Customized quantum gate¶

The numqi.sim submodule supports customized quantum gate, even the not-unitary "gate"

In [1]:

import numpy as np

try:
    import numqi
except ImportError:
    %pip install numqi
    import numqi

import numpy as np try: import numqi except ImportError: %pip install numqi import numqi

Let's define a measurement "gate"

In [2]:

class MeasureGate:
    def __init__(self, index, seed=None, name='measure'):
        self.kind = 'custom'
        self.name = name
        self.requires_grad = False
        index = numqi.utils.hf_tuple_of_int(index)
        assert all(x==y for x,y in zip(sorted(index),index)), 'index must be sorted'
        self.index = index
        self.np_rng = numqi.random.get_numpy_rng(seed)

        self.bitstr = None
        self.probability = None

    def forward(self, q0):
        self.bitstr,self.probability,q1 = numqi.sim.state.measure_quantum_vector(q0, self.index, self.np_rng)
        return q1

class MeasureGate: def __init__(self, index, seed=None, name='measure'): self.kind = 'custom' self.name = name self.requires_grad = False index = numqi.utils.hf_tuple_of_int(index) assert all(x==y for x,y in zip(sorted(index),index)), 'index must be sorted' self.index = index self.np_rng = numqi.random.get_numpy_rng(seed) self.bitstr = None self.probability = None def forward(self, q0): self.bitstr,self.probability,q1 = numqi.sim.state.measure_quantum_vector(q0, self.index, self.np_rng) return q1

The function numqi.sim.state.measure_quantum_vector is used to measure a quantum vector on some of qubits. After the measurement, thoes qubits will be collapsed to the computational basis state self.bitstr according to the probability distribution of the measurement result self.probablity. The final quantum state will become q1.

Actually, numqi.sim has builtin measurement operation, let's name this newer one as measure_custom().

In [3]:

circ = numqi.sim.Circuit()
circ.register_custom_gate('measure_custom', MeasureGate)
circ.H(0)
circ.cnot(0, 1)
gate_measure = circ.measure_custom(index=(0,1))

circ = numqi.sim.Circuit() circ.register_custom_gate('measure_custom', MeasureGate) circ.H(0) circ.cnot(0, 1) gate_measure = circ.measure_custom(index=(0,1))

Above, we make a Bell state and measure it.

In [4]:

q0 = numqi.sim.state.new_base(num_qubit=2)
q1 = circ.apply_state(q0)
print(f'{gate_measure.bitstr=}')
print(f'{gate_measure.probability=}')
print(f'{q1=}')

q0 = numqi.sim.state.new_base(num_qubit=2) q1 = circ.apply_state(q0) print(f'{gate_measure.bitstr=}') print(f'{gate_measure.probability=}') print(f'{q1=}')

gate_measure.bitstr=[1, 1]
gate_measure.probability=array([0.5, 0. , 0. , 0.5])
q1=array([0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j])

As expected, only 00 and 11 are possible. Let's make a GHZ state.

In [5]:

circ = numqi.sim.Circuit()
circ.register_custom_gate('measure_custom', MeasureGate)
circ.H(0)
circ.cnot(0, 1)
circ.cnot(1, 2)
gate_measure = circ.measure_custom(index=(0,1,2))

q0 = numqi.sim.state.new_base(num_qubit=3)
q1 = circ.apply_state(q0)
print(f'{gate_measure.bitstr=}')
print(f'{gate_measure.probability=}')
print(f'{q1=}')

circ = numqi.sim.Circuit() circ.register_custom_gate('measure_custom', MeasureGate) circ.H(0) circ.cnot(0, 1) circ.cnot(1, 2) gate_measure = circ.measure_custom(index=(0,1,2)) q0 = numqi.sim.state.new_base(num_qubit=3) q1 = circ.apply_state(q0) print(f'{gate_measure.bitstr=}') print(f'{gate_measure.probability=}') print(f'{q1=}')

gate_measure.bitstr=[1, 1, 1]
gate_measure.probability=array([0.5, 0. , 0. , 0. , 0. , 0. , 0. , 0.5])
q1=array([0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j])

One can also measure many times, and one can insert quantum circuits between these measurements.

In [6]:

num_qubit = 5
num_layer = 3
measure_gate_list = []
circ = numqi.sim.Circuit()
circ.register_custom_gate('measure_custom', MeasureGate)
np_rng = np.random.default_rng()

for _ in range(num_layer):
    for ind0 in range(num_qubit):
        circ.u3(ind0, args=np_rng.uniform(0, 2*np.pi, size=3))
    tmp0 = list(range(0, num_qubit-1, 2)) + list(range(1, num_qubit-1, 2))
    for ind0 in tmp0:
        circ.cnot(ind0, ind0+1)
    measure_gate_list.append(circ.measure_custom(index=(0,1)))

q0 = numqi.sim.state.new_base(num_qubit)
q1 = circ.apply_state(q0)
print(np.linalg.norm(q1)) #1
print('probability:', measure_gate_list[0].probability)
for ind0,gate_i in enumerate(measure_gate_list):
    print(f'[gate-{ind0}] bitstr:', gate_i.bitstr)

num_qubit = 5 num_layer = 3 measure_gate_list = [] circ = numqi.sim.Circuit() circ.register_custom_gate('measure_custom', MeasureGate) np_rng = np.random.default_rng() for _ in range(num_layer): for ind0 in range(num_qubit): circ.u3(ind0, args=np_rng.uniform(0, 2*np.pi, size=3)) tmp0 = list(range(0, num_qubit-1, 2)) + list(range(1, num_qubit-1, 2)) for ind0 in tmp0: circ.cnot(ind0, ind0+1) measure_gate_list.append(circ.measure_custom(index=(0,1))) q0 = numqi.sim.state.new_base(num_qubit) q1 = circ.apply_state(q0) print(np.linalg.norm(q1)) #1 print('probability:', measure_gate_list[0].probability) for ind0,gate_i in enumerate(measure_gate_list): print(f'[gate-{ind0}] bitstr:', gate_i.bitstr)

1.0
probability: [2.68804750e-01 7.03602687e-06 1.91385206e-05 7.31169075e-01]
[gate-0] bitstr: [1, 1]
[gate-1] bitstr: [1, 1]
[gate-2] bitstr: [1, 0]