Implementing qubit gates using phase-shifted microwave pulses

A method for applying a gate sequence of quantum gates to a qubit comprising:

• implementing a first quantum gate in the gate sequence by applying a first sequence of phase-shifted pulses to the qubit;
• and
• after applying the first quantum gate, implementing a second quantum gate in the gate sequence by applying a second sequence of phase-shifted pulses to the qubit, an additional rotation introduced by the implementation of the second quantum gate being independent of the implementation of the first quantum gate, a pulse in the second sequence configured to implement:
• a virtual Z gate having a first rotation angle;
• an X gate having a second rotation angle;
• and
• the virtual Z gate having a negative of the first rotation angle.

A method for implementing a composition of a two-qubit gate and the tensor product of a first single-qubit gate and a second single-qubit gate, comprising:

• applying a first sequence of phase-shifted pulses to a first qubit to implement the first single-qubit gate, the implementation of the first single-qubit gate introducing an additional rotation phase shift;
• applying a second sequence of phase-shifted pulses to a second qubit to implement a product of the additional rotation and the second single-qubit gate;
• and
• applying the two-qubit gate to the first qubit and the second qubit to obtain a phase-shifted version of the composition of the two-qubit gate and the tensor product of the first single-qubit gate and the second single-qubit gate.

A non-transitory computer-readable medium containing instructions that are executable by a processor of a quantum controller coupled to a qubit to cause the quantum controller to perform operations for applying a single-qubit quantum gate to the qubit, the single-qubit quantum gate having a unitary specifiable by a first, a second, and a third real parameter, the operations comprising:

• applying to the qubit a sequence of phase-shifted Pauli gates, each phase-shifted Pauli gate in the sequence having a rotation angle and a phase shift;
• and
• wherein the first, second, and third real parameters correspond to:
• a rotation angle and the phase shifts in the sequence;
• or
• the phase shifts in the sequence.