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1500 questions
8
votes
5 answers
How accurate is this figure by TIME magazine?
Below is a figure from a TIME magazine edition. I have a few questions regarding this representation of quantum computing:
Is saying "0 and 1 at the same time" a correct statement? Isn't the qubit just in a superposition of both states, not "both…
Rydberg
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8
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Is LOCC equivalence the same as LU equivalence?
I'm currently learning on LOCC transformations. In the Dur, 2000 paper, there is a statement that
(...) two pure states $|\psi\rangle$ and $|\phi\rangle$ can be obtained with certainty from each other by means of LOCC if and only if they are…
Steve J.
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8
votes
1 answer
Inverses and the Clifford Hierarchy
Elements of the (qubit) Clifford Hierarchy are unitary matrices. For a good definition of the Clifford Hierarchy see: Is there a closure property for the entire Clifford hierarchy?
While a complete structure theorem for the Clifford Hierarchy,…
Jonas Anderson
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8
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What is a gate-level circuit used in the 2022 Jafferis et al. experiment on Sycamore?
A recently published Nature paper of Jafferis et al. describes an experiment with a handful of qubits performed on Google's Sycamore processor to explore the SYK model in the context of AdS/CFT and quantum gravity, and states that the experiment…
Mark Spinelli
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8
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1 answer
Is there a CPTP map that takes $\rho_{AB}$ to $\rho_A\otimes\rho_B$?
Given some joint state $\rho_{AB}$, one can find either the marginal state $\rho_A$ or the marginal state $\rho_B$ through a CPTP map. The proof being that partial tracing is indeed CPTP.
Is a CPTP map that outputs $\rho_A\otimes\rho_B$ possible?
user1936752
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8
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1 answer
If a quantum algorithm requires a measurement, how can we use that as a subroutine in another quantum algorithm?
Some algorithms (like period finding), use one or more measurement step. The post measurement state is then acted upon by another set of gates to complete the algorithm.
If I imagine this as blackbox algorithm $f$ which takes $x$ as input and…
ssj009
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8
votes
1 answer
What is the minimum number of non-Clifford gates does it take to prepare a superposition over all "two-hot" basis vectors?
The generalized W state:
$$W_n=\frac{1}{\sqrt{n}}(|100\cdots 0\rangle + |010\cdots 0\rangle + \ldots + |00\cdots 01\rangle)$$
is often thought of as the uniform superposition over all "one-hot" basis vectors, as each such vector has a single qubit…
Mark Spinelli
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8
votes
1 answer
How to derive the quantum Fisher information from the relative entropy?
The quantum relative entropy (QRE) between two states $\rho$ and $\sigma$ is given by
$$
S(\rho\|\sigma)=\operatorname{Tr}(\rho\ln\rho)-\operatorname{Tr}(\rho\ln\sigma)
$$
Now if $\rho$ and $\sigma$ are infinitesimally related i.e,…
m1rohit
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8
votes
3 answers
Is quantum computer without entanglement no better than anything classically achievable?
Today I saw a tweet by Tom Wong which writes: "Did you know? Without quantum entanglement, quantum computers would be no better than traditional computers."
But I remember I came up with papers like this one, which says in the abstract: "We present…
user777
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8
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1 answer
Are indistinguishable bosons and fermions computationally equivalent to distinguishable qubits?
From the middle-late decades of the last century, many researchers such as Bennett, Benoif, Deutsch, Feynman, Manin, Wiesner, among others, had some intuition that qubits are computationally more powerful or more interesting than classical…
Mark Spinelli
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8
votes
2 answers
Additive Codes: What are they? And how are they related to stabilizer codes?
I recently encountered the term "additive code" in the answer to my question here
What are nontrivial examples of stabilizer codes whose codewords have some $\pm i$ coefficients?
Implicit in the answer seems to be the claim that additive codes are…
Ian Gershon Teixeira
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8
votes
3 answers
What is the difference between Error Mitigation (EM) and Quantum Error Correction (QEC)?
From what I understood, EM is mostly post-processing and does not affect quantum circuit complexity whereas QEC has overheads and integrates as part of a quantum circuit. Is this correct?
Also, which method is better or more promising? Could you…
MonteNero
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8
votes
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Do we have to trust the bank in "Quantum Money from Hidden Subspaces?"
What level of trust in the bank is needed in "Quantum Money from Hidden Subspaces" of Aaronson and Christiano (arXiv)?
The bank's mint works by first generating a uniformly random classical secret string $r$, and then generating a banknote…
Mark Spinelli
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8
votes
1 answer
SWAP gate(s) in the $R(\lambda^{-1})$ step of the HHL circuit for $4\times 4$ systems
Context:
On the 5th page of the paper Quantum circuit design for solving linear systems of equations (Cao et al, 2012) there's this circuit:
Schematic:
A brief schematic of what's actually happening in the circuit is:
Question:
Cao et al.'s…
Sanchayan Dutta
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8
votes
2 answers
Matrix representation of continuous-variable gates
In the introduction to continuous-variable quantum computing by Strawberry Fields (Xanadu), it lists the primary CV gates (rotation, displacement, squeezing, beamsplitter, cubic phase) along with their unitary:
What are the matrix representations…
user820789
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