Gate

Quantum gate is expressed as Gate. This holds indices of target and control qubits, types of Gate (ex: X, H, RY, DenseMatrix…), and other properties. Properties of a Gate differ by its type. To access these properties, down-casting to specific class is required. (See Downcast to GateType-specific function)

Unlike Qulacs, Gate objects are immutable. You have to pass all properties when generating the gate. This change enables us to provide fast and safe copy.

Creating Gate

Gate type instances are created from factory functions in gate.

from scaluq.default.f64.gate import X, Swap, RX, DenseMatrix
import math
import numpy as np

x = X(0) # X gate with target 0
swap = Swap(2, 4) # Swap gate with target 2, 4
rx = RX(1, math.pi/4) # RX(pi/4) gate with target 1

mat = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
# DenseMatrix gate with certain unitary matrix and target 1,2
mat_gate = DenseMatrix([1, 2], mat, is_unitary=True)

For detail usage of creating each types of gate, see API document of gate module.

You can add arbitrary number of control qubits to almost all types of Gates. Control-values can be passed. All control-values are set to \(1\) when omitted.

from scaluq.default.f64.gate import H

ch = H(0, controls=[1]) # H(0) applied when 1st qubit is |1>
cch = H(0, controls=[1, 2]) # H(0) applied when 1st qubit is |1> and 2nd qubit is |1>
cch = H(0, controls=[1, 2], control_values=[1, 0]) # H(0) applied when 1st qubit is |1> and 2nd qubit is |0>

Getting properties of Gate.

General properties are simply gotten by using methods of Gate class.

from scaluq.default.f64.gate import H

cch = H(0, controls=[1, 2], control_values=[1, 0])
print(cch.target_qubit_list()) # [0]
print(cch.control_qubit_list()) # [1, 2]
print(cch.control_value_list()) # [1, 0]

Matrix representation is showed by get_matrix. Unlike Qulacs, control qubits are ignored.

from scaluq.default.f64.gate import H

cch = H(0, controls=[1, 2], control_values=[1, 0])
print(cch.get_matrix())
'''
[[ 0.70710678+0.j  0.70710678+0.j]
 [ 0.70710678+0.j -0.70710678+0.j]]
'''

Inverse gate is gotten by get_inverse. If inverse gate is completely same as the original gate, the gate is shallow-copied.

from scaluq.default.f64.gate import H, S

h = H(0)
h_inv = h.get_inverse()
print(h_inv)
'''
Gate Type: H
  Target Qubits: {0}
  Control Qubits: {}
  Control Value: {}
'''
s = S(1)
s_inv = s.get_inverse()
print(s_inv)
'''
Gate Type: Sdag
  Target Qubits: {0}
  Control Qubits: {}
  Control Value: {}
'''

Downcast to GateType-specific function

To get GateType-specific properties, downcast to specific class is required.

Scaluq Gate is implemented by tag-based polymorphism. Each Gate has detailed type as enum GateType. You can get type of Gate by get_type.

There is a specific Gate class for each type. You can use functions of these specific types by downcast.

from scaluq import GateType
from scaluq.default.f64 import RXGate
from scaluq.default.f64.gate import RX
import math

rx = RX(0, math.pi/4)
assert rx.gate_type() == GateType.RX
rx = RXGate(rx) # downcast to RXGate class
print(rx.angle())

Since this inheritance relation is not shown in language layer, explicit upcast is required when you pass the Gate as Gate type.

from scaluq.default.f64 import Gate, RXGate, Circuit
from scaluq.default.f64.gate import RX
import math

rx = RXGate(RX(0, math.pi/4))
circuit = Circuit()
rx = Gate(rx) # omitting this downcast causes error on next line
circuit.add_gate(rx)

Apply to StateVector

Gate can be applied to StateVector object by function update_quantum_state. Indices of Target/control qubits of Gate are corresponded to that of StateVector.

from scaluq.default.f64 import StateVector
from scaluq.default.f64.gate import H, CX

h0 = H(0)
cx01 = CX(0, 1)
state = StateVector(2)
print(state.get_amplitudes()) # [(1+0j), 0j, 0j, 0j]
h0.update_quantum_state(state)
print(state.get_amplitudes()) # [(0.7071067811865476+0j), (0.7071067811865476+0j), 0j, 0j]
cx01.update_quantum_state(state)
print(state.get_amplitudes()) # [(0.7071067811865476+0j), 0j, 0j, (0.7071067811865476+0j)]

Merge two Gates

You can merge two Gates by merge_gate The type of result gate is flexible.

from scaluq.default.f64.gate import X, Y, RX, RY, RZ, S
from scaluq.default.f64 import merge_gate
import math

def print_merge_result(gate1, gate2):
    mgate, phase = merge_gate(gate1, gate2)
    print("Gate:")
    print(mgate.to_string())
    print("Phase:", phase)

print_merge_result(X(0), X(0)) # Gate=I(), Phase=0
print_merge_result(X(0), Y(0)) # Gate=Z(0), Phase=-pi/2
print_merge_result(RZ(0, -math.pi/8*3), S(0)) # Gate=U1(0, math.pi/8), Phase=math.pi/16*3)
print_merge_result(RX(2, math.pi/6, controls=[1]), RY(2, math.pi/3, controls=[0, 1])) # gate=DenseMatrix([0,2], [...], controls=[1], Phase=0)