Proposed experiments in achieving quantum supremacy, such as with BosonSampling or using random circuits, have been described as using a (not necessarily Turing complete) quantum computer to perform some sampling problem. An example would be to sample the distribution of, say, $72$ qubits after ...

Let $\vec{v}$ be any real three - dimensional unit vector and $\theta$ a real number. Prove that $exp(i\theta \vec{v}\cdot\vec{\sigma}) = cos(\theta)I + isin(\theta)\vec{v}\cdot\vec{\sigma}$ where $\vec{v}\cdot\vec{\sigma} \equiv \sum_{k=1}^{3}v_{k}\sigma_{k}$. $\vec{v}\cdot\vec{\sigma}$ is ...

In superconducting Quantum Computers, we use mostly superconducting qubits or trapped ions. However, those systems are quite large because their environment either requires near absolute zero temperature(for superconducting to happen), or vacuum(to trap ions). Also, they need a lot of shielding f...

The quantum state of a spin- 1/2 particle can be written, in the momentum representation, as a two-component spinor, $$\textit{Ψ}(\textbf{p})=\left(\begin{matrix}a_{1}(\textbf{p})\\a_{2}(\textbf{p})\end{matrix}\right),$$ With the density matrix corresponding to 2-component spinor above is $$\...