Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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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An impossible quantum adder claimed by a journal article?

In Quantum adder of two states that are themselves superpositions, I asked: I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\sum_{j=0}^ {N-1} |j\rangle|b_j\rangle$,…
Paulske
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What's meant by the depth of a quantum circuit?

I'm using Qiskit to create quantum circuits wherein I've this attribute called depth. The documentation states it is the length of the critical path here. What does it represent and how to find it out manually?
Van Peer
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Given circuits preparing $|\psi\rangle$ and $|\phi\rangle$, what's a circuit preparing $|\psi\rangle+|\phi\rangle$?

Given a quantum circuit $C_1$ that generates a state $\vert\psi\rangle$ and another circuit $C_2$ that generates $\vert\phi\rangle$, is there a way to construct a circuit that outputs $$\frac{1}{\sqrt{2}}(\vert \psi\rangle +\vert\phi\rangle)$$ using…
Kolp
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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 algorithms are usually describe employing the…
madeel
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Block encoding technique: what is it and what is it used for?

I was wondering if someone could explain to me what this technique called "block encoding" does, and what it is used for at a high level, found in arXiv:1806.01838. It is in section 4.1, definition 43; shown below. I encountered this topic while…
chois3
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How to check if a quantum circuit can be constructed for a given matrix representation?

Let's say I have a matrix representation, e.g. $$ \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}. $$ How can I determine whether a quantum circuit can be constructed given said matrix representation?…
Dorijan Cirkveni
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Why can all quantum circuits be converted into circuits that use only real matrices?

I know that you need to add an additional ancilla qubit to "keep track" of whether or not you are in real space or imaginary space, but how exactly does this work? What is the proof for this? I tried looking online but I could not find a proof. I…
Rydberg
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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 rotations. Is there a theorem that gives…
Nichola
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Are SU($n$) operations enough for quantum computation?

Usually we want a quantum computer that can perform all foreseeable unitary operations U($n$). A quantum processor that can naturally perform at least 2 rotation operators $R_k(\theta)=\exp(-i\theta\sigma_k/2)$, where $\sigma_k$ are the Pauli…
Mauricio
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Exponentiating a product of QFT-related operators

Is there a smart way to implement $e^{i\theta\,\Phi\,\rm{QFT} \, \Phi \, \rm{QFT}^\dagger}$, where both $\Phi \propto\sum_j2^jZ_j$ and $\rm{QFT}$ act on the same set of registers? Even an approximate implementation valid for small $\theta$ would be…
mavzolej
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What is a gate-level circuit used in the 2022 Jafferis et al. experiment on Sycamore?

A recently published Nature paper of Jafferis et al. describes an experiment with a handful of qubits performed on Google's Sycamore processor to explore the SYK model in the context of AdS/CFT and quantum gravity, and states that the experiment…
Mark Spinelli
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Why do we care about the number of $T$ gates in a quantum circuit?

When reading this question and quickly reading some of the linked papers, I wondered why was the number of $T$ gates specified along the number of controlled-$X$ gates. I've often read that implementing a controlled-$X$ gate was more costly than…
Tristan Nemoz
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Apply readout error mitigation to mid-circuit measurement

I'm trying to construct a quantum circuit with 3 mid-circuit measurements, here's an example: qrz = QuantumRegister(2,'q') crz = ClassicalRegister(3,'c') qc = QuantumCircuit(qrz,crz) for i in range (3): qc.append(qc1(...),[0,1]). # qc1 is…
ZR-
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How to distinguish between collapsed and uncertain qubits in a quantum circuit?

I have been through the Young's double slit experiment. It's a direct proof or instance of showing that a wave is collapsed via observation or measurement, and shows no interference patterns. I want to do something similar in a quantum circuit, not…
Sayan Dey
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How to compute the measurement probability in swap test?

The figure of a circuit and the state are as follows. The final state before the measurement is…
karry
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