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glS ♦
glS ♦
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Prove that any Hermitian Matrix is a real linear combination of Pauli Operators using only real coefficientsoperators

Hi I don't feel that this is a duplicate since I am asking about Hermitian matrices and how they can be expressed as linear combinations with REAL numbers. The other questions were asking about how Pauli matrices span the whole vector space and those require COMPLEX numbers.
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shashvat
shashvat
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This is an important result in Quantum Computing because it means that the Hamiltonian of a Quantum System can be encoded as a sequence of real numbers and their corresponding Pauli Operator.

How do we prove this result?

(Note I am assuming that the Hermitian is of size $2^n \times 2^n$, and so by Pauli Operator I mean n-fold tensor products of the 2x2 Pauli Matrices)

This is an important result in Quantum Computing because it means that the Hamiltonian of a Quantum System can be encoded as a sequence of real numbers and their corresponding Pauli Operator.

How do we prove this result?

(Note I am assuming that the Hermitian is of size $2^n \times 2^n$, and so by Pauli Operator I mean n-fold tensor products of the 2x2 Pauli Matrices)

This is an important result in Quantum Computing because it means that the Hamiltonian of a Quantum System can be encoded as a sequence of real numbers and their corresponding Pauli Operator.

How do we prove this result?

(Note I am assuming that the Hermitian is of size $2^n \times 2^n$, and so by Pauli Operator I mean n-fold tensor products of the 2x2 Pauli Matrices)

Post Closed as "Duplicate" by glS♦, ryanhill1, luciano, met927, forky40
added 151 characters in body; edited title
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shashvat
shashvat
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Prove that any Hermitian Matrix is a linear combination of Pauli MatricesOperators using only real coefficients

This is an important result in Quantum Computing because it means that the Hamiltonian of a Quantum System can be encoded as a sequence of real numbers and their corresponding Pauli Operator.

How do we prove this result?

(Note I am assuming that the Hermitian is of size $2^n \times 2^n$, and so by Pauli Operator I mean n-fold tensor products of the 2x2 Pauli Matrices)

Prove that any Hermitian Matrix is a linear combination of Pauli Matrices using only real coefficients

This is an important result in Quantum Computing because it means that the Hamiltonian of a Quantum System can be encoded as a sequence of real numbers and their corresponding Pauli Operator.

How do we prove this result?

Prove that any Hermitian Matrix is a linear combination of Pauli Operators using only real coefficients

This is an important result in Quantum Computing because it means that the Hamiltonian of a Quantum System can be encoded as a sequence of real numbers and their corresponding Pauli Operator.

How do we prove this result?

(Note I am assuming that the Hermitian is of size $2^n \times 2^n$, and so by Pauli Operator I mean n-fold tensor products of the 2x2 Pauli Matrices)

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shashvat
shashvat
  • 857
  • 5
  • 13