Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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What are min and max overlaps of a maximally entangled state with a separable state?

Let $A,B$ be Hilbert spaces of dimension $d$. Let $\rho$ be some separable quantum state of the composite system $AB$. Given a maximally entangled state: $$\vert\phi\rangle = \frac{1}{\sqrt{d}}\sum_{i=1}^d \vert i\rangle_A\vert…
Jules
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Degeneracy of Quantum Error Correction Codes

The feature of quantum error correcting codes called degeneracy is that they can sometimes be used to correct more errors than they can uniquely identify. It seems that codes exhibiting such characteristic are able to overcome the performance of…
Josu Etxezarreta Martinez
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Using a fractional number of classical bits within quantum teleportation

Recently, I heard that there can be transfer of rational classical bits (for example 1.5 cbits) from one party to another via quantum teleportation. In the Standard Teleportation Protocol, 2 classical bits and 1 maximally entangled shared resource…
Vijeth Aradhya
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Block encoding technique: what is it and what is it used for?

I was wondering if someone could explain to me what this technique called "block encoding" does, and what it is used for at a high level, found in arXiv:1806.01838. It is in section 4.1, definition 43; shown below. I encountered this topic while…
chois3
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Why is the Pauli group used for stabilizers?

When it comes to error correction, we take our stabilizers to be members of the Pauli group. Why is the Pauli group used for this and not, say, the group of all unitary matrices?
Quantum spaghettification
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What is the minimum integer value to make quantum factorization to be worthwhile?

Let us assume that we have quantum and classical computers such that, experimentally, each elementary logical operation of mathematical factorization is equally time-costing in classical and in quantum factorization: Which is the lowest integer…
SalvaCardona
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How do you rotate a Fock state qubit?

I read that a qubit can be encoded in a Fock state, such as the presence or absence of a photon. How do you perform single qubit rotations on Fock states?
Daniel Tordera
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How does Fourier sampling actually work (and solve the parity problem)?

I'm writing with respect to part I and part II of the Fourier sampling video lectures by Professor Umesh Vazirani. In part I they start with: In the Hadamard Transform: $$|0...0\rangle \to \sum_{\{0,1\}^n}\frac{1}{2^{n/2}}|x\rangle$$ $$|u\rangle…
Sanchayan Dutta
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Does anyone know the list of all known universal sets of quantum gates?

Does anyone know the list of all known universal sets of quantum gates? I know only two such sets: Cliffords + $T$ and rotations + CNOT.
Игорь Токарев
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Good introductory material on quantum computational complexity classes

I wish to learn more about computational complexity classes in the context of quantum computing. The medium is not so important; it could be a book, online lecture notes or the like. What matters the most are the contents. The material should…
Kiro
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Can quantum computer solve NP-complete problems?

As far as I know, quantum computers are able to solve only some of the NP-Problems in polynomial time, using the Grovers algorithm. I read that if one manages to create a reduction of Grovers algorithm on one of the NP-Complete algorithms, for…
nindo32
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Comparing method of differentiation in variational quantum circuit

Training of variational circuits needs to calculate the derivative to be optimized. Several methods were proposed (1), the most famous ones being the finite difference and the parameter shift rule. What's the difference between the two methods? Is…
incud
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Does the Curry-Howard correspondence have a quantum-specific type system?

In Wikipedia we can read that the Curry–Howard correspondence is a correspondence between formal proof calculi and type systems for models of computation. In particular, it splits into two correspondences. One at the level of formulas and types…
fr_andres
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Is HHL still BQP-complete when the matrix entries are only in {0,1}?

I'm studying BQP-completeness proofs of a number of interesting problems of Janzing and Wocjan, and Wocjan and Zhang. Janzing and Wocjan show that estimating entries of matrix powers $(A^m)_{ij}$ with $A_{ij}\in\{-1,0,1\}$ is (promise) BQP-complete.…
Mark Spinelli
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Who built the first quantum computer using at least two qubits?

In my previous question I asked who invented a quantum computer using qubits. As a follow-up to this question I want to ask who built the first quantum computer using at least two qubits. During my research I have discovered that in 1998, Jonathan…
User that hates AI
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