Quantum Information

Knowing the underpinnings of randomized benchmarking addressed in the last part, we first begin with the standard protocol. Standard RB is used to assess the error rate over gates of Clifford group with an assumption that these gates have the same error rate. After that, another improvement of the technique will be introduced, namely Interleaved Randomized Benchmarking. The upgraded version was proposed not to investigate the Clifford group as a whole, but restricted to one single kind of Clifford gate of our choice. ...

As you can see in the cover figure, quantum computing is just at the onset of its journey. There are tons of work to do before we can move to the next stage of quantum computing, quantum supremacy. Two pivotal constraints to the realization of any useful quantum processor are decoherence and the high error rate of quantum operators, or quantum gates experimentally. It’s been suggested that the probability of error per unitary gate should be less than $10^{-2}$ (better $10^{-4}$) for the outcome to be reliable. ...

In the article of Bernsterin-Vazirani implementation, I’ve addressed one of the most crucial challenges of quantum computing. The field is yet to flourish because quantum gates aren’t constructed to be good enough. One major difference of quantum gates versus classical counterparts is that quantum gates have to be reversible, which means we’re able to retrieve a prior state of a qubit without loss of information. Scientists are now on their way to establish a proper scheme for building decent quantum gates. ...

In this text I’ll do some review on the definition of quantum state and quantum measurement, which was introduced here, and reasonably expand the notions into the most general instances of quantum bits. Review Given a state $$|\psi\rangle = \sum_i \alpha_i |\varphi_i \rangle,$$ it’s possible to perform a Von Neumann measurement on the state’s space $\mathscr{H}$ with respect to the orthonormal basis $B = \{|\varphi_i \rangle\}$. The output would be a label $i$ with corresponding probability $|\alpha_i|^2$ and the system left in state $|\varphi_i\rangle$. ...

Throughout previous posts, I’ve delivered a way to understand what is a quantum measurement. That way of understanding is simple and may suit our normal intuition, but measurement is a non-trivial physical process and somewhat counter-intuitive for several reasons. First, a measurement in general results in probabilistic outcomes. No matter how careful you prepare for the measurement procedure, it is inherent that possible outcomes of a measure is distributed according to a certain probability distribution determined by the state space of your quantum system. ...

Source of image: Quantum Computer Explained - Limits of Human Technology (Kurzgesagt – In a Nutshell) In classical computation, there are four basic operations that act on information bits, namely Identity (no operation), Negation (NOT), Conjunction (AND), and Disjunction (OR). All other operations are secondary and built upon these four operations. That being said, with the primary and secondary operations, one is able to perform any calculation in classical fashion. ...