# Questions tagged [quantum-computation]

Quantum Computation deals with considering computation as fundamentally physical, as well as replacing the classical binary digit (bit) with the quantum binary digit (qubit). While the classical bit is either 0 or 1, the qubit can be in a superposition of these states. Computation systems that use quantum phenomena, such as superposition and entanglement, can solve certain complex problems very quickly.

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### if $(|a\rangle - |b\rangle)\langle b| + |b\rangle(\langle a| - \langle b|) = 0$ then $|a\rangle = |b\rangle$, where $|a\rangle, |b\rangle$ unit

Essentially the problem above. I've tried approaching it by arguing that $|b\rangle(\langle a| - \langle b|)$ is the adjoint of $(|a\rangle - |b\rangle)\langle b|$, and since $|b\rangle$ nonzero, ...
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### How are spin network edges related to anti-symmetric projectors on the Hilbert space of the fundamental rep of SU(2)?

In the paper here https://arxiv.org/pdf/gr-qc/9905020.pdf we see an introduction to Spin-networks of the original Penrose type i.e an undirected open graph whose edges have labels that are irreducible ...
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### A logic better adapted to quantum phenomena?

Our way of mathematical thinking is totally controlled by a simple two-valued logic $(\mathbf{false}, \mathbf{true})$. All deductions are due to this logic and we are unable to think otherwise. But ...
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### Definition of indistinguishable states in classical statistics and separability

The problem of indistinguishable particles motivated new statistics such as Bose-Einstein or Fermi-Dirac that were later formalized by von Neumann as Quantum Statistics. In quantum statistics, states ...
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### Testing a solution of a vector-valued differential equation

I'm working through a book on Quantum Computing. The section is regarding the Time Evolution Postulate of quantum mechanics, and it has sort of thrown me a curveball. Given time-independent ...
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### Entries of a unitary matrix

In the solution a a problem in quantum computation I saw this line: $$U_{ij}=\langle\psi_i|\left(\sum_k|\phi_k\rangle\!\langle\psi_k|\right) |\psi_j\rangle.$$ Where $U_{ij}$ are the entries of a ...
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### Showing that any linear operator can be written as a sum of Hermitian matrices [duplicate]

Let $(V, \mathbb{C})$ be a complex - valued vector space. Let $A$ be any linear operator acting on this vector space. Suppose that $B = \{|v\rangle_{k}\}_{k=1}^{n}$ is a basis set for $(V, \mathbb{C})$...
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### Apply the Hadamard transform to different state vectors

I am in the process of understanding a proof. First, the following is said there: $$H\begin{pmatrix}1\\0\\\vdots\\0\end{pmatrix}=\frac{1}{\sqrt{N}}\begin{pmatrix}1\\1\\1\\1\end{pmatrix}$$ This is ...