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1500 questions
7
votes
1 answer
Finding the norm of a Hamiltonian
I am experimenting with https://journals.aps.org/prx/pdf/10.1103/PhysRevX.8.041015 and in equation 36 I find that they use the norm of the Hamiltonian.
Is there a clean way to compute it, or an upper bound lower than $\lambda = \sum_j |w_j|$ for the…
Pablo
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7
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1 answer
'Best practices' for making Stim run as fast as possible?
I'm currently testing out an error-correction surface code circuit in Stim.
I've tried a 19x19 surface code over 10k rounds of syndrome extraction sampled 256 times, and this takes about 165 seconds. This comes out to roughly ~100s of nanoseconds…
squiggles
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7
votes
2 answers
Which qiskit backend is faster in execution of the quantum circuit prepared?
I have a quantum circuit of 40 qubits with mutliple gate operations being applied to many of the qubits. Currently I am using qasm simulator which for shots=1 took 10 hour of time. Is there any other backend which can execute my circuit faster or is…
Binshumesh sachan
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7
votes
1 answer
Quantum indistinguishability using density operators
There is something that bugs me concerning the use of density matrices. For instance, to argue that quantum teleportation does not spread an information faster than light, Nielsen and Chuang state the following:
Measuring in Alice's computational…
Tristan Nemoz
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7
votes
2 answers
What is the physical intuition behind taking the partial trace of a state?
I want to confirm my understanding of a partial trace.
Essentially, we have a system that $H_a \otimes H_b$. When we trace out system $b$, what we are doing is basically reducing the system down to as if we had just measured system $a$. Essentially,…
snickers_stickers
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7
votes
1 answer
Quantum Algorithm SAT structure
"Quantum magic won't be enough" (Bennett et al. 1997)
If you throw away the problem structure, and just consider the space of $2^n$ possible solutions, then even a quantum computer needs about $\sqrt{2^n}$ steps to find the correct one (using…
Didix
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7
votes
1 answer
Quantum Circuit for $e^{iAt}$ Hamiltonian Simulation in HHL algorithm
In HHL algorithm, there is a step in Quantum Phase Estimation where we have to apply powers of $e^{iAt}$ to the register (see pic). I am not able to understand how to find the quantum circuit corresponding to this unitary transformation i.e. if I…
quankid
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7
votes
3 answers
Are entangled and Bell states the same thing?
I am a little confused whether the entangled state and Bell state are the same thing? If they have a bit of contrast, what is the difference between them?
P.Chian
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7
votes
1 answer
How is a promise gap related to a spectral gap?
In linear algebra one often concerns oneself with the spectral gap of a given matrix, which may be defined as the difference between the smallest and second-smallest eigenvalue (or, depending on convention and context, between the largest and…
Mark Spinelli
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7
votes
2 answers
How do I get the names of all currently available IBMQ devices?
How do I get the names of all currently available IBMQ devices?
Holger
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7
votes
1 answer
How can a D-Wave style Annealing QPU help sampling?
This question is a follow-up on this one, with the hope of getting more specific clues, and was motivated by this answer by user Rob.
Also please note this posts that handle the topic of QA in much more…
fr_andres
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7
votes
1 answer
How to prove that a naive quantum random walk is non-unitary
A 2000 paper by Nayak and Vishwanath provides an analysis of the dynamics of quantum random walks. In this paper, they mention a "naive" approach to defining a walk. I include the quote as follows:
In direct analogy, one may naively try to define…
Shadow43375
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7
votes
2 answers
How do I decompose the given $4\times 4$ matrix in terms of Pauli matrices?
I have been working on a question where I have to decompose this matrix in terms of Pauli Matrices:
\begin{bmatrix}1&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&1\end{bmatrix}
I already have a solution but I don't understand the solution I've been given, this is…
Sire
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7
votes
3 answers
Partial Cyclic Permutation with only Toffoli and CNOT gates?
I have been trying to solve this puzzle of constructing this transformation from CNOT and Toffoli gates as mentioned in NC page 193 (Ex 4.27)
Here is what I have done:
First observation is it has 8 rows and columns, so it is showing the table for…
user27286
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7
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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