Tagged Questions

Quantum Computation deals with considering computation as fundamentally physical, as well as replacing the classical binary digit (bit) with the quantum binary digit (qubit). While the classical bit is either 0 or 1, the qubit can be in a superposition of these states. Computation systems that use ...

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Exercising elementary toolkit for quantum computing

One of the major challenges for me (and I expect for many as a beginning students with only general maths skills) in studying quantum computation is that while the background and calculations required ...
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How to plot a qubit on the Bloch sphere?

I've been reading pages such as this one: http://comp.uark.edu/~jgeabana/blochapps/bloch.html Which talk about the Bloch sphere, but I've been unable to figure out how to plot states on the sphere ...
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mapping of local Pauli operators

Let $A, B \subseteq P_n$, 2 finite sets of k-local commuting Pauli operators from the Pauli group $P_n$. Can we always a finite depth unitary $U$ such that $U^ \dagger AU=B$?
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Dimension of $\left(\lambda |\psi\rangle \langle\psi| +(1-\lambda)\frac{\mathrm{I}}{2}\right)^{\otimes N}$

I have the $N$-fold tensor product of a convex combination of a pure state, i.e. $|\psi\rangle\langle\psi|$ with $|\psi\rangle$ a unit vector in a complex Hilbert space of dimension two, and the ...
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Ignoring the workspace in quantum computation

In his book Quantum Computer Science, Mermin says that, although we'll need lots of "workspace" qubits in addition to those in the input and output registers, we can essentially ignore these in our ...
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Matrix for Control-Z gate

Can someone help me to prove that this Matrix: I - 2|11...1><11...1| represent (n-1) Control-Z gate (Z operator is applied to n-th qubit only if all remaining qubits are state |1>)
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Quantum algorithm writing

I'm interested in learning to write quantum algorithms, but I don't know where to start. Could someone recommend some resources for me?
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Coset state for non-abelian hidden subgroup problem

On page 14 of his classic paper, Quantum factoring, discrete logarithms and the hidden subgroup problem, Jozsa introduced a function $f$ for the non-abelian hidden subgroup representation of the graph ...
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Decomposition of a matrix into a product of two-level unitaries

I am working through example 4.12 and 4.13 from 'Quantum Computing: From Linear Algebra to Physical Realizations' (Pages 83-84 and 405-406) and I can't seem to figure out some what the '*' in figure (...
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Prove that the trace of a normal matrix is equal to the sum of the eigenvalues

Prove that the trace (main diagonal sum) of a normal matrix is equal to the sum of the eigenvalues. Note: For a matrix A to be normal we must have AA*=A* A where A* is the Hermitian Conjugate I am ...
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Toffoli gates can be decomposed into single and two-qubit gates

I'm not sure what the "I" and "-I" gates do. I can't seem to apply them correctly. When I do hadimard I get |00>(Tensor)Hadimard. If I then apply the tensor product to apply the 'i' gate on the last 2 ...
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How to represent controlled quantum circuits as matrices?

I'm trying to implement (actually, simulate) the quantum algorithm by Harrow, Hassidim and Lloyd - http://arxiv.org/abs/0811.3171 - to solve linear systems of equations using a simple $2\times2$ case ...
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Notation in formula for tensor product of Hadamard matrix

I'm having trouble understanding the notation used in a linear algebra exercise (it's exercise 2.33 of Nielsen and Chuang's "Quantum Computation and Quantum Information", page 74). The exercise gives ...
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Understanding the Quantum Fourier Transform

I have a question about the Quantum Fourier Transform. I would like to understand it because I have a re-take for an exam. I have studied the provided / recommended literature extensively. ...
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Specific system of equations with multiplications

I'm facing a math problem that I thought easy, but I'm stuck with a solution that doesn't seem optimal. The problem is the following : I have "registers" which are the expanded representation of ...