Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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Why, in Grover's algorithm, $H^{\otimes n}(2|0\rangle\! \langle0| - \mathcal{I})H^{\otimes n}=2|\psi\rangle \!\langle\psi| - \mathcal{I}$?

I've been working through Grovers algorithm. I've read many times that $*^1H^{\otimes n}(2|0\rangle \langle0| - \mathcal{I})H^{\otimes n}$ is equivalent to $*^22|\psi\rangle \langle\psi| - \mathcal{I}$. I did verify that $*^2$ turns $\sum_x…
Leander Behr
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What does the error rate on the IBMQ website mean？

How is the error rate pointed by the arrow defined? How did you get it? thanks!
wei zi
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Self reducibility of QCMA problems

Self reducibility is when search version of the problems in a language reduce to decision versions of the same problems. NP-complete problems are self reducible. Are QCMA complete problems self reducible?
BlackHat18
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How to construct a circuit to perform this operation? Is there a general way of getting a circuit from a matrix?

I want to build a circuit that performs the following operation: $$ U_f = \left(\begin{array}{cccccccccc} 1 & 0 & 0 & \dots & \dots & \dots & \dots & \dots & \dots & 0 \\ 0 & 1 & 0 & & & & & & & \vdots\\ 0 & 0 & 1 & & & & & & & \vdots \\ \vdots & &…
SrJaimito
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How to draw Qiskit's HHL algorithm as a circuit?

Qiskit Aqua has a module that implements the HHL algorithm: https://qiskit.org/documentation/stable/0.32/stubs/qiskit.aqua.algorithms.HHL.html How does one draw the implemented circuit? *** EDIT *** I'm working with an example from the github. I…
user727041
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How is the partial trace related to the operator sum representation?

In Quantum Computation and Quantum Information by Nielsen and Chuang, the authors introduce operator sum representation in Section 8.2.3. They denote the evolution of a density matrix, when given an environment, is the following: $$\varepsilon…
C. Ardayfio
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How to define a quantum channel for the partial trace?

I understand that the partial trace is a linear map, a completely positive map and a trace-preserving map. However, I have no idea how to define a quantum channel with the partial trace because partial trace depends on an index $i$(i.e. $i$ of…
John
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Marriott-Watrous style amplification with a quantum input

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$ In MW05 the authors demonstrate so-called "in-place" amplitude amplification for QMA, exhibiting a method for Arthur to amplify his success probability without…
bean
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What is the location of the Qiskit config file?

I'm trying to follow the instructions here https://qiskit.org/documentation/getting_started.html. It says The default backend for qiskit.visualization.circuit_drawer() or QuantumCircuit.draw() is the text backend. However, depending on your …
user1936752
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How do quantum states collapse to the right answer?

I am a computer engineer and have recently started understanding quantum computers. I am still struggling to wrap my head around some concepts. One such query is the following - It is said that during the computation the qubits exist in the…
dhiraj suvarna
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Can I imagine quantum computers as working via parallel computing?

Beginners question, so please stay on the beginner's level with possible answers. I know very well what a qubit, superposition, and entanglement is. Also, I am familiar with several physical realizations so to speak of qubits and entanglement and…
Gerard
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How to parallelly run a quantum circuit on IBMQ?

I am trying to implement the following circuit and my code is The above circuit has size 5 and depth 3. My question is, how can I run the circuit parallelly. I mean, the gate circuit.cx(qr[0], qr[1]) and gate circuit.cx(qr[2], qr[3]) will be run…
wei zi
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What does W stand for in the W entangled state?

For the $|W_3\rangle=\frac{1}{\sqrt{3}}(|001\rangle+|010\rangle+|100\rangle)$, what does W stand for? Does it refer to an author name? Anyone knows a reference? Thanks
czwang
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How to check if a two-qubit gate is entangling?

I would like to know if there's an analog for Schmidt rank that can tell me if a two-qubit unitary is entangling? Suppose I have a parametrized two-qubit unitary $U^{(2)}(\theta)$. I would like to know a test to tell the degree of entanglement this…
forky40
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Shor's Code: Understanding how it satisfies Knill Laflamme Theorem

I'm new to Quantum Error Correction, and I have a question on Shor's Code. If we have a protected subspace, $V \subset \mathbf{C}^2\otimes \cdots \otimes \mathbf{C}^2$ $V=\operatorname{span}\{|0_{l}\rangle, |1_{L}\rangle.$ We also consider Pauli…
Anon
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