6534953321

Committed 16 Oct 2023 02:19PM UTC coverage: 35.674% (-22.7%) from 58.421%

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51.23

/waveforms/qlisp/simulator/simple.py

from concurrent.futures import process
import itertools
from functools import partial, reduce

import numpy as np

from .mat import U, fSim, make_immutable, rfUnitary

__matrix_of_gates = {}


def regesterGateMatrix(gate, mat, N=None, docs=''):
    if isinstance(mat, np.ndarray):
        mat = make_immutable(mat)
    if N is None:
        N = round(np.log2(mat.shape[0]))
    __matrix_of_gates[gate] = (mat, N, docs)


def gate_name(gate):
    if isinstance(gate, tuple):
        return gate_name(gate[0])
    elif isinstance(gate, str):
        return gate
    else:
        raise ValueError(f'Unexcept gate {gate}')


def gate2mat(gate):
    if isinstance(gate, str) and gate in __matrix_of_gates:
        return __matrix_of_gates[gate][:2]
    elif isinstance(gate, tuple) and gate[0] in __matrix_of_gates:
        if callable(__matrix_of_gates[gate[0]][0]):
            return __matrix_of_gates[gate[0]][0](
                *gate[1:]), __matrix_of_gates[gate[0]][1]
        else:
            raise ValueError(
                f"Could not call {gate[0]}(*{gate[1:]}), `{gate[0]}` is not callable."
            )
    elif gate_name(gate) == 'C':
        U, N = gate2mat(gate[1])
        ret = np.eye(2 * U.shape[0], dtype=complex)
        ret[U.shape[0]:, U.shape[0]:] = U
        return ret, N + 1
    else:
        raise ValueError(f'Unexcept gate {gate}')


def splite_at(l, bits):
    """将 l 的二进制位于 bits 所列的位置上断开插上0
    
    如 splite_at(int('1111',2), [0,2,4,6]) == int('10101010', 2)
    bits 必须从小到大排列
    """
    r = l
    for n in bits:
        mask = (1 << n) - 1
        low = r & mask
        high = r - low
        r = (high << 1) + low
    return r


def place_at(l, bits):
    """将 l 的二进制位置于 bits 所列的位置上
    
    如 place_at(int('10111',2), [0,2,4,5,6]) == int('01010101', 2)
    """
    r = 0
    for index, n in enumerate(bits):
        b = (l >> index) & 1
        r += b << n
    return r


def reduceSubspace(targets, N, inputMat, func, args):
    innerDim = 2**len(targets)
    outerDim = 2**(N - len(targets))

    targets = tuple(reversed([N - i - 1 for i in targets]))

    def index(targets, i, j):
        return splite_at(j, sorted(targets)) | place_at(i, targets)

    if len(inputMat.shape) == 1:
        for k in range(outerDim):
            innerIndex = [index(targets, i, k) for i in range(innerDim)]
            inputMat[innerIndex] = func(inputMat[innerIndex], *args)
    else:
        for k, l in itertools.product(range(outerDim), repeat=2):
            innerIndex = np.asarray(
                [[index(targets, i, k),
                  index(targets, j, l)]
                 for i, j in itertools.product(range(innerDim), repeat=2)]).T
            sub = inputMat[innerIndex[0], innerIndex[1]].reshape(
                (innerDim, innerDim))
            inputMat[innerIndex[0], innerIndex[1]] = func(sub, *args).flatten()
    return inputMat


def _apply_gate(gate, inputMat, unitary_process, qubits, N):
    U, n = gate2mat(gate)
    if len(qubits) == n and all(isinstance(qubit, int) for qubit in qubits):
        reduceSubspace(qubits, N, inputMat, unitary_process, (U, ))
    elif n == 1 and all(isinstance(qubit, int) for qubit in qubits):
        for qubit in qubits:
            reduceSubspace([qubit], N, inputMat, unitary_process, (U, ))
    elif len(qubits) == n and all(
            isinstance(qubit, [tuple, list]) for qubit in qubits):
        for qubit_tuple in zip(*qubits):
            reduceSubspace(qubit_tuple, N, inputMat, unitary_process, (U, ))
    else:
        raise ValueError(f'Unexcept gate {gate} and qubits {qubits}')


