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1500 questions
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votes
2 answers
Why do we use ancilla qubits for error syndrome measurements?
Consider the measurement of the syndrome for the standard 3-qubit code to correct bit…
Quantum spaghettification
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9
votes
2 answers
Minimum number of 2 qubit gates to build any unitary
Any unitary $U$ acting on $N$ qubits can be decomposed in a finite product $U=U_1U_2...U_n$ where every $U_i$ acts on only 2 qubits, for example through decomposition in CNOT, phase shifts and 1 qubit rotations.
Is there a theorem that gives…
Nichola
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9
votes
2 answers
Do any specific types of qudits other than qubits and qutrits have a name?
For example, has anyone seen something like:
"quqrit" for a 4-level system[1], or
"qupit" for a 5-level system[2] ?
1 From "quad" or "quart" since "tetra" would be qutrit, which is already a 3-level system.
2 From "penta" since "quint" would…
user1271772 No more free time
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9
votes
2 answers
How does the size of a toric code torus affect its ability to protect qubits?
The Toric code Hamiltonian is:
$\sum_{x,y}\left( \prod_{i\in p(x,y)} Z_{ixy} + \prod_{i\in v(x,y)} X_{ixy} \right),$
where the $v$ and $p$ are defined according to this picture (courtesy of James Wooton's contribution to Wikipedia):
At the moment…
user1271772 No more free time
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9
votes
0 answers
How can time crystals be useful in qRAM design?
A time crystal is a phase of a matter which is ordered in time, similar to classical crystals which are ordered spatially. In other words, the structure of a time crystal is ever-changing but with some period. In fact, time crystals are quantum…
Martin Vesely
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9
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1 answer
Approximate Cloning
Question
Consider two single qubit states $\left\{|\alpha_0\rangle,|\alpha_1\rangle\right\}$ which are not orthogonal or parallel, i.e. $\left|\langle\alpha_0|\alpha_1\rangle\right|\ne0,1$. Additionally, consider the unitary operation:…
Chris Long
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9
votes
2 answers
Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?
Consider the task of fully determining an $n$-qubit state $\rho$ which can be written as
\begin{equation}\tag{1}
\rho = \sum_{p \in \{I, X, Y, Z\}^n} \text{Tr}(\rho P_{p}) P_{p}
\end{equation}
and each $P_{p} = P_{p_1} \otimes \dots \otimes…
forky40
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9
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2 answers
Is the Kraus representation of a quantum channel equivalent to a unitary evolution in an enlarged space?
I understand that there are two ways to think about 'general quantum operators'.
Way 1
We can think of them as trace-preserving completely positive operators. These can be written in the form
$$\rho'=\sum_k A_k \rho A_k^\dagger \tag{1}$$
where…
Quantum spaghettification
- 1,452
- 10
- 27
9
votes
2 answers
What precisely is Reverse Annealing?
Quantum Annealing, (related questions Quantum Annealing, or hamiltonian related) is the process used in D-Waves' Quantum Annealer, in which the energy landscapes are explored, for different solutions, and by tuning a suitable Hamiltonian, zero in to…
user3483902
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9
votes
1 answer
Quantum chemistry: references
I have heard about Quantum chemistry as one of the main applications of quantum computers. However, I have not found concrete related articles with circuit-implementations for these applications.
Does anyone have articles on simulating molecules…
nippon
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9
votes
2 answers
What is the maximum separation between two entangled qubits that has been achieved experimentally?
Considering two entangled flying qubits, as far as I know, there is no physical limit for separating them without losing quantum information.
See: Is there any theoretical limit to the distance at which particles can remain…
SalvaCardona
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9
votes
1 answer
Is there an intuitive way to conceptualize the ground and excited states of a transmon qubit?
I understand how a transmon qubit is analogous to an LC circuit, but has an anharmonic energy spectrum due to the nonlinearity of the Josephson junction. I also understand how to write out the Hamiltonian and the significance of the contributing…
taryn3194
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9
votes
1 answer
How efficient is Qiskit's unitary decomposition?
In Qiskit's extension package we have the UnitaryGate module that you can initialize using a unitary matrix and then add it to your circuit. How efficiently is this decomposition done under the hood?
Also, if I wanted to do the decomposition myself,…
Dani007
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9
votes
5 answers
Why can't quantum computation replace classical computation?
I am not a total novice of quantum computation (have read the first 6 chapters of Nielsen and Chuang, though not familiar with every part), but there are some fundamental questions that I don't know answers well.
One question that has bothered me is…
Liren Lin
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9
votes
2 answers
Transpilation into custom gate set in qiskit
In qiskit, I can transpile a given circuit into a some predefined gate set as follows (just an example)
from qiskit import QuantumCircuit
from qiskit.compiler import transpile
from qiskit.circuit.random import random_circuit
basis_gates = ['id',…
Nikita Nemkov
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