Not all quantum devices can realize all quantum gates. In practice this is not an issue since any quantum gate can be constructed from a series of universal quantum gates provided the device can execute them. The downside is that the combination of gates takes longer to perform and hence introduces a higher error rate.
For example, on spin-qubit devices the CNOT gate is not directly available. We can however realize this gate by a combination of single qubit rotations and a CZ gate. In this section the restrictions of Spin-2 are specified.
Topology and allowed gate set
Each of the quantum processors has a specific topology the way the qubits are connected) and a specific allowed gate set (supported qubit operations).
Spin-2 has two qubits (q0, q1) which are connected. You can execute the following single-and two-qubit gates on this system (native operations are given in bold, other operations are decomposed using specific decomposition rules for this quantum processor):
- All single-qubit operations in cQASM
- All two-qubit gates in cQASM
- All measure commands
- All prep/initialization commands
More specific, the following operations and commands are not allowed
- Binary controlled operations
Spin-2 basically has five operations that can be executed directly on the chip (native operations):
- Initialization of the qubits in the ground state with
- single-qubit rotation around the z-axis with
Rz(angle), executed as a virtual operation
- a single-qubit rotation around the x-axis with
- measurement of the qubits in z using
The compiler/transpiler decomposes all other allowed operations into this native gate set using the following methods:
- Two-qubit operations
CRkare decomposed to
CZoperations in combination with single-qubit operations
- Sequences of single-qubit operations on one qubit are decomposed using the method described in McKay - Efficient Z-Gates for Quantum Computing resulting in a sequence of five single-qubit operations, namely three
Rz(..)operations with different angles of rotation and two
- Consecutive operations which result in identity are removed from the algorithm (such as two consecutive
Initialization, execution and readout
The qubits are initialized in the ground state at the start of each shot.
Rx() operations are executed by sending a microwave pulse of the required duration, amplitude and phase to the qubits. The
Rz() operation is executed by a phase-update (virtual Z-gate) of the the microwave signals. The two-qubit
CZ operation is executed by a calibrated exchange interaction between the qubits which results in a controlled 180 degree phase change of the |11> state of the qubits. Single-qubit operations on two different qubits are executed in sequence, not in parallel. At the end of the algorithm both qubits are measured.