def _measure_process(rho):
    return np.array([[rho[0, 0], 0], [0, rho[1, 1]]])


def _reset_process(rho, p1):
    s0 = np.array([[rho[0, 0] + rho[1, 1], 0], [0, 0]])
    s1 = np.array([[0, 0], [0, rho[0, 0] + rho[1, 1]]])
    return (1 - p1) * s0 + p1 * s1


def _decohherence_process(rho, Gamma_t, gamma_t):
    rho00 = rho[0, 0] + rho[1, 1] * (1 - np.exp(-Gamma_t))
    rho11 = rho[1, 1] * np.exp(-Gamma_t)
    rho01 = rho[0, 1] * np.exp(-Gamma_t / 2 - gamma_t**2)
    rho10 = rho[1, 0] * np.exp(-Gamma_t / 2 - gamma_t**2)
    return np.array([[rho00, rho01], [rho10, rho11]])


def applySeq(seq, psi0=None):

    def _set_vector_to_rho(psi):
        psi = psi.reshape(-1, 1).conj() @ psi.reshape(1, -1)
        unitary_process = lambda psi, U: U @ psi @ U.T.conj()
        return psi, unitary_process, np.array([[1, 0], [0, 0]])

    if psi0 is None:
        psi = np.array([1, 0], dtype=complex)
        N = 1
    else:
        psi = psi0
        N = round(np.log2(psi.shape[0]))

    psi0 = np.array([1, 0])
    unitary_process = lambda psi, U: U @ psi

    if psi.ndim == 2:
        psi, unitary_process, psi0 = _set_vector_to_rho(psi)

    for gate, *qubits in seq:
        M = max(qubits)
        if M >= N:
            psi = reduce(np.kron, itertools.repeat(psi0, times=M - N + 1), psi)
            N = M + 1

        if gate_name(gate) in ['Barrier']:
            continue
        if gate_name(gate) in ['Delay']:
            if len(gate) == 2:
                continue
            else:
                if len(gate) == 3:
                    _, t, T1 = gate
                    Gamma_t = t / T1
                    gamma_t = 0
                else:
                    _, t, T1, Tphi = gate
                    Gamma_t = t / T1
                    gamma_t = t / Tphi
        if gate_name(gate) in ['Reset']:
            if isinstance(gate, tuple) and len(gate) == 2:
                _, p1 = gate
            else:
                p1 = 0.0
        if gate_name(gate) in ['Measure', 'Reset', 'Delay'] and psi.ndim == 1:
            psi, unitary_process, psi0 = _set_vector_to_rho(psi)

        if gate_name(gate) == 'Measure':
            reduceSubspace(qubits, N, psi, _measure_process, ())
        elif gate_name(gate) == 'Reset':
            reduceSubspace(qubits, N, psi, _reset_process, (p1, ))
        elif gate_name(gate) == 'Delay':
            reduceSubspace(qubits, N, psi, _decohherence_process,
                           (Gamma_t, gamma_t))
        else:
            _apply_gate(gate, psi, unitary_process, qubits, N)

    return psi


def seq2mat(seq, U=None):
    I = np.eye(2, dtype=complex)
    if U is None:
        U = np.eye(2, dtype=complex)
        N = 1
    else:
        N = round(np.log2(U.shape[0]))

    unitary_process = lambda U0, U: U @ U0

    for gate, *qubits in seq:
        M = max(qubits)
        if M >= N:
            U = reduce(np.kron, itertools.repeat(I, times=M - N + 1), U)
            N = M + 1
        if gate_name(gate) in ['Delay', 'Barrier']:
            continue
        if gate_name(gate) in ['Measure', 'Reset']:
            raise ValueError(
                'Measure and Reset must be applied to a state vector')
        else:
            _apply_gate(gate, U, unitary_process, qubits, N)
    return U


