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Quantum Belief Propagation decoding
I have been reading about a family of quantum error correction codes called Quantum Turbo Codes, which are the quantum analog of the well-known classical Turbo codes. This codes were introduced in quantum serial turbo codes and the…
Josu Etxezarreta Martinez
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6
votes
1 answer
Why no $Z$'s in the $\operatorname{F} (\sum_{j=0}^{n-1} 2^j Z_j) \operatorname{F}^\dagger$ operator?
An interesting numerical observation is that an operator defined as $\phi=\sum_{j=0}^{n-1} 2^j Z_j$ upon a QFT is rotated into an operator $\pi=\operatorname{F} \phi \operatorname{F}^\dagger$ which does not have any Pauli $Z$'s in its expansion. Is…
mavzolej
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6
votes
2 answers
Just want to confirm: Do two CNOT gates cancel each other?
I see somewhere that this happens:
But I wonder if this is just identity.
Ka Wa Yip
- 171
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6
votes
1 answer
Efficient method to find square root of a Hamiltonian
I'm working with a Hamiltonian $H$ represented as a linear combination of Pauli strings:
$$H = \sum_j \alpha_j P_j,$$
where $P_j \in \{I, X, Y, Z\}^{\otimes n}$ are tensor products of Pauli matrices and $n$ is the number of qubits.
I'm looking for…
Kushagra Garg
- 63
- 4
6
votes
2 answers
Is there a tool that can give you the unitary representing a quantum circuit from just a string?
Say I have a string representing the operations of a quantum circuit.
I want to have the unitary operator representing it.
Is there a tool for doing so in Python or else?
cnada
- 4,802
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6
votes
2 answers
How do we code the matrix for a controlled operation knowing the control qubit, the target qubit and the $2\times 2$ unitary?
Having n qubits, I want to have the unitary described a controlled operation.
Say for example you get as input a unitary, an index for a controlled qubit and another for a target.
How would you code this unitary operation?
cnada
- 4,802
- 1
- 9
- 22
6
votes
2 answers
Incorrectly Calculating Probability Amplitudes for 3-qbit Circuit
I’m trying to calculate the probability amplitudes for this circuit:
My Octave code is:
sys = kron([1; 0], [1;0], [1;0])
h = 1/sqrt(2) * [1 1; 1 -1];
c = [1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 1 0];
op1 = kron(h, eye(2), eye(2));
op2 = kron(c,…
Sam Kennedy
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6
votes
2 answers
Why do Bell states have all real coefficients?
Canonically, the four Bell or EPR states for 2-qubit systems are given by:
$|\Phi^{\pm}\rangle = \frac{1}{\sqrt{2}} \left( |00\rangle \pm |11\rangle\right)$
$|\psi^{\pm}\rangle = \frac{1}{\sqrt{2}} \left( |01\rangle \pm |10\rangle\right)$.
I'm…
Danyel
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6
votes
1 answer
Which currently known quantum algorithms cannot be derived from the QSVT algorithm?
I have just started reading the paper A Grand Unification of Quantum Algorithms. There is a claim on page 2 that "by simply adjusting the parameters of QSVT, one can construct nearly all known quantum algorithms".
On the same page, the paper states…
Miriam K.
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6
votes
0 answers
Universal gate set for the $ [[15,1,3]] $ code
The $ [[15,1,3]] $ triorthogonal code implements transversal $ T $. Since it is a CSS code, two blocks will also have a transversal $ CNOT $ gate. To get a universal gate set all that is required is an implementation of the Hadamard gate $ H $.
The…
Ian Gershon Teixeira
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6
votes
4 answers
Are there even distance color codes?
The surface code comes in both odd-distance and even-distance forms. Color codes always seem to come in odd-distance. Presumably this is due to the fact that the X and Z observables overlap at the boundary of a color code, and they must anticommute,…
Craig Gidney
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6
votes
1 answer
What is the definition of color codes?
Is there a generally accepted definition of what a color code is?
I have found two definitions that I am not able to reconciliate with each other:
The error correction zoo defines color codes via homogeneous simplicial complexes as the…
qubitzer
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6
votes
2 answers
How many qubits are simulable with a normal computer and freely accessible simulators?
I want to simulate an arbitrary isolated quantum circuit acting on $n$ qubits (i.e. a pure state of $n$ qubits).
As I know RAM is the bottleneck for quantum simulators, you can consider a "normal" computer to have between $4$ and $8$ Gio of RAM, all…
Adrien Suau
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6
votes
1 answer
Is there a concentration inequality for the quantum gate fidelity $F(C,U)$ for a channel $C$ such that $\int dU F(C,U)=X$?
For a fixed quantum channel $N$ and a unitary channel $U$, we define $N$'s gate fidelity as
$$ F(N,U) = \int \langle \psi| U \, N(| \psi \rangle \langle \psi |) \, U^\dagger| \psi \rangle d\mu_H(\psi)$$
where $\mu_H$ is the Haar measure over…
Davide Li Calsi
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- 3
6
votes
2 answers
What are some good quantum computing simulator and visualiser?
I am looking for some good software to simulate quantum computing, visually if possible.
I know about quirk (http://algassert.com/quirk)
and IBM Q Experience (https://quantumexperience.ng.bluemix.net)
I just saw this question ( Does conditional gate…
Adrien Nivaggioli
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