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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Does QFT exploit entanglement?

I was studying the quantum circuit for the Quantum Fourier Transform (QFT) on the Mike & Ike, and they write the result of the transformation as a product state. More precisely they wrote the ...
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Why does quantum teleportation need more than one Hadamard and two CNOTs? [closed]

Why does quantum teleportation require anything more than Hadamard on Q1 then CNOT between Q1 and Q2 and then CNOT between Q0 and Q1? I will do my best to understand notation, but I am new and do not ...
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How to create superposition of states with fixed parity with a quantum circuit?

I'm searching for a circuit to generate, starting from the $|00\, ...\,0\rangle$ state, an arbitrary superposition of all states with either even or odd parity. The gate choice is irrelevant for now, ...
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How to create a Bell state with asymmetric amplitudes using single-qubit and CNOT gates?

Is there a systematic way - in terms of a quantum circuit with single qubit and CNOT gates - to create a bell state with asymmetric amplitudes, e.g., $$ \alpha |00\rangle + \beta|11\rangle $$ where $\...
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How does a quantum circuit capture the "non-halting ability" of classical Turing machines?

It is claimed that a quantum Turing machine is "computationally" equivalent to the circuit model. Quantum computing also includes all classical computing. However, we know that there are ...
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What is the difference between the two entanglement circuits?

For a three qubits system to be in an entanglement(GHZ) state, the circuit can be built as per Qiskit, Here, the control bit of the second X gate is on q0. what if the control bit is shifted to q1. ...
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From the final quantum state to the quantum circuit composition

When I build a quantum circuit and my initial state is the one composed only by zeros ($|000\ldots 0\rangle$), I have a final state $|\psi\rangle$ that is the result of the application of the quantum ...
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How should I think about circuit metrics like "qubit count," "circuit depth," and "gate count" when dealing with the OpenQASM 3 `ctrl` modifier?

It seems like circuit metrics like qubit count, circuit depth, and gate count are pretty useful. Qubit count determines whether a it's even possible to run a program on resource-limited quantum ...
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Tweak the parameter `p` of QAOA in qiskit

I am solving a QUBO using QAOA. It works flawlessly with default parameters for smaller instances of the problem, but my RAM is saturated when I try to solve a problem of size 15. I suspect this can ...
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Compute the output of this Approximate Quantum Cloning three-qubit circuit

Above is a circuit for "Approximate Quantum Cloning" The preparation state is given by $$|\psi\rangle =\alpha|0\rangle+\beta|1\rangle$$ The gates labelled $\theta_i$ denote single qubit ...
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How to tranfer given superposition to quantum circuit?

Let's say I have a superposition of qubit defined as $\frac{1}{2} (| 000 \rangle + | 001 \rangle + | 111 \rangle + | 110 \rangle)$ (as given in the answer here: Explanation of output produced by the ...
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Are there ''interesting'' examples of circuits where gates can all commute each other?

Are there ''interesting'' examples of circuits where gates can all commute each other? More formally, there may be some group of circuits where gates and, particularly, CNOTs (as the only two-qubit ...
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How to Construct Swap Gates from Permutation Matrix?

This is a follow-up question from here. Let's say after an LUP decomposition, we have an 8x8 permutation matrix: $ P^{-1} = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ ...
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Evaluating the derivative of a Quantum Circuit

After this post this weekend which got an excellent response, I've been trying to get into the solution that is given by the paper and applying it to my circuit. My original circuit is far bigger and ...
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What exactly is the "quantum singular value decomposition"?

I know what is singular value decomposition, meaning given a matrix and write it as multiplication three different matrices, and middle matrix being diagonal and entries are singular values. So, what ...
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Is there a quantum circuit builder package that allows you to import/export a circuit as a JSON?

I've done a superficial search in each of the qiskit, cirq, and braket open source repositories for such a feature, but can't find any explicit examples of this functionality. I'm wondering if anyone ...
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FRQI wrong interpretation

I try to use FRQI https://qiskit.org/textbook/ch-applications