regesterGateMatrix('U', U, 1)
regesterGateMatrix('u1', lambda p: U(theta=0, phi=0, lambda_=p), 1)
regesterGateMatrix('u2', lambda phi, lam: U(np.pi / 2, phi, lam), 1)
regesterGateMatrix('u3', U, 1)
regesterGateMatrix('P', lambda p: U(theta=0, phi=0, lambda_=p), 1)
regesterGateMatrix('rfUnitary', rfUnitary, 1)
regesterGateMatrix('R', lambda phi: rfUnitary(np.pi / 2, phi), 1)
regesterGateMatrix('Rx', partial(rfUnitary, phi=0), 1)
regesterGateMatrix('Ry', partial(rfUnitary, phi=np.pi / 2), 1)
regesterGateMatrix('Rz', lambda p: U(theta=0, phi=0, lambda_=p), 1)
regesterGateMatrix('fSim', fSim, 2)
regesterGateMatrix('Cphase', lambda phi: fSim(theta=0, phi=phi), 2)

# one qubit
regesterGateMatrix('I', np.array([[1, 0], [0, 1]]))
regesterGateMatrix('X', np.array([[0, -1j], [-1j, 0]]))
regesterGateMatrix('Y', np.array([[0, -1], [1, 0]]))
regesterGateMatrix('X/2', np.array([[1, -1j], [-1j, 1]]) / np.sqrt(2))
regesterGateMatrix('Y/2', np.array([[1, -1], [1, 1]]) / np.sqrt(2))
regesterGateMatrix('-X/2', np.array([[1, 1j], [1j, 1]]) / np.sqrt(2))
regesterGateMatrix('-Y/2', np.array([[1, 1], [-1, 1]]) / np.sqrt(2))
regesterGateMatrix('Z', np.array([[1, 0], [0, -1]]))
regesterGateMatrix('S', np.array([[1, 0], [0, 1j]]))
regesterGateMatrix('-S', np.array([[1, 0], [0, -1j]]))
regesterGateMatrix('H', np.array([[1, 1], [1, -1]]) / np.sqrt(2))

# non-clifford
regesterGateMatrix('T',
                   np.array([[1, 0], [0, 1 / np.sqrt(2) + 1j / np.sqrt(2)]]))
regesterGateMatrix('-T',
                   np.array([[1, 0], [0, 1 / np.sqrt(2) - 1j / np.sqrt(2)]]))
regesterGateMatrix('W/2', rfUnitary(np.pi / 2, np.pi / 4))
regesterGateMatrix('-W/2', rfUnitary(-np.pi / 2, np.pi / 4))
regesterGateMatrix('V/2', rfUnitary(np.pi / 2, 3 * np.pi / 4))
regesterGateMatrix('-V/2', rfUnitary(-np.pi / 2, 3 * np.pi / 4))

# two qubits
regesterGateMatrix(
    'CZ', np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]]))
regesterGateMatrix(
    'Cnot', np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]))
regesterGateMatrix(
    'iSWAP',
    np.array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0], [0, 0, 0, 1]]))
regesterGateMatrix(
    'SWAP', np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]))
regesterGateMatrix(
    'CR',
    np.array([[1, 1j, 0, 0], [1j, 1, 0, 0], [0, 0, 1, -1j], [0, 0, -1j, 1]]) /
    np.sqrt(2))

