Shota Nagayama

Shota Nagayama

Quantum Computer/Network Architecture based on Quantum Error Correction. Post-Quantum Cryptography. After he got Ph.D. in quantum, now he enjoys AI research for 9 months and will go back to quantum.

Location Budapest

Activity

  • More or less correct. Physically, only "relative phase" between a and b is meaningful. We can observe only the "relative phase". This means that we can apply "global phase" to the state, by multiplying e^{iθ} to both of a and b. This operation does not change the state because it changes neither the real parts nor the relative phase. We can choose arbitrary θ,...

  • More or less correct. One thing, let's imagine |0>/√2 + (1+i)|1>/2. The imaginary part of this state is i/2. However, this state is actually equal to (|0> + (cos(π/4) + i sin(π/4)) |1>)/√2 = (|0> + e^{iπ/4} |1>)/√2 because of Euler's formula. This π/4 is the phase hence (1+i)/√2 refers to the phase.

  • If a and b are the amplitude, it means the phase term is 1. So e^{i\phi} = 1, hence \phi = 0.

  • However, there are problems that we don't know how to achieve the "correct" answer explicitly. In such cases, still we may be able to find, prepare or maybe define, a means to measure the degree of correctness or optimality. Then we have no alternative but to use (sometimes probabilistic) algorithms to look for "better" answers relying on the measure; those...

  • No, it's not a problem here. This is an example to tell the simplest rules of quantum computation. Take it easy.

  • Right, except that "if C is 0 or 3?" in 3) should be "if C is 0 or 6", maybe typo.

  • The answer for your first question is no. Let me talk about the case with complete confidence first.
    Trial and error is very important when we think about algorithms. There are problems and probabilistic algorithms for them, which stochastically result in the correct answer and sometimes they result in wrong answers. Shor’s algorithm is in fact a...

  • We still have superposition even if there is no decoherence, hence the probabilistic manner of measurement still exists.

  • When I was very beginner, the notation concerning phase looked confusing too. Especially it was so confusing to me that the opposite direction in Bloch sphere was orthogonal. I obeyed the rules, calculated and thought one by one and finally it was no longer confusing for me before I realize it. Take it easy and let's obey the rules one by one.

  • Thank you for comment. As you say, entangled two qubits at a distance is very impressive. In fact, to create an entanglement, the two qubits have to be placed so close because we need quantum interaction between them. Then we can move one of them away and achieve entangled two qubits at a distance. Actually this discussion leads to quantum networking and hence...

  • Post-quantum cryptography has been researched. Some post-quantum cryptography uses quantum information tech such as quantum key distribution, some does not use quantum. Factoring large number would not break our infrastructure practically. We can update/replace our crypto system.
    Factoring large numbers itself is an important scientific topic.

  • When we measure a qubit in entangled three qubits, the measured qubit's state collapses at the same time and the remaining two-qubit state is changed to the state corresponding to the found value at the same time too. We cannot control which value is found and cannot control the collapse timing.

  • Euclidean of complex numbers is enough good understanding in this course. Hilbert space is a vector space of real or complex numbers which has inner product, norm and is complete. Its strict definition is important in (deep) quantum information theory. We lecturer have to use the term for correctness. Please take it easy.

  • I hope you to enjoy this entrance to new world!