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14 votes

Does control and target matter in the CZ (Controlled-Z) Gate?

First, note that the Controlled-X gate can be written as: $$ CX = |0\rangle \langle 0| \otimes I + |1 \rangle \langle 1| \otimes X $$ This tells us that the first qubit is the controlled, and the ...
KAJ226's user avatar
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5 votes
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Does quantum control allow to implement any gate?

There is the concept of controllability of a quantum system, i.e. do the given set of controls permit you to create any state or unitary? Usually this is computed by looking at the Lie Algebra of the ...
DaftWullie's user avatar
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4 votes
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Gate cancellations in Hamiltonian simulation

It is true that these two circuits are equivalent: as the the controlled qubit $q_1$ is the same. So if $q_1$ is a $|1\rangle$ then you can see that it will apply two $X$ gates to $q_2$ and they will ...
KAJ226's user avatar
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3 votes

What is the matrix representation of a generic two-qubit controlled unitary operation?

Note that if you have the first qubit as the control qubit, and the second qubit as the target, then you can write $CU$ gate as follow: $$ CU_{12} = |0\rangle \langle 0| \otimes I + |1 \rangle \...
KAJ226's user avatar
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3 votes
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What are examples of Kraus operators describing the process of control error?

Control errors The term control error is generally used to refer to errors due to imperfections of the qubit control system. Hardware devices that control qubit evolution have a number of knobs that ...
Adam Zalcman's user avatar
3 votes
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How do you produce an algebra from a set $\{H, H_i\}$ via commutation?

In general, an algebra $\mathcal{A}$ generated from a set $\{H_1, H_2,..., H_n\}$ by commutation refers to the algebra whose generators are $H_1,H_2,...,H_n$, all their first-order commutators $C_{ij} ...
Sanchayan Dutta's user avatar
2 votes
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Hamiltonian simulation: how can I incorporate the constant before each term?

You'll place the phase within the CRz gate. The approach you've taken essentially argues that: $$ e^{it H_3} \approx e^{it \alpha X_1 \otimes Y_2} e^{it \beta Z_1 \otimes Z_2} $$ So, when you're ...
C. Kang's user avatar
  • 1,754
2 votes

Does the Lie closure of a set of Hamiltonians describe all unitaries you can generate with them?

Theorem. Given $H_1, \ldots, H_k\in\mathbb C^{d\times d}$ Hermitian let $\mathfrak{g} := \langle iH_1, ... iH_k \rangle_{\text{Lie}}$ denote the associated Lie algebra and let $e^{\mathfrak g}$ be the ...
Frederik vom Ende's user avatar
2 votes
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What does ramp mean in the context of quantum control/pulse shape?

A ramp up (or down) is just a gradual increase (cq. decrease) of a signal. By 'fixed' I think they just mean at a fixed rate, i.e. linear. See also: https://en.wikipedia.org/wiki/Ramp_function https://...
Johan's user avatar
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2 votes

Quantum gates for more than two basis states

If you want the best possible evolution for your qubit space, then you simply don't define what your target is on the rest of the space - so long as you always start in the two-dimensional subspace/...
DaftWullie's user avatar
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2 votes
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Multi-control multi-target gate

We can create a quantum gate from any unitary operator $U$ using UnitaryGate class. And we can add any number of controls to any gate using ...
Egretta.Thula's user avatar
1 vote

How to embed Qiskit into proprietary setting

Creating a custom backend is a bit complicated task (I might be wrong). But for what you want I would suggest you to take a look at the GenericBackendV2 python code ...
Shravan Patel's user avatar
1 vote

Underlying Hamiltonians and pulse level controls of different commercially available quantum computers

This hamiltonian is a very basic approximation of the underlying device and in general does not accurately reflect the complexity of the device. It is up to each provider to decide whether to return ...
ThomasAlexander's user avatar
1 vote

Understanding the Quantum Circuit for Bell State Creation with Dynamic Circuit using Qiskit

Hadamard gate creates equal superposition on qubit 0. Qubit 1 remains in state $|0\rangle$. Then qubit 0 is measured. If the result is $|1\rangle$, then this qubit is inverted and it is finally in ...
Martin Vesely's user avatar
1 vote
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Why can't I derive the scale of DRAG pulse's Q-component by making f_{ef} vanish?

I will answer my own question: I forgot the modulation. After putting it back, we will have $$\hat{s}(\omega)=(1-\beta(\omega-\omega_c))\hat{g}(\omega-\omega_c)\Longrightarrow\beta=1/(\omega_{ef}-\...
Ziyuan's user avatar
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1 vote
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impossible to design a quantum circuit that uses ‘black box ’ U to implement the controlled unitary CU

Why not try controlled-$S$? i.e. $$ U=S=\begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix}. $$ If I act controlled-$S$ on $(|00\rangle+|11\rangle)/\sqrt{2}$, it produces $(|00\rangle+i|11\rangle)/\...
DaftWullie's user avatar
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1 vote

GRAPE with Python?

I ended up modifying qutip for this purpose and it was kind of painful. There are several classes that need to be modified. You can check my repo for that version. https://github.com/PiggsBoson/qutip
Will Yang's user avatar
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1 vote

What is the matrix representation of a generic two-qubit controlled unitary operation?

For your first question, you are right, so here are 2 examples: And for the second question, since operation happen only in case second qubit is 1, and nothing is changing when second qubit is 0: ...
Ron Cohen's user avatar
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1 vote

Do individual qubits on IBM quantum processors share the same control unit?

From Demonstration of quantum volume 64 on a superconducting quantum computing system chapter IV on dynamical decoupling, we read: When quantum circuits are mapped to physical hardware, not all ...
3yakuya's user avatar
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1 vote
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How to obtain control and drift Hamiltonians for device in Qiskit?

The Qiskit units are unitless and require the drive Hamiltonian provided by the backend to link the program into a simulatable format. Keep in mind the Hamiltonian unit's are angular frequencies. Real ...
ThomasAlexander's user avatar
1 vote

What are the runtimes of the different modes of qiskit's mcx?

"Runtime" is not so easily quantified, it depends a lot on the compilation, the other operations in your circuit and whether you simulate or have a real backend. Generally, the different ...
Cryoris's user avatar
  • 2,953
1 vote

What is the difference between quantum control and quantum optimal control?

Indeed,quantum control theory studies whether a system is controllable or not. For example, if you have a Hamiltonian, there are several tests that rely on the Lie algebra, such as the Lie-Trotter ...
quest's user avatar
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1 vote

Deriving Bloch vector $dr$ from master equation

While I'm of course 4 years late I'd like to answer this question for the sake of posterity. tl;dr: Your calculations for the $Z$-measurement ($X=\sqrt{2\kappa}\sigma_z$) are correct and for the ...
Frederik vom Ende's user avatar
1 vote

The control phase gate in Quantum fourier transform and the question it brings up regarding control gates in general

You are correct that a controlled-gate should be written in the form $P_0\otimes I+P_1\otimes U$ for a unitary $U$. It certainly should not be of the form $I\otimes U$. I don't have a copy of your ...
DaftWullie's user avatar
  • 59.4k
1 vote

control gate with 3 inputs, two control and rotation gate

...
Enrique Segura's user avatar

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