---
title: U2Register (latest version)
description: API reference for samplomatic.virtual_registers.U2Register in the latest version of samplomatic
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/samplomatic/auto/virtual-registers-u-2-register
---

# U2Register

*class* `samplomatic.virtual_registers.U2Register(virtual_gates: ndarray)`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/virtual_registers/u2_register.py#L25-L115)

Bases: [`GroupRegister`](/docs/api/samplomatic/auto/virtual-registers-group-register "samplomatic.virtual_registers.group_register.GroupRegister")

Virtual register of 2x2 Unitary matrices.

The equality method of this class is overridden to ignore global phase.

**Attributes Summary**

|                                                                                                                                                 |                                                                   |
| ----------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------- |
| [`CONVERTABLE_TYPES`](#samplomatic.virtual_registers.U2Register.CONVERTABLE_TYPES "samplomatic.virtual_registers.U2Register.CONVERTABLE_TYPES") | Valid arguments for `convert_to()`.                               |
| [`GATE_SHAPE`](#samplomatic.virtual_registers.U2Register.GATE_SHAPE "samplomatic.virtual_registers.U2Register.GATE_SHAPE")                      | The array shape of any single virtual gate.                       |
| [`SUBSYSTEM_SIZE`](#samplomatic.virtual_registers.U2Register.SUBSYSTEM_SIZE "samplomatic.virtual_registers.U2Register.SUBSYSTEM_SIZE")          | The number of qubits each virtual gate acts on.                   |
| [`TYPE`](#samplomatic.virtual_registers.U2Register.TYPE "samplomatic.virtual_registers.U2Register.TYPE")                                        | The group name in 1-1 correspondence with this virtual gate type. |

**Methods Summary**

|                                                                                                                                                                                        |                                                                                    |
| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------- |
| [`identity`](#samplomatic.virtual_registers.U2Register.identity "samplomatic.virtual_registers.U2Register.identity")(num\_subsystems, num\_samples)                                    | Instantiate a new register of identity virtual gates.                              |
| [`inplace_multiply`](#samplomatic.virtual_registers.U2Register.inplace_multiply "samplomatic.virtual_registers.U2Register.inplace_multiply")(other\[, subsystem\_idxs])                | Inplace-multiply each virtual gate with the corresponding element of `other`.      |
| [`invert`](#samplomatic.virtual_registers.U2Register.invert "samplomatic.virtual_registers.U2Register.invert")()                                                                       | Return a new virtual register that inverts each virtual gate.                      |
| [`left_inplace_multiply`](#samplomatic.virtual_registers.U2Register.left_inplace_multiply "samplomatic.virtual_registers.U2Register.left_inplace_multiply")(other\[, subsystem\_idxs]) | Left inplace-multiply each virtual gate with the corresponding element of `other`. |
| [`left_multiply`](#samplomatic.virtual_registers.U2Register.left_multiply "samplomatic.virtual_registers.U2Register.left_multiply")(other\[, subsystem\_idxs])                         | Left multiply each virtual gate with the corresponding element of `other`.         |
| [`multiply`](#samplomatic.virtual_registers.U2Register.multiply "samplomatic.virtual_registers.U2Register.multiply")(other\[, subsystem\_idxs])                                        | Multiply each virtual gate with the corresponding element of `other`.              |

**Attributes Documentation**

### CONVERTABLE\_TYPES

Type: [`frozenset`](https://docs.python.org/3/builtins/stdtypes.html#frozenset)\[[`VirtualType`](/docs/api/samplomatic/auto/virtual-registers-virtual-type "samplomatic.virtual_registers.virtual_type.VirtualType")]

Default value: `frozenset({VirtualType.U2})`

Valid arguments for `convert_to()`.

### GATE\_SHAPE

Type: [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple)\[[`int`](https://docs.python.org/3/builtins/functions.html#int), ...]

Default value: `(2, 2)`

The array shape of any single virtual gate.

### SUBSYSTEM\_SIZE

Type: [`int`](https://docs.python.org/3/builtins/functions.html#int)

Default value: `1`

The number of qubits each virtual gate acts on.

### TYPE

Type: [`VirtualType`](/docs/api/samplomatic/auto/virtual-registers-virtual-type "samplomatic.virtual_registers.virtual_type.VirtualType")

Default value: `'u2'`

The group name in 1-1 correspondence with this virtual gate type.

**Methods Documentation**

### identity

*classmethod* `identity(num_subsystems, num_samples)`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/virtual_registers/u2_register.py#L37-L41)

Instantiate a new register of identity virtual gates.

### inplace\_multiply

`inplace_multiply(other, subsystem_idxs: list[int] | slice = slice(None, None, None))`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/virtual_registers/u2_register.py#L59-L71)

Inplace-multiply each virtual gate with the corresponding element of `other`.

**Parameters**

- **other** – Another virtual register of the same type.
- **subsystem\_idxs** – The indices of the subsystems to multiply, in self.

**Raises**

[**VirtualGateError**](/docs/api/samplomatic/auto/exceptions-virtual-gate-error "samplomatic.exceptions.VirtualGateError") – When the shapes do not match.

### invert

`invert()`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/virtual_registers/u2_register.py#L105-L106)

Return a new virtual register that inverts each virtual gate.

### left\_inplace\_multiply

`left_inplace_multiply(other, subsystem_idxs: list[int] | slice = slice(None, None, None))`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/virtual_registers/u2_register.py#L89-L103)

Left inplace-multiply each virtual gate with the corresponding element of `other`.

**Parameters**

- **other** – Another virtual register of the same type.
- **subsystem\_idxs** – The indices of the subsystems to multiply, in self.

**Raises**

[**VirtualGateError**](/docs/api/samplomatic/auto/exceptions-virtual-gate-error "samplomatic.exceptions.VirtualGateError") – When the shapes do not match.

### left\_multiply

`left_multiply(other, subsystem_idxs: list[int] | slice = slice(None, None, None))`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/virtual_registers/u2_register.py#L73-L87)

Left multiply each virtual gate with the corresponding element of `other`.

**Parameters**

- **other** – Another virtual register of the same type.
- **subsystem\_idxs** – The indices of the subsystems to multiply, in self.

**Returns**

A new virtual register of the same type.

**Raises**

[**VirtualGateError**](/docs/api/samplomatic/auto/exceptions-virtual-gate-error "samplomatic.exceptions.VirtualGateError") – When the shapes do not match.

### multiply

`multiply(other, subsystem_idxs: list[int] | slice = slice(None, None, None))`

[GitHub](https://github.com/Qiskit/samplomatic/tree/main/samplomatic/virtual_registers/u2_register.py#L43-L57)

Multiply each virtual gate with the corresponding element of `other`.

**Parameters**

- **other** – Another virtual register of the same type.
- **subsystem\_idxs** – The indices of the subsystems to multiply, in self.

**Returns**

A new virtual register of the same type.

**Raises**

[**VirtualGateError**](/docs/api/samplomatic/auto/exceptions-virtual-gate-error "samplomatic.exceptions.VirtualGateError") – When the shapes do not match.