# non-clifford
regesterGateMatrix(
    'SQiSWAP',
    np.array([[1, 0, 0, 0], [0, 1 / np.sqrt(2), 1j / np.sqrt(2), 0],
              [0, 1j / np.sqrt(2), 1 / np.sqrt(2), 0], [0, 0, 0, 1]]))

if __name__ == '__main__':
    # Porter-Thomas distribution

    def randomSeq(depth, N):
        seq = []
        for i in range(depth):
            for j in range(N):
                seq.append((np.random.choice(['X/2', 'Y/2', 'W/2']), j))
            for j in range(i % 2, N, 2):
                seq.append(('SQiSWAP', j, (j + 1) % N))
        return seq

    p = []
    # run 1000 random circuit on 6 qubits
    for i in range(1000):
        print('    ', i, end='')
        seq = randomSeq(50, 6)
        psi = applySeq(seq)
        p.extend(list(np.abs(psi)**2))
        print('    ', i)
    p = np.asarray(p)

    # plot distribution of probabilities
    N = 2**6
    y, x = np.histogram(N * p, bins=50, density=True)

    import matplotlib.pyplot as plt

    plt.semilogy((x[:-1] + x[1:]) / 2, y)
    plt.show()

1	from concurrent.futures import process	9✔
2	import itertools	9✔
3	from functools import partial, reduce	9✔
4
5	import numpy as np	9✔
6
7	from .mat import U, fSim, make_immutable, rfUnitary	9✔
8
9	__matrix_of_gates = {}	9✔
10
11
12	def regesterGateMatrix(gate, mat, N=None, docs=''):	9✔
13	if isinstance(mat, np.ndarray):	9✔
14	mat = make_immutable(mat)	9✔
15	if N is None:	9✔
16	N = round(np.log2(mat.shape[0]))	9✔
17	__matrix_of_gates[gate] = (mat, N, docs)	9✔
18
19
20	def gate_name(gate):	9✔
21	if isinstance(gate, tuple):	9✔
22	return gate_name(gate[0])	×
23	elif isinstance(gate, str):	9✔
24	return gate	9✔
25	else:
26	raise ValueError(f'Unexcept gate {gate}')	×
27
28
29	def gate2mat(gate):	9✔
30	if isinstance(gate, str) and gate in __matrix_of_gates:	9✔
31	return __matrix_of_gates[gate][:2]	9✔
32	elif isinstance(gate, tuple) and gate[0] in __matrix_of_gates:	×
33	if callable(__matrix_of_gates[gate[0]][0]):	×
34	return __matrix_of_gates[gate[0]][0](	×
35	*gate[1:]), __matrix_of_gates[gate[0]][1]
36	else:
37	raise ValueError(	×
38	f"Could not call {gate[0]}(*{gate[1:]}), `{gate[0]}` is not callable."
39	)
40	elif gate_name(gate) == 'C':	×
41	U, N = gate2mat(gate[1])	×
42	ret = np.eye(2 * U.shape[0], dtype=complex)	×
43	ret[U.shape[0]:, U.shape[0]:] = U	×
44	return ret, N + 1	×
45	else:
46	raise ValueError(f'Unexcept gate {gate}')	×
47
48
49	def splite_at(l, bits):	9✔
50	"""将 l 的二进制位于 bits 所列的位置上断开插上0
51
52	如 splite_at(int('1111',2), [0,2,4,6]) == int('10101010', 2)
53	bits 必须从小到大排列
54	"""
55	r = l	9✔
56	for n in bits:	9✔
57	mask = (1 << n) - 1	9✔
58	low = r & mask	9✔
59	high = r - low	9✔
60	r = (high << 1) + low	9✔
61	return r	9✔
62
63
64	def place_at(l, bits):	9✔
65	"""将 l 的二进制位置于 bits 所列的位置上
66
67	如 place_at(int('10111',2), [0,2,4,5,6]) == int('01010101', 2)
68	"""
69	r = 0	9✔
