# Spin-2: Operational specifics

## 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 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
• X, Y, Z, I
• H
• S, Sdag, T, Tdag
• X90, Y90, mX90, mY90
• Rx(angle), Ry(angle), Rz(angle)
• All two-qubit 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

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 prep_z
• single-qubit rotation around the z-axis with Rz(angle), executed as a virtual operation
• a single-qubit rotation around the x-axis with Rx(angle)
• two-qubit 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:

1. Two-qubit operations CNOT, SWAP, CR and CRk are decomposed to CZ operations in combination with single-qubit operations
2. 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 Rx(pi/2) operations.
3. Consecutive operations which result in identity are removed from the algorithm (such as two consecutive CZ operations).