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1500 questions
6
votes
2 answers
Partial trace and SWAP in the basis of subsystems
I'm trying to derive equation $(1)$ on p.2 in Lloyd et al, 2013 which reads
$$
\text{Tr}_A\left[\exp(-i\theta S_{AB}) (\rho_A \otimes \sigma_B) \exp(i\theta S_{AB}) \right] = (\cos^2 \theta) \sigma_B + (\sin^2 \theta) \rho_B - i \sin \theta [\rho_B,…
forky40
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6
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1 answer
List of problems in the query complexity model with no super-polynomial quantum speedup
Similar to this list over at cstheory, I'm looking for a list of computational problems in the query complexity model for which it is known that no super-polynomial quantum speedups exist. What are some natural problems for which quantum computers…
gen
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6
votes
1 answer
Properties of QAOA
The QAOA algorithm consists of two elements:
The outer loop, basically a classical optimization algorithm
The quantum circuit, taking $2p$ parameters (where $p$ is the number of layers, where each layer is a gate representation of the cost and…
Nepomuk Hirsch
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6
votes
1 answer
How does the subtraction gate work in Fourier space
I am currently reading Shor's algorithm on my own and I come across a paper via this link. It shows the circuit for implementing Shor's alogrithm. Here it depicts that taking a QFT circuit on the number a on the qubits b that are already in fourier…
devance
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6
votes
1 answer
CERTIFICATE_VERIFY_FAILED after updating Python when trying to access results in IBM QE
I had a question earlier about the Numpy DeprecationWarning flooding issue. I just updated the Python in my regular jupyter notebook and have trouble running the following cell:
cal_job = execute(cal_circuits,
backend = backend,
…
ZR-
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6
votes
2 answers
How can quantum interference happen in real world if a wave function does not have any physical meaning?
I understood quantum interference as a heart of quantum computing, because it enables two possibilities to cancel each other. Quantum algorithms utilize this property to reduce the probability of returning wrong answers and thus give higher chance…
suhdonghwi
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6
votes
2 answers
Preparing Bell state $(1/\sqrt{2}) (|01\rangle + |10\rangle)$ in Qiskit
I'm working through the Qiskit textbook right now, and wanted to complete part 1 of exercise 3.4, which asks me to use qiskit to produce the Bell state:
$$\frac{|01\rangle + |10\rangle}{\sqrt{2}}$$
which is equivalent to
$$\begin{bmatrix}
0…
aikky
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6
votes
1 answer
Confusion about the output distribution of Haar random quantum states
Consider a Haar random quantum state $|\psi \rangle$. I was confused between two facts about $|\psi \rangle$, which appear related:
Consider the output distribution of a particular $n$-qubit $|\psi \rangle$. For a large enough $n$, the probability…
BlackHat18
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6
votes
2 answers
How to generalize the relationship HXH = Z for higher dimensions
Concerning the Hadamard gate and the Pauli $X$ and $Z$ gates for qubits, it is straightforward to show the following relationship via direct substitution:
$$ HXH = Z.\tag{1}$$
And I would like to demonstrate this relationship for higher dimensions…
Coconut
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6
votes
2 answers
Aren't qubits just ternary?
Qubits have 3 states: 1, 0, and 1 and 0 at the same time. If a qubit can have 3 states, then how come they are seen as different from ternary computing, which also has 3 states?
Is it that the 3 states are represented in different ways, or what?
jort57
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6
votes
3 answers
Why can I not apply a control gate/function to a gate like T, S, S dagger, ... (using IBM Quantum Experience)? Is there another option?
I am trying to use the circuit composer of the IBM QE. I am doing the inverse QFT on 3 qubits and therefore need a control on T and S dagger gates, but it won't let me.
Does anyone know why or know a way around it? I've been stuck on this for a…
Natasha
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6
votes
1 answer
Assessing speed-up via Quantum-Stochastic correspondence
You can make a natural correspondence between a quantum state vector and a classical probability vector, and between a quantum unitary operator and a classical stochastic matrix. There is also a correspondence between the quantum annealing algorithm…
hopefully coherent
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6
votes
3 answers
How to create the state $\vert 0 \rangle+i \vert 1 \rangle$ using elementary gates?
I am trying to write $|0\rangle+i|1\rangle$ in terms of elementary gates like H, CNOT, Pauli Y, using the IBM QE circuit composer.
I was thinking some kind of combination of H and Y since $Y|0\rangle=i|1\rangle$, so it is close but not…
Natasha
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6
votes
1 answer
What does $M_m |\psi_i\rangle$ mean in the equation $p(m|i)=\langle\psi_i|M_m^\dagger M_m|\psi_i\rangle$?
I have trouble understanding two equations in the Nielsen & Chuang textbook. Suppose we perform a measurement described by the operator $M_m$. If the initial state is $|\psi_i\rangle$, then the probability of getting result m…
ZR-
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6
votes
2 answers
Topology graphs of IBM's quantum computers
What is the meaning of the topology graphs of IBM's quantum computers? How should it be interpreted?
For example, how should I understand the following graph?
AL_P
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