70	for index, n in enumerate(bits):	9✔
71	b = (l >> index) & 1	9✔
72	r += b << n	9✔
73	return r	9✔
74
75
76	def reduceSubspace(targets, N, inputMat, func, args):	9✔
77	innerDim = 2**len(targets)	9✔
78	outerDim = 2**(N - len(targets))	9✔
79
80	targets = tuple(reversed([N - i - 1 for i in targets]))	9✔
81
82	def index(targets, i, j):	9✔
83	return splite_at(j, sorted(targets)) \| place_at(i, targets)	9✔
84
85	if len(inputMat.shape) == 1:	9✔
86	for k in range(outerDim):	×
87	innerIndex = [index(targets, i, k) for i in range(innerDim)]	×
88	inputMat[innerIndex] = func(inputMat[innerIndex], *args)	×
89	else:
90	for k, l in itertools.product(range(outerDim), repeat=2):	9✔
91	innerIndex = np.asarray(	9✔
92	[[index(targets, i, k),
93	index(targets, j, l)]
94	for i, j in itertools.product(range(innerDim), repeat=2)]).T
95	sub = inputMat[innerIndex[0], innerIndex[1]].reshape(	9✔
96	(innerDim, innerDim))
97	inputMat[innerIndex[0], innerIndex[1]] = func(sub, *args).flatten()	9✔
98	return inputMat	9✔
99
100
101	def _apply_gate(gate, inputMat, unitary_process, qubits, N):	9✔
102	U, n = gate2mat(gate)	9✔
103	if len(qubits) == n and all(isinstance(qubit, int) for qubit in qubits):	9✔
104	reduceSubspace(qubits, N, inputMat, unitary_process, (U, ))	9✔
105	elif n == 1 and all(isinstance(qubit, int) for qubit in qubits):	×
106	for qubit in qubits:	×
107	reduceSubspace([qubit], N, inputMat, unitary_process, (U, ))	×
108	elif len(qubits) == n and all(	×
109	isinstance(qubit, [tuple, list]) for qubit in qubits):
110	for qubit_tuple in zip(*qubits):	×
111	reduceSubspace(qubit_tuple, N, inputMat, unitary_process, (U, ))	×
112	else:
113	raise ValueError(f'Unexcept gate {gate} and qubits {qubits}')	×
114
115
116	def _measure_process(rho):	9✔
117	return np.array([[rho[0, 0], 0], [0, rho[1, 1]]])	×
118
119
120	def _reset_process(rho, p1):	9✔
121	s0 = np.array([[rho[0, 0] + rho[1, 1], 0], [0, 0]])	×
122	s1 = np.array([[0, 0], [0, rho[0, 0] + rho[1, 1]]])	×
123	return (1 - p1) * s0 + p1 * s1	×
124
125
126	def _decohherence_process(rho, Gamma_t, gamma_t):	9✔
127	rho00 = rho[0, 0] + rho[1, 1] * (1 - np.exp(-Gamma_t))	×
128	rho11 = rho[1, 1] * np.exp(-Gamma_t)	×
129	rho01 = rho[0, 1] * np.exp(-Gamma_t / 2 - gamma_t**2)	×
130	rho10 = rho[1, 0] * np.exp(-Gamma_t / 2 - gamma_t**2)	×
131	return np.array([[rho00, rho01], [rho10, rho11]])	×
132
133
134	def applySeq(seq, psi0=None):	9✔
135
136	def _set_vector_to_rho(psi):	×
137	psi = psi.reshape(-1, 1).conj() @ psi.reshape(1, -1)	×
138	unitary_process = lambda psi, U: U @ psi @ U.T.conj()	×
139	return psi, unitary_process, np.array([[1, 0], [0, 0]])	×
140
141	if psi0 is None:	×
142	psi = np.array([1, 0], dtype=complex)	×
143	N = 1	×
144	else:
145	psi = psi0	×
146	N = round(np.log2(psi.shape[0]))	×
147
148	psi0 = np.array([1, 0])	×
149	unitary_process = lambda psi, U: U @ psi	×
