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).

Initialization, execution and readout

The qubits are initialized in the ground state at the start of each shot. The single-qubit 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.