Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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Quantum channel representation of projective measurement

Let $P$ be a projector and $Q = I-P$ be its complement. How to find probability $p$ and unitaries $U_1, U_2$ such that for any $\rho$, $P\rho P + Q\rho Q = p U_1\rho U_1^\dagger + (1-p)U_2\rho U_2^\dagger$? (This is Nielsen and Chuang Exercise…
snsunx
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Clarification of the "Calculations" section of the (HHL09) paper

I am reading this paper entitled "Quantum algorithm for linear systems of equations" and am trying to understand a portion of the algorithm described on page 2 and in more detail in the appendix starting at the bottom of page 10 (section 3. Phase…
IntegrateThis
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Sequential circuit using quantum gates

Without feedback/loop how can we build a sequential circuit? The basic feature of sequential circuit is that is depends not only on the current inputs but also on the previous inputs/outputs. I've gone through few papers on reversible gates and I'm…
Nikhil Ayyadevara
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Grover's diffusion on subset of input space

Is it possible to run grover's diffusion step on a subset of the possible input space? By this, I mean is it possible to do the diffusion process with a state space isn't in a total superposition of all states. Let's say I have a 2 qubit system in a…
Chase Roberts
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Summation of amplitudes

I was wondering how to create generalized entangled superpositions of qubits when I came to need of an algorithm to generate the following: Suppose we have two $n$ qubit states, $$|\psi\rangle = \sum_X \alpha_X\ |X\rangle$$ and, $$|\phi\rangle =…
kichapps
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How to calculate the fidelity of a certain gate of a IBMQ device in Qiskit using randomized benchmarking/tomography?

For example, I want to calculate the fidelity of a 1-qubit and 2-qubit gates (similar to the result shown in figure 2 in this paper). Is there any way to do that in Qiskit? I've gone through the Qiskit Ignis documentation, but I didn't see if it's…
Trong Duong
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How to make qubits more stable towards noise?

In this paper and this paper, the "Noise Stability of Qubits" (the stability of qubits to external noise) has been discussed. In the first one, Gil Kalai states that it is difficult to create a quantum computer since the noise produced in creating a…
SchrodingersCat
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Most efficient way for general state generation

Assume we are given an $n$-qubit system and complex numbers $a_0, \ldots, a_{m-1}$ with $m = 2^n$. Assume further we start with the initial state $|0 \ldots 0\rangle$ and want to make the transformation $$|0 \ldots 0\rangle \rightarrow…
tobias
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Understanding the oracle in Deutsch's algorithm

I am reading John Watrous' notes from his course CPSC 519 on quantum computing. In a pre-discussion before presenting Deutsch's algorithm to determine whether a function is constant or not, the author presents a function $B_f |x \rangle |y \rangle =…
IntegrateThis
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Are there disadvantages in using the inner product between states instead of the fidelity?

Would there be any disadvantages of using inner product, that is, $\mathrm{Tr}(A^{\dagger}B)$ (say making it, $\mathrm{Tr}(\sqrt A \sqrt B)$ to normalise) to quantify how far two quantum states are instead of fidelity, which is…
Mahathi Vempati
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Degradable channels and their quantum capacity

Note: I'm reposting this question as it was deleted by the original author, so that we do not lose out on the existing answer there, by Prof. Watrous. Further answers are obviously welcome. I have two questions: What are degradable channels? Given…
Sanchayan Dutta
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Quantum circuit for computing fidelity

Suppose we use Uhlmann-Jozsa fidelity $$ F(\rho, \sigma):=\left(\mathrm{tr}\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}}\right)^2. $$ Can we construct a quantum circuit that helps us calculate the fidelity of two mixed states?
raycosine
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How should we interpret these quantum logic gates as physical observables?

In quantum mechanics each operator corresponds to some physical observable, but say we have the operators $X,Y,Z,H, \operatorname{CNOT}$. I understand how these gates act on qubits, but what do they actually represent in terms of a physical…
bhapi
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What's the difference between Kraus operators and measurement operators?

It is said in a lecture note[1] by John Preskill that, Equivalently, we may imagine measuring system $B$ in the basis $\{|a\rangle\}$, but failing to record the measurement outcome, so we are forced to average over all the possible post-measurement…
Shuai
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How to show a density matrix is in a pure/mixed state?

Say we have a single qubit with some density matrix, for example lets say we have the density matrix $\rho=\begin{pmatrix}3/4&1/2\\1/2&1/2\end{pmatrix}$. I would like to know what is the procedure for checking whether this state is pure or mixed. I…
bhapi
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