517 lines
17 KiB
Python
517 lines
17 KiB
Python
from __future__ import annotations
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import random
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from collections import defaultdict
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from functools import reduce
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from typing import Union
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import numpy as np
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from numbers import Complex
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from load_test import sizeof_fmt
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ListOrNdarray = Union[list, np.ndarray]
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class Matrix(object):
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"""Represents a quantum state as a vector in Hilbert space"""
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def __init__(self, m: ListOrNdarray = None, *args, **kwargs):
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"""
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Can be initialized with a matrix, e.g. for |0> this is [[0],[1]]
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:param m: a matrix representing the quantum state
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:param name: the name of the state (optional)
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"""
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if m is None:
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self.m = np.array([])
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elif type(m) is list:
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self.m = np.array(m)
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elif type(m) is np.ndarray:
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self.m = m
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else:
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raise TypeError("m needs to be a list or ndarray type")
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def __add__(self, other):
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return other.__class__(self.m + other.m)
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def __eq__(self, other):
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if isinstance(other, Complex):
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return bool(np.allclose(self.m, other))
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elif isinstance(other, TwoQubitGate):
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return False
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return np.allclose(self.m, other.m)
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def __mul_or_kron__(self, other):
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"""
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Multiplication with a number is Linear op;
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with another state is a composition via the Kronecker/Tensor product
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"""
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if isinstance(other, Complex):
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return self.__class__(self.m * other)
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elif isinstance(other, Matrix):
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return other.__class__(np.kron(self.m, other.m))
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raise NotImplementedError
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def __rmul__(self, other):
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return self.__mul_or_kron__(other)
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def __mul__(self, other):
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return self.__mul_or_kron__(other)
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def __or__(self, other):
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"""Define inner product: <self|other>
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"""
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return other.__class__(np.dot(self._conjugate_transpose(), other.m))
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def __len__(self):
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return len(self.m)
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def outer(self, other):
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"""Define outer product |0><0|"""
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return self.__class__(np.outer(self.m, other.m))
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def x(self, other):
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"""Define outer product |0><0| looks like |0x0| which is 0.x(0)"""
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return self.outer(other)
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def _conjugate_transpose(self):
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return self.m.transpose().conjugate()
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def _complex_conjugate(self):
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return self.m.conjugate()
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def conjugate_transpose(self):
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return self.__class__(self._conjugate_transpose())
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def complex_conjugate(self):
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return self.__class__(self._complex_conjugate())
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class State(Matrix):
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def __init__(self, m: ListOrNdarray = None, name: str = '', *args, **kwargs):
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"""An Operator turns one function into another"""
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super().__init__(m)
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self.name = name
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def __repr__(self):
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if self.name:
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return '|{}>'.format(self.name)
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return str(self.m)
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def norm(self):
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"""Norm/Length of the vector = sqrt(<self|self>)"""
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return self.length()
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def length(self):
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"""Norm/Length of the vector = sqrt(<self|self>)"""
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return np.sqrt((self | self).m).item(0)
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def is_orthogonal(self, other):
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"""If the inner (dot) product is zero, this vector is orthogonal to other"""
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return self | other == 0
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def get_prob(self, j):
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"""pr(j) = |<e_j|self>|^2"""
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# j_th basis vector
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e_j = State([[1] if i == int(j) else [0] for i in range(len(self.m))])
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return np.absolute((e_j | self).m.item(0)) ** 2
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def measure(self):
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weights = [self.get_prob(j) for j in range(len(self))]
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format_str = "{:0" + str(int(np.ceil(np.log2(len(weights))))) + "b}"
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choices = [format_str.format(i) for i in range(len(weights))]
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return random.choices(choices, weights)[0]
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class Operator(object):
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def __init__(self, func=None, *args, **kwargs):
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"""An Operator turns one function into another"""
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self.func = func
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def on(self, *args, **kwargs):
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return self(*args, **kwargs)
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def __call__(self, *args, **kwargs):
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return self.func(*args, **kwargs)
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class UnitaryMatrix(Matrix):
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def __init__(self, m: ListOrNdarray, *args, **kwargs):
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"""Represents a Unitary matrix that satisfies UU+ = I"""
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super().__init__(m, *args, **kwargs)
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if not self._is_unitary():
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raise TypeError("Not a Unitary matrix")
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def _is_unitary(self):
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"""Checks if the matrix is
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1. square and
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2. the product of itself with conjugate transpose is Identity UU+ = I"""
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is_square = self.m.shape[0] == self.m.shape[1]
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UU_ = np.dot(self._conjugate_transpose(), self.m)
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I = np.eye(self.m.shape[0])
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return is_square and np.isclose(UU_, I).all()
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class UnitaryOperator(Operator, UnitaryMatrix):
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def __init__(self, m: ListOrNdarray, name: str = '', *args, **kwargs):
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"""UnitaryOperator inherits from both Operator and a Unitary matrix
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It is used to act on a State vector by defining the operator to be the dot product"""
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self.name = name
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UnitaryMatrix.__init__(self, m=m, *args, **kwargs)
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Operator.__init__(self, func=lambda other: State(np.dot(self.m, other.m)), *args, **kwargs)
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def __repr__(self):
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if self.name:
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return '-{}-'.format(self.name)
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return str(self.m)
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"""
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Define States and Operators
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"""
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_0 = State([[1],
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[0]],
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name='0')
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_1 = State([[0],
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[1]],
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name='1')
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_ = I = UnitaryOperator([[1, 0],
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[0, 1]],
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name="-")
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X = UnitaryOperator([[0, 1],
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[1, 0]],
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name="X")
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Y = UnitaryOperator([[0, -1j],
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[1j, 0]],
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name="Y")
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Z = UnitaryOperator([[1, 0],
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[0, -1]],
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name="Z")
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H = UnitaryOperator([[1 / np.sqrt(2), 1 / np.sqrt(2)],
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[1 / np.sqrt(2), -1 / np.sqrt(2)], ],
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name="H")
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CNOT = UnitaryOperator([[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 0, 1],
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[0, 0, 1, 0], ])
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# TODO - How to add a CNOT gate to the Quantum Processor?
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# Imagine if I have to act on a 3-qubit computer and CNOT(q1, q3)
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#
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# Decomposed CNOT :
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# reverse engineered from
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# https://quantumcomputing.stackexchange.com/questions/4252/how-to-derive-the-cnot-matrix-for-a-3-qbit-system-where-the-control-target-qbi
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#
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# CNOT(q1, I, q2):
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# |0><0| x I_2 x I_2 + |1><1| x I_2 x X
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# np.kron(np.kron(np.outer(_0.m, _0.m), np.eye(2)), np.eye(2)) + np.kron(np.kron(np.outer(_1.m, _1.m), np.eye(2)), X.m)
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#
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#
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# CNOT(q1, q2):
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# |0><0| x I + |1><1| x X
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# np.kron(np.outer(_0.m, _0.m), np.eye(2)) + np.kron(np.outer(_1.m, _1.m), X.m)
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# _0.x(_0) * Matrix(I.m) + _1.x(_1) * Matrix(X.m)
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class TwoQubitGate(object):
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def __init__(self, rpr):
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self.rpr = rpr
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def __repr__(self):
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return str("-{}-".format(self.rpr))
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C = TwoQubitGate("C")
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x = TwoQubitGate("x")
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# TODO: End Hacky way to define 2-qbit gate
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###########################################################
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def test():
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_p = State([[1 / np.sqrt(2)], [1 / np.sqrt(2)]], name='+')
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# Test properties of Hilbert vector space
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# The four postulates of Quantum Mechanics
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# I: States | Associated to any physical system is a complex vector space
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# known as the state space of the system. If the system is closed
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# then the system is described completely by its state vector
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# which is a unit vector in the space.
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# Mathematically, this vector space is also a function space
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assert _0 + _1 == _1 + _0 # commutativity of vector addition
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assert _0 + (_1 + _p) == (_0 + _1) + _p # associativity of vector addition
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assert 8 * (_0 + _1) == 8 * _0 + 8 * _1 # Linear when multiplying by constants
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assert _0 | _0 == 1 # parallel have 1 product
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assert _0 | _1 == 0 # orthogonal have 0 product
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assert _0.is_orthogonal(_1)
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assert _1 | (8 * _0) == 8 * (_1 | _0) # Inner product is linear multiplied by constants
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assert _p | (_1 + _0) == (_p | _1) + (_p | _0) # Inner product is linear in superpos of vectors
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assert np.isclose(_1.length(), 1.0) # all of the vector lengths are normalized
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assert np.isclose(_0.length(), 1.0)
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assert np.isclose(_p.length(), 1.0)
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assert _0 | _1 == (_1 | _0).complex_conjugate() # non-commutative inner product
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# II: Dynamics | The evolution of a closed system is described by a unitary transformation
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#
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# Operators turn one vector into another
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# the times 2 operator should return the times two multiplication
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_times_2 = Operator(lambda x: 2 * x)
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assert _times_2.on(5) == 10
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assert _times_2(5) == 10
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# Pauli X gate flips the |0> to |1> and the |1> to |0>
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assert X | _1 == _0
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assert X | _0 == _1
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# Test the Y Pauli operator with complex number literal notation
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assert Y | _0 == State([[0],
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[1j]])
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assert Y | _1 == State([[-1j],
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[0]])
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# III: Measurement | A quantum measurement is described by an orthonormal basis |e_j>
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# for state space. If the initial state of the system is |psi>
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# then we get outcome j with probability pr(j) = |<e_j|psi>|^2
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assert _0.get_prob(0) == 1 # Probability for |0> in 0 is 1
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assert _0.get_prob(1) == 0 # Probability for |0> in 1 is 0
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assert _1.get_prob(0) == 0 # Probability for |1> in 0 is 0
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assert _1.get_prob(1) == 1 # Probability for |1> in 1 is 1
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assert np.isclose(_p.get_prob(0), 0.5) # Probability for |+> in 0 is 0.5
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assert np.isclose(_p.get_prob(1), 0.5) # Probability for |+> in 1 is 0.5
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# IV: Compositing | tensor/kronecker product when composing
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assert _0 * _0 == State([[1], [0], [0], [0]])
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assert _0 * _1 == State([[0], [1], [0], [0]])
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assert _1 * _0 == State([[0], [0], [1], [0]])
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assert _1 * _1 == State([[0], [0], [0], [1]])
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# CNOT applies a control qubit on a target.
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# If the control is a |0>, target remains unchanged.
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# If the control is a |1>, target is flipped.
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assert CNOT.on(_0 * _0) == _0 * _0
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assert CNOT.on(_0 * _1) == _0 * _1
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assert CNOT.on(_1 * _0) == _1 * _1
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assert CNOT.on(_1 * _1) == _1 * _0
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# ALL FOUR NOW - Create a Bell state (I) that has H|0> (II), measures (III) and composition in CNOT (IV)
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# Bell state
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# First - create a superposition
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H = UnitaryOperator([[1 / np.sqrt(2), 1 / np.sqrt(2)],
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[1 / np.sqrt(2), -1 / np.sqrt(2)], ])
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superpos = H | _0
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assert superpos == _p
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# Then CNOT the superposition with a |0> qubit
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bell = CNOT | (superpos * _0)
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assert bell == State([[1 / np.sqrt(2)],
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[0.],
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[0.],
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[1 / np.sqrt(2)], ])
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assert np.isclose(bell.get_prob(0b00), 0.5) # Probability for bell in 00 is 0.5
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assert np.isclose(bell.get_prob(0b01), 0) # Probability for bell in 01 is 0.
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assert np.isclose(bell.get_prob(0b10), 0) # Probability for bell in 10 is 0.
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assert np.isclose(bell.get_prob(0b11), 0.5) # Probability for bell in 11 is 0.5
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################################
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# TODO: Don't know where outer product fits...
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assert _0.x(_0) == Matrix([[1, 0],
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[0, 0]])
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assert _0.x(_1) == Matrix([[0, 1],
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[0, 0]])
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assert _1.x(_0) == Matrix([[0, 0],
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[1, 0]])
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assert _1.x(_1) == Matrix([[0, 0],
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[0, 1]])
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def naive_load_test(N):
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import os
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import psutil
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import gc
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from time import time
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from sys import getsizeof
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print("{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10}".format(
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"qbits",
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"kron_len",
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"mem_used",
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"mem_per_q",
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"getsizeof",
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"getsiz/len",
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"nbytes",
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"nbytes/len",
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"time"))
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_0 = State([[1], [0]], name='0')
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process = psutil.Process(os.getpid())
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mem_init = process.memory_info().rss
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for i in range(2, N + 1):
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start = time()
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m = _0
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for _ in range(i):
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m = m * _0
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len_m = len(m)
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elapsed = time() - start
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mem_b = process.memory_info().rss - mem_init
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print("{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10}".format(
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i,
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len(m),
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sizeof_fmt(mem_b),
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sizeof_fmt(mem_b / len_m),
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sizeof_fmt(getsizeof(m)),
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sizeof_fmt(getsizeof(m) / len_m),
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sizeof_fmt(m.m.nbytes),
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sizeof_fmt(m.m.nbytes / len_m),
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np.round(elapsed, 2)))
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gc.collect()
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class QuantumProcessor(object):
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HALT_STATE = "HALT"
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RUNNING_STATE = "RUNNING"
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def __init__(self, n_qubits: int):
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self.n_qubits = n_qubits
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self.steps = [[_0 for _ in range(n_qubits)], ]
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self._called_add_row = 0
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self.current_step = 0
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self.current_quantum_state = None
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self.current_state = self.HALT_STATE
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self.reset()
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def add_row_step(self, row: int, step: int, qbit_state):
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if len(self.steps) <= step:
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self.steps += [[I for _ in range(self.n_qubits)] for _ in range(len(self.steps) - step + 1)]
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self.steps[step][row] = qbit_state
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def add_step(self, step_data: list):
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if len(step_data) != self.n_qubits:
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raise RuntimeError("Length of step is: {}, should be: {}".format(len(step_data), self.n_qubits))
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step_i = len(step_data)
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for row, qubit_state in enumerate(step_data):
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self.add_row_step(row, step_i, qubit_state)
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def add_steps(self, steps_data: list):
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for step_data in steps_data:
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self.add_step(step_data)
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def add_row(self, row_data: list):
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if self._called_add_row >= self.n_qubits:
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raise RuntimeError("Adding more rows than qubits")
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for step_i, qubit_state in enumerate(row_data):
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self.add_row_step(self._called_add_row, step_i + 1, qubit_state)
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self._called_add_row += 1
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def add_rows(self, rows_data: list):
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for row_data in rows_data:
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self.add_row(row_data)
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def compose_quantum_state(self, step):
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if C in step or x in step:
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if not (step.count(C) == 1 and step.count(x) == 1):
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raise RuntimeError("Both CONTROL and TARGET need to be defined in the same step exactly once")
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# TODO: Hacky way to do CNOT
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# Should generalize for a 2-Qubit gate
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# _0.x(_0) * Matrix(I.m) + _1.x(_1) * Matrix(X.m)
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outer_0, outer_1 = [], []
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for s in step:
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if s == C:
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outer_0.append(_0.x(_0))
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outer_1.append(_1.x(_1))
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elif s == x:
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outer_0.append(Matrix(I.m))
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outer_1.append(Matrix(X.m))
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else:
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outer_0.append(Matrix(s.m))
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outer_1.append(Matrix(s.m))
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return reduce((lambda x, y: x * y), outer_0) + reduce((lambda x, y: x * y), outer_1)
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return reduce((lambda x, y: x * y), step)
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def step(self):
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if self.current_step == 0 and self.current_state == self.HALT_STATE:
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self.current_state = self.RUNNING_STATE
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if self.current_step >= len(self.steps):
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self.current_state = self.HALT_STATE
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raise RuntimeWarning("Halted")
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running_step = self.steps[self.current_step]
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step_quantum_state = self.compose_quantum_state(running_step)
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if not self.current_quantum_state:
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self.current_quantum_state = step_quantum_state
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else:
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self.current_quantum_state = step_quantum_state | self.current_quantum_state
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self.current_step += 1
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def run(self):
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for _ in self.steps:
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self.step()
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self.current_state = self.HALT_STATE
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def reset(self):
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self.current_step = 0
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self.current_quantum_state = None
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self.current_state = self.HALT_STATE
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def print(self):
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print("=" * 3 * len(self.steps))
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for line_no in range(self.n_qubits):
|
|
line = ''
|
|
for step in self.steps:
|
|
state_repr = repr(step[line_no])
|
|
line += state_repr
|
|
print(line)
|
|
print("=" * 3 * len(self.steps))
|
|
|
|
def measure(self):
|
|
if self.current_state != self.HALT_STATE:
|
|
raise RuntimeError("Processor is still running")
|
|
return self.current_quantum_state.measure()
|
|
|
|
def run_n(self, n: int):
|
|
for i in range(n):
|
|
self.run()
|
|
result = self.measure()
|
|
print("Run {}: {}".format(i, result))
|
|
self.reset()
|
|
|
|
def get_sample(self, n: int):
|
|
rv = defaultdict(int)
|
|
for i in range(n):
|
|
self.run()
|
|
result = self.measure()
|
|
rv[result] += 1
|
|
self.reset()
|
|
for k, v in sorted(rv.items(), key=lambda x: x[0]):
|
|
print("{}: {}".format(k, v))
|
|
return rv
|
|
|
|
|
|
def test_quantum_processor():
|
|
# Produce Bell state between 0 and 2 qubit
|
|
qp = QuantumProcessor(3)
|
|
qp.add_row([H, C])
|
|
qp.add_row([_, _])
|
|
qp.add_row([_, x])
|
|
qp.print()
|
|
qp.get_sample(100)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
test()
|
|
test_quantum_processor()
|