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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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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?
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
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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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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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What are theta, phi and lambda in cu1(theta, ctl, tgt) and cu3(theta, phi, lam, ctl, tgt)? What are the rotation matrices being used?
I was reading the documentation for qiskit.QuantumCircuit and came across the functions cu1(theta, ctl, tgt) and cu3(theta, phi, lam, ctl, tgt). Looking at the names they seem to be controlled rotations. ctrl represents the controlled qubit and tgt…
Sanchayan Dutta
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8
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How to translate between continuous variable model and discrete model?
If I understand correctly, the discrete and continuous variable (CV) version of quantum computation are equivalent. However, the continuous aspect of the CV model makes me wonder to what extent can both models be compared. Given a discrete-gate…
Mauricio
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HHL algorithm -- problem with the outcome of postselection
See edit at the end of the question
All the references in this question refer to Quantum algorithm for solving linear systems of equations (Harrow, Hassidim & Lloyd, 2009).
HHL algorithm consists in an application of the quantum phase estimation…
Adrien Suau
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2 answers
Why doesn't Shor's algorithm output a solution for some numbers?
I've been trying to mess around with Qiskit's implementation of Shor's algorithm, and while trying I've noticed that Shor(33), for example, would not output a solution (even with an absurd number of attempts). Qiskit's implementation would retry by…
Nuno Costa
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What channels preserve the purity of all pure inputs?
Consider channels $\Phi$ such that $\Phi(|\psi\rangle\!\langle\psi|)$ is pure for all $|\psi\rangle$. Is there a simple way to characterise channels with this property?
Let's suppose $\Phi$ acts between input and output spaces of the same dimension.…
glS
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8
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2 answers
What is the matrix of the iSwap gate?
Mostly I'm confused over whether the common convention is to use +$i$ or -$i$ along the anti-diagonal of the middle $2\times 2$ block.
Craig Gidney
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What are the possible Kraus operators of the identity channel?
Consider a Kraus representation $\{A_a\}_a$ of the identity channel $\mathcal{I}$ that maps any state to itself. Of course, $\{A_a\}_a$ are not the simplest Kraus operators, which would just be $\{I\}$, and they need not to be orthogonal. Is there a…
Shadumu
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Can quantum money be reliably "burned?"
One of the novel features of Bitcoin and other cryptocurrencies is that coins can be irrefutably "burned" or destroyed, by creating a transaction to send the money to a junk burn address.
Thinking similarly about quantum money - from knots, or…
Mark Spinelli
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8
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Two definitions of the Clifford group and their relation
Clifford groups are used in at least 3 places I've encountered so far in QIP:
A circuit that contains only Clifford operations, which are generated from CNOT, H and P, is sufficient for a wide variety of quantum circuits, as shown here.
Clifford…
Lior
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8
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What are the P(0) and P(1) probabilities for the T transformation in quantum computing?
I'm just starting of on quantum computing, specifically following the IBM Q Experience documentation [1]. In here, they are explaining the following experiment:
$T|+\rangle$
The expected outcomes according to the document:
Phase angle: $\pi/4$…
Thomas Hubregtsen
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Construct Controlled-$G^{\dagger}$ from known Controlled-$G$
Let there be a known a scheme (quantum circuit) of Controlled-G, where unitary gate G has G$^†$ such that G≠G$^†$ and GG$^†$=I (for example S and S$^†$, T and T$^†$, V and V$^†$, but not Pauli and H gates).
My question for the experts is:
How is…
John Lancaster
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