Chris Bernhardt > Quotes

“Popular descriptions of quantum algorithms describe them as being much faster than regular algorithms. This speedup, it is explained, comes from being able to put the input into a superposition of all possible inputs and then performing the algorithm on the superposition. Consequently, instead of running the algorithm on just one input, as you do classically, you can run the algorithm using “quantum parallelism” on all possible inputs at the same time.”
― Chris Bernhardt, Quantum Computing for Everyone

“If a problem can be solved in polynomial time we say it belongs to the complexity class P. So the problem that consists of multiplying two numbers together belongs to P. Suppose that instead of solving the problem, someone gives you the answer and you just have to check that the answer is correct. If this process of checking that an answer is correct takes polynomial time, then we say the problem belongs to complexity class NP.* The problem of factoring a large number into the product of two primes belongs to NP.”
― Chris Bernhardt, Quantum Computing for Everyone

“Alice cannot tell from her measurements whether they were made before or after Bob’s. All entangled states behave this way. If there is no way of Alice and Bob being able to tell from their measurements who went first, there certainly can be no way of sending any information from one to the other.”
― Chris Bernhardt, Quantum Computing for Everyone

“one of our immediate thoughts is that superluminal communication should not be possible.”
― Chris Bernhardt, Quantum Computing for Everyone

“First, we look at how physical experiments create entangled particles. Then we look at how quantum gates create entangled qubits. The most commonly used method at this time involves photons. The process is called spontaneous parametric down-conversion. A laser beam sends photons through a special crystal. Most of the photons just pass through, but some photons split into two. Energy and momentum must be conserved—the total energy and momentum of the two resulting photons must equal the energy and momentum of the initial photon. The conservation laws guarantee that the state describing the polarization of the two photons is entangled.”
― Chris Bernhardt, Quantum Computing for Everyone

“verbal descriptions often give the impression that we have understood something when we really haven’t.”
― Chris Bernhardt, Quantum Computing for Everyone

“but essentially local realism means that a particle can only be influenced by something changing in its vicinity.”
― Chris Bernhardt, Quantum Computing for Everyone

“Superluminal communication is communication faster than the speed of light.”
― Chris Bernhardt, Quantum Computing for Everyone

“Let’s start with a basic introduction to describe spin and polarization. To do this we describe the foundational experiment performed by Otto Stern and Walther Gerlach on the spin of silver atoms.”
― Chris Bernhardt, Quantum Computing for Everyone

“Now that we have seen that superluminal communication is not possible, we turn to the more prosaic task of writing tensor products using standard bases.”
― Chris Bernhardt, Quantum Computing for Everyone

“David Deutsch is one of the founders of quantum computing. In 1985, he published a landmark paper that described quantum Turing machines and quantum computation.** This paper also includes the following algorithm—the first to show that a quantum algorithm could be faster than a classical one.”
― Chris Bernhardt, Quantum Computing for Everyone

“A qubit can be represented by the spin of an electron or the polarization of a photon.”
― Chris Bernhardt, Quantum Computing for Everyone

“Shor’s algorithm gives a way of factoring a large number into the product of its prime factors. This might not seem that important, but our Internet security depends on this problem being hard to solve. Being able to factor products of large primes threatens our current methods of securing transactions between computers. It might be some time until we have quantum computers powerful enough to factor the large numbers that are currently in use, but the threat is real, and it is already forcing us to think about how to redesign the ways that computers can securely talk to one another.”
― Chris Bernhardt, Quantum Computing for Everyone