150
151	if psi.ndim == 2:	×
152	psi, unitary_process, psi0 = _set_vector_to_rho(psi)	×
153
154	for gate, *qubits in seq:	×
155	M = max(qubits)	×
156	if M >= N:	×
157	psi = reduce(np.kron, itertools.repeat(psi0, times=M - N + 1), psi)	×
158	N = M + 1	×
159
160	if gate_name(gate) in ['Barrier']:	×
161	continue	×
162	if gate_name(gate) in ['Delay']:	×
163	if len(gate) == 2:	×
164	continue	×
165	else:
166	if len(gate) == 3:	×
167	_, t, T1 = gate	×
168	Gamma_t = t / T1	×
169	gamma_t = 0	×
170	else:
171	_, t, T1, Tphi = gate	×
172	Gamma_t = t / T1	×
173	gamma_t = t / Tphi	×
174	if gate_name(gate) in ['Reset']:	×
175	if isinstance(gate, tuple) and len(gate) == 2:	×
176	_, p1 = gate	×
177	else:
178	p1 = 0.0	×
179	if gate_name(gate) in ['Measure', 'Reset', 'Delay'] and psi.ndim == 1:	×
180	psi, unitary_process, psi0 = _set_vector_to_rho(psi)	×
181
182	if gate_name(gate) == 'Measure':	×
183	reduceSubspace(qubits, N, psi, _measure_process, ())	×
184	elif gate_name(gate) == 'Reset':	×
185	reduceSubspace(qubits, N, psi, _reset_process, (p1, ))	×
186	elif gate_name(gate) == 'Delay':	×
187	reduceSubspace(qubits, N, psi, _decohherence_process,	×
188	(Gamma_t, gamma_t))
189	else:
190	_apply_gate(gate, psi, unitary_process, qubits, N)	×
191
192	return psi	×
193
194
195	def seq2mat(seq, U=None):	9✔
196	I = np.eye(2, dtype=complex)	9✔
197	if U is None:	9✔
198	U = np.eye(2, dtype=complex)	9✔
199	N = 1	9✔
200	else:
201	N = round(np.log2(U.shape[0]))	×
202
203	unitary_process = lambda U0, U: U @ U0	9✔
204
205	for gate, *qubits in seq:	9✔
206	M = max(qubits)	9✔
207	if M >= N:	9✔
208	U = reduce(np.kron, itertools.repeat(I, times=M - N + 1), U)	9✔
209	N = M + 1	9✔
210	if gate_name(gate) in ['Delay', 'Barrier']:	9✔
211	continue	×
212	if gate_name(gate) in ['Measure', 'Reset']:	9✔
213	raise ValueError(	×
214	'Measure and Reset must be applied to a state vector')
215	else:
216	_apply_gate(gate, U, unitary_process, qubits, N)	9✔
217	return U	9✔
218
219
220	regesterGateMatrix('U', U, 1)	9✔
221	regesterGateMatrix('u1', lambda p: U(theta=0, phi=0, lambda_=p), 1)	9✔
222	regesterGateMatrix('u2', lambda phi, lam: U(np.pi / 2, phi, lam), 1)	9✔
223	regesterGateMatrix('u3', U, 1)	9✔
224	regesterGateMatrix('P', lambda p: U(theta=0, phi=0, lambda_=p), 1)	9✔
225	regesterGateMatrix('rfUnitary', rfUnitary, 1)	9✔
226	regesterGateMatrix('R', lambda phi: rfUnitary(np.pi / 2, phi), 1)	9✔
227	regesterGateMatrix('Rx', partial(rfUnitary, phi=0), 1)	9✔
228	regesterGateMatrix('Ry', partial(rfUnitary, phi=np.pi / 2), 1)	9✔
229	regesterGateMatrix('Rz', lambda p: U(theta=0, phi=0, lambda_=p), 1)	9✔
230	regesterGateMatrix('fSim', fSim, 2)	9✔
231	regesterGateMatrix('Cphase', lambda phi: fSim(theta=0, phi=phi), 2)	9✔
232
233	# one qubit
234	regesterGateMatrix('I', np.array([[1, 0], [0, 1]]))	9✔
