# Questions tagged [quantum-circuit]

a model in which a computation is a sequence of quantum gates, which are reversible transformations on an n-qubit register (the quantum-mechanical analog of an n-bit register)

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### 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 ...
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### Is it possible to use the mitigation process on a teleportation circuit?

Is it possible to use the mitigation process on a teleportation circuit? Sorry, i'm still starting, if someone can get me out of this doubt, I would appreciate it. The circuit I'm trying to make this ...
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### Complexity of quantum circuits in a specific protocol

Consider the following simultaneous communication problem. Alice and Bob do not share any entanglement or any common randomness, and cannot communicate directly with each other. As inputs, $x$ is ...
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### How to design a RF-SQUID qubit by Qiskit Metal?

I am now learning how to use Qiskit Metal to design superconducting circuits. I found that there are only several transmon qubits in the library. Can I design an RF-SQUID qubit by using Qiskit metal? ...
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### Writing circuits in Qiskit using only Clifford and T gates

Is there a way in Qiskit to write my circuit using only Clifford and T gates (CX, S, H, T and I think also $S^\dagger$ and $T^\dagger$)? With the function compile (with aer simulator) it gives me some ...
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### Random quantum circuits and general efficient POVM measurement

Let's consider a random quantum circuit $C$, applied to the $n$ qubit initial state $|0^{n}\rangle$, producing the state $|\psi\rangle$. Consider a general efficiently implementable $m$-outcome POVM ...
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### How can one define contextuality within the circuit model?

It is in general believed that contextuality is one of the quantum resource that provides the quantum advantage. A context is usually defined in terms of a set of commuting observables. The quantum ...
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### How is quantum transpilation scaled?

While thinking about a quantum transpiler's working I had a pretty basic doubt. Say that we are trying to transpile an $n$ qubit circuit where $n > 100$. What transpiler does is that it first tries ...
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### Why does the output from FANOUT appear on the second and third bits?

Figure 1.16: FANOUT with the Toffoli gate, with the second bit being the input to the FANOUT (and the other two bits standard ancilla states), and the output from the FANOUT appearing on the second ...
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### How do successive operators act in the Heisenberg picture?

In the Schrodinger picture, it is clear how write a single gate for two operators. For example if operators $A$ then $B$ act on a state $\vert \psi \rangle$, this gives $BA\vert \psi \rangle$, (noting ...
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### How does a quantum circuit calculating the inverse of a non-injective function act?

Lets say I have a non-injective function $f()$, adding image for reference. Now lets say I build a quantum circuit to calculate $f^{-1}()$. If the input register has the value $i$, does the output ...
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### Restrictions on Quantum Gates and Pure Partially Traced Output States

Suppose we have a quantum circuit that contains an arbitrary number of quantum gates and takes as an input more than a single qubit, say three. What are the restrictions on the quantum gates and the ...
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### Quantum fourier transform with classical vibrations

Is there any difference in effect between a quantum circuit and a carefully constructed analogue one relying on interference? For example, why couldn't I take a series of $N$ carefully shaped pipes, ...
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### Generalized push for $\land_{ab}(X)$ gate

EDIT: In the following I am using the Feynman notation for controlled operations - e.g. $\land_{ab}(X)$ is equivalent to a $CNOT$ with control qubit $q_a$ and target $q_b$. Ultimately, for any single-...
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### What is the correlation between Toffoli and a more generic rotation shown in qiskit textbook

Can someone help me understand the correlation between the 2 diagrams in the qiskit textbook.
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### Why are these two QFT circuits equivalent?

I am new to quantum computing and have been trying to understand the Quantum Fourier Transform (QFT). Through my research using both the Qiskit textbook and other sources, I see differences in how the ...
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### Understand the circuit of Normal Distribution

This is the circuit for NormalDistribution(3, mu=1, sigma=1, bounds=(0, 2)). How do I understand what this circuit is doing?
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### How do I find the state of each qubit at the end of the circuit?

I have this Quantum Fourier Transform (QFT) and I want to know how to find the final state of each qubit if q0, q1, ...
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### How to construct a controlled $V$ gate in qiskit?

I have come across most of the quantum circuit which contains gate such as controlled $V$ and $V^{\dagger}$ but I dont know how to code it in Qiskit.
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### Feynman method and polynomial time algorithm for XQUATH

Consider the Feynman algorithm for simulating quantum circuits, as given here. Consider the XQUATH conjecture for random quantum circuits from here, given by (XQUATH, or Linear Cross-Entropy Quantum ...
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### Exercise 4.41 in N&C book QCQI: how can i implement $R_z(\theta)$ using the circuit shown and $Z$?

I'm studying Nielsen and Chuang's book. I cannot solve one of the questions in the exercise 4.41. The question is the last one that is Explain how repeated use of this circuit and Z gates may be used ...
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### Query complexity on Quantum Pattern Matching of Mateus Algorithm

I am trying to understand the complexity of the Mateus and Omar algorithm for quantum pattern matching, it is clear to me from the pseudocode that the query complexity is $O(\sqrt{N})$, apart from the ...
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### Marginal output probability of first bit for constant-depth circuits

Consider a constant depth $1\text{D}$ quantum circuit, which is applied to the input state $|0^{n}\rangle$, and whose output is measured in the standard basis. You can assume that the gates of the ...
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### How to visualize Hadamard gate as $X$-$Z$-$X$ decomposition?

In the book Quantum Computation and Quantum Information by Nielsen and Chuang, chapter 4, exercise 4.4 (pg. 175), the author has asked to express Hadamard gate as product of $R_x$, $R_z$ rotations and ...
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I would like to know if it is possible implement the following situation in Qiskit (either using the simulators or real quantum computers). Consider this illustrative toy example: The arrows ...
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### How can I write unit tests for a pennylane circuit?

I have several mixing unitary circuits written using Pennylane to be used in the QAOA algorithm. Furthermore, I'd like to write unit tests for these mixing circuits to ensure that the code is doing ...