Introduction
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 spinqubit 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 Spin2 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).
Spin2 has two qubits (q0, q1) which are connected. You can execute the following singleand twoqubit gates on this system (native operations are given in bold, other operations are decomposed using specific decomposition rules for this quantum processor):
 All singlequbit operations in cQASM
X
,Y
,Z
,I
H
S
,Sdag
,T
,Tdag
X90
,Y90
,mX90
,mY90
Rx(angle)
,Ry(angle)
,Rz(angle)
 All twoqubit gates in cQASM
CZ
,CNOT
,SWAP
,CR
,CRk
 All measure commands
measure_z
,measure
,measure_all
,measure_x
,measure_y
 All prep/initialization commands
prep_z
,prep_y
,prep_x
More specific, the following operations and commands are not allowed

Display

Display_binary

Not
 Binary controlled operations
c

Toffoli
Gate decompositions
Spin2 basically has five operations that can be executed directly on the chip (native operations):
 Initialization of the qubits in the ground state with
prep_z
 singlequbit rotation around the zaxis with
Rz(angle)
, executed as a virtual operation  a singlequbit rotation around the xaxis with
Rx(angle)
 twoqubit
CZ
gate  measurement of the qubits in z using
measure_z
The compiler/transpiler decomposes all other allowed operations into this native gate set using the following methods:
 Twoqubit operations
CNOT
,SWAP
,CR
andCRk
are decomposed toCZ
operations in combination with singlequbit operations  Sequences of singlequbit operations on one qubit are decomposed using the method described in McKay  Efficient ZGates for Quantum Computing resulting in a sequence of five singlequbit operations, namely three
Rz(..)
operations with different angles of rotation and twoRx(pi/2)
operations.  Consecutive operations which result in identity are removed from the algorithm (such as two consecutive
CZ
operations).
Initialization, execution and readout
The qubits are initialized in the ground state at the start of each shot.
The singlequbit 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 phaseupdate (virtual Zgate) of the the microwave signals. The twoqubit 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. Singlequbit operations on two different qubits are executed in sequence, not in parallel. At the end of the algorithm both qubits are measured.