235	regesterGateMatrix('X', np.array([[0, -1j], [-1j, 0]]))	9✔
236	regesterGateMatrix('Y', np.array([[0, -1], [1, 0]]))	9✔
237	regesterGateMatrix('X/2', np.array([[1, -1j], [-1j, 1]]) / np.sqrt(2))	9✔
238	regesterGateMatrix('Y/2', np.array([[1, -1], [1, 1]]) / np.sqrt(2))	9✔
239	regesterGateMatrix('-X/2', np.array([[1, 1j], [1j, 1]]) / np.sqrt(2))	9✔
240	regesterGateMatrix('-Y/2', np.array([[1, 1], [-1, 1]]) / np.sqrt(2))	9✔
241	regesterGateMatrix('Z', np.array([[1, 0], [0, -1]]))	9✔
242	regesterGateMatrix('S', np.array([[1, 0], [0, 1j]]))	9✔
243	regesterGateMatrix('-S', np.array([[1, 0], [0, -1j]]))	9✔
244	regesterGateMatrix('H', np.array([[1, 1], [1, -1]]) / np.sqrt(2))	9✔
245
246	# non-clifford
247	regesterGateMatrix('T',	9✔
248	np.array([[1, 0], [0, 1 / np.sqrt(2) + 1j / np.sqrt(2)]]))
249	regesterGateMatrix('-T',	9✔
250	np.array([[1, 0], [0, 1 / np.sqrt(2) - 1j / np.sqrt(2)]]))
251	regesterGateMatrix('W/2', rfUnitary(np.pi / 2, np.pi / 4))	9✔
252	regesterGateMatrix('-W/2', rfUnitary(-np.pi / 2, np.pi / 4))	9✔
253	regesterGateMatrix('V/2', rfUnitary(np.pi / 2, 3 * np.pi / 4))	9✔
254	regesterGateMatrix('-V/2', rfUnitary(-np.pi / 2, 3 * np.pi / 4))	9✔
255
256	# two qubits
257	regesterGateMatrix(	9✔
258	'CZ', np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]]))
259	regesterGateMatrix(	9✔
260	'Cnot', np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]))
261	regesterGateMatrix(	9✔
262	'iSWAP',
263	np.array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0], [0, 0, 0, 1]]))
264	regesterGateMatrix(	9✔
265	'SWAP', np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]))
266	regesterGateMatrix(	9✔
267	'CR',
268	np.array([[1, 1j, 0, 0], [1j, 1, 0, 0], [0, 0, 1, -1j], [0, 0, -1j, 1]]) /
269	np.sqrt(2))
270
271	# non-clifford
272	regesterGateMatrix(	9✔
273	'SQiSWAP',
274	np.array([[1, 0, 0, 0], [0, 1 / np.sqrt(2), 1j / np.sqrt(2), 0],
275	[0, 1j / np.sqrt(2), 1 / np.sqrt(2), 0], [0, 0, 0, 1]]))
276
277	if __name__ == '__main__':	9✔
278	# Porter-Thomas distribution
279
280	def randomSeq(depth, N):	×
281	seq = []	×
282	for i in range(depth):	×
283	for j in range(N):	×
284	seq.append((np.random.choice(['X/2', 'Y/2', 'W/2']), j))	×
285	for j in range(i % 2, N, 2):	×
286	seq.append(('SQiSWAP', j, (j + 1) % N))	×
287	return seq	×
288
289	p = []	×
290	# run 1000 random circuit on 6 qubits
291	for i in range(1000):	×
292	print(' ', i, end='')	×
293	seq = randomSeq(50, 6)	×
294	psi = applySeq(seq)	×
295	p.extend(list(np.abs(psi)**2))	×
296	print(' ', i)	×
297	p = np.asarray(p)	×
298
299	# plot distribution of probabilities
300	N = 2**6	×
301	y, x = np.histogram(N * p, bins=50, density=True)	×
302
303	import matplotlib.pyplot as plt	×
304
305	plt.semilogy((x[:-1] + x[1:]) / 2, y)	×
306	plt.show()	×

feihoo87 / waveforms / 6534953321

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