unitary gate with either of the first and second data qubits. The method further comprises the following operations: (iii) performing a first one-qubit state teleportation of the first data qubit to the ancilla qubit from the first basis (Formula (I)) to a second basis (Formula (II)) by: (a) preparing a two-qubit state entangling the first data qubit and the ancilla qubit, and (b) subsequently performing a measurement-based uncomputation of the first data qubit; (iv) performing an ancilla-data controlled-unitary gate between the ancilla qubit as control in the second basis (Formula (II)) and the second data qubit as target; (vi) performing a second one-qubit state teleportation of the ancilla qubit to the first data qubit from the basis (Formula (II)) to the basis (Formula (I)) by: (a) preparing a second two-qubit state entangling the ancilla qubit and the first data qubit, and (b) subsequently performing a measurement-based uncomputation of the ancilla qubit. Operation (iv) is performed at any time before operation (vi)(b), operation (vi)(a) is performed after operation (iii)(b), and wherein (I) the unitary gate of the ancilla-data controlled-unitary gate is defined by the unitary matrix U, or (II) the unitary gate of the ancilla-data controlled-unitary gate is defined by another unitary matrix V and the method comprises a sequence of one or more gates that, in combination with the unitary V-gate of the ancilla-data controlled-unitary gate, performs the function of applying the unitary U-gate on the second data qubit. There is also provided a quantum system, a computer program product, and a computer-readable medium.

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