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1500 questions
13
votes
1 answer
Advantage of simulating sparse Hamiltonians
In @DaftWullie's answer to this question he showed how to represent in terms of quantum gates the matrix used as example in this article. However, I believe it to be unlikely to have such well structured matrices in real life examples, therefore I…
FSic
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13
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2 answers
Hamiltonian simulation with complex coefficients
As part of a variational algorithm, I would like to construct a quantum circuit (ideally with pyQuil) that simulates a Hamiltonian of the form:
$H = 0.3 \cdot Z_3Z_4 + 0.12\cdot Z_1Z_3 + [...] +
- 11.03 \cdot Z_3 - 10.92 \cdot Z_4 + \mathbf{0.12i…
Mark Fingerhuth
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13
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What are physically allowed CNOTs for Rigetti's 19 qubit chip and Google's 72 qubit BristleCone chip?
For each IBM quantum chip, one can write a dictionary mapping each control qubit j to a list of its physically allowed targets, assuming j is the control of a CNOT. For example,
ibmqx4_c_to_tars = {
0: [],
1: [0],
2: [0, 1, 4],
3:…
rrtucci
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13
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1 answer
Does the Quantum Fourier Transform require universality?
Background:
In most setups of fault-tolerant quantum computation, universality is achieved using Clifford gates such as $(S, H, \text{CNOT})$ and the $T$-gate.
The Eastin-Knill theorem can be informally stated that it will be difficult (although…
Frederik Ravn Klausen
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3 answers
Are there any quantum algorithms conjectured to give an exponential speedup for a non-oracle problem that don't use the Quantum Fourier Transform?
The Quantum Fourier Transform (QFT) subroutine seems ubiquitous in most quantum algorithms that are conjectured to give an exponential (or at least superpolynomial) speedup over the best classical algorithms for the same classical (non-oracle,…
tparker
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13
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How does the number of copies affect the diamond distance?
Suppose we are given two maps $\Phi$ and $\Psi$ such that
$$\|\Phi-\Psi\|_{\diamond}\leqslant\varepsilon.$$
What can we say about $\left\|\Phi^{\otimes t}-\Psi^{\otimes t}\right\|_{\diamond}$? Is it upper-bounded by $t\varepsilon$? Is the result…
Tristan Nemoz
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13
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1 answer
Prove that the trace distance is upper-bounded by the Hilbert-Schmidt distance
In (Haah et al. 2015), in the third page, second column, the authors use the following result: given a pair of states $\rho,\sigma$, we have
$$
\|\rho-\sigma\|_1 \le 2\sqrt{\min(\operatorname{rank}(\rho),\operatorname{rank}(\sigma))}…
glS
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13
votes
3 answers
What are the possible ways to visualise large, entangled states?
What are the prominent visualizations used to depict large, entangled states and in what context are they most commonly applied?
What are their advantages and disadvantages?
SLesslyTall
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13
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1 answer
How to implement a matrix exponential in a quantum circuit?
Maybe it is a naive question, but I cannot figure out how to actually exponentiate a matrix in a quantum circuit.
Assuming to have a generic square matrix A, if I want to obtain its exponential, $e^{A}$, i can use the series
$$e^{A} \simeq I+…
FSic
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13
votes
1 answer
How can classical bits be copied if qubits cannot be copied?
The no-cloning theorem of quantum mechanics tells us there can be no general quantum circuit that can copy arbitrary qubit states, i.e. a quantum gate or circuit cannot send $|0\rangle |\psi\rangle\mapsto|\psi\rangle |\psi\rangle$ for arbitrary…
MaximusIdeal
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13
votes
1 answer
What is the relationship between the Toffoli gate and the Popescu-Rohrlich box?
Background
The Toffoli gate is a 3-input, 3-output classical logic gate. It sends $(x, y, a)$ to $(x, y, a \oplus (x \cdot y))$. It is significant in that it is universal for reversible (classical) computation.
The Popescu-Rohrlich box is the…
Evan Jenkins
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13
votes
2 answers
Quantum XNOR Gate Construction
Tried asking here first, since a similar question had been asked on that site. Seems more relevant for this site however.
It is my current understanding that a quantum XOR gate is the CNOT gate. Is the quantum XNOR gate a CCNOT gate?
user820789
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13
votes
3 answers
What is the actual power of Quantum Phase Estimation?
I have some perplexity concerning the concept of phase estimation: by definition, given a unitary operator $U$ and an eigenvector $|u\rangle$ with related eigenvalue $\text{exp}(2\pi i \phi)$, the phase estimation allows to find the value of…
FSic
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13
votes
6 answers
Resources for quantum algorithm basics
I have just started to learn about quantum computing, and I know a little bit about qubits. What is a resource where I can learn a basic quantum algorithm and the concepts behind how it works?
Vashi
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13
votes
3 answers
Quantum advantage with only Clifford gates (Gottesman Knill theorem)
Let's say I want to solve a computational task which input can be encoded in $n$ bits of information.
The look for a quantum advantage is (usually) asking to find a quantum algorithm in which there are exponentially fewer gates and qubits required…
Marco Fellous-Asiani
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