ProductOperator Class Reference
[Objects with a TPS]

A tensor product of operators (complex matrices). More...

#include <quantum.h>

Collaboration diagram for ProductOperator:

[legend]List of all members.

Public Member Functions
	ProductOperator (const TensorProductStructure &Uinit)
	Constructor: constructs the zero operator on a given TensorProductStructure.
	ProductOperator (const ProductOperator &other)
	Copy constructor: constructs an exact copy of another ProductOperator.
	~ProductOperator ()
	Destructor: de-allocates the array of subsystem operators.
Operator &	Realize (Operator &fulloperator) const
	Realizes the dense matrix represented by this ProductOperator, assigning it to the provided fulloperator.
Operator &	AddTo (Operator &fulloperator, complex amplitude=complex(1.0, 0)) const
	Realizes a scalar multiple of this ProductOperator, adding it to the provided fulloperator.
Operator &	Component (itype index) const
	Returns a reference to an operator on the index'th subsystem.
Operator &	operator[] (itype index) const
	Returns a reference to an operator on the index'th subsystem.
complex	Amplitude () const
	Returns the overall scaling factor of this ProductOperator.
const TensorProductStructure &	TPS () const
	Returns a const reference to this ProductOperator's underlying TensorProductStructure.
void	ApplyTo (const State &psi, State &result) const
	Acts on the dense State psi with this ProductOperator, storing the result in result.
void	ApplyAndAddTo (const State &psi, State &result, complex coefficient=complex(1.0)) const
	Acts on the dense State psi with this ProductOperator; adds a scalar multiple of the result to result.
State	operator * (State &psi) const
	Returns a new dense State which is psi transformed by this rProductOperator.
ProductOperator	operator * (complex scalar) const
	Returns a new ProductOperator, scaled by scalar. Much slower than the *= operator!
ProductOperator	operator/ (complex scalar) const
	Returns a new ProductOperator, scaled by 1/scalar. Much slower than the /= operator!
ProductOperator &	operator *= (complex scalar)
	Scales this ProductOperator in place by scalar, and returns a reference to the result.
ProductOperator &	operator/= (complex scalar)
	Scales this ProductOperator in place by 1/scalar, and returns a reference to the result.
double	Norm () const
	Calculates the squared 2-norm of this operator, as the product of all the subsystem operators' squared 2-norms.

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Detailed Description

A tensor product of operators (complex matrices).

ProductOperator is exactly what anyone familiar with quantum info would expect; it's a complex matrix defined as a tensor product of matrices, each of which acts on a vector space that represents a subsystem. This provides a tremendous savings in space. An arbitrary Operator on a 4x4x4-dimensional space requires storing (4x4x4)^2=4096 complex numbers, while a ProductOpereator only requires 4^2+4^2+4^2=48 numbers. The advantage is exponential in the number of subsystems.

Each of the subsystem operators in a ProductOperator can be accessed and changed at will, but the overall operator's elements are not writable (and, as of 6/06, not directly accessible at all). Things you can do with a ProductOperator:

• apply it to a dense State [ApplyTo(), ApplyAndAddTo(), operator*()]
• assign or add it to a dense Operator [Realize(), AddTo()]
• access operators on subsystems [Component(), operator[]()]
• multiply or divide it by a scalar [Amplitude(), operator*=(), operator*(), operator/(), operator/=()]
• obtain its squared 2-norm [Norm()]

The ProductOperator class was put together rather hurriedly in late 2004 for a particular project, so it's not as well structured as it could be. At some point, it should be revised, but this will require updating old code (the Spinbath project) to make sure that it still works. Things to change include: make ProductOperator inherit from Matrix<complex>, etc.

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Member Function Documentation

void ProductOperator::ApplyTo (  const State &  psi, State &  result )  const

Acts on the dense State psi with this ProductOperator, storing the result in result. WARNING: psi and result must not share any data, otherwise the result will be undefined!

void ProductOperator::ApplyAndAddTo (  const State &  psi, State &  result, complex  coefficient = complex(1.0) )  const

Acts on the dense State psi with this ProductOperator; adds a scalar multiple of the result to result. WARNING: psi and result must not share any data, otherwise the result will be undefined!

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The documentation for this class was generated from the following files:

• quantum.h
• productstate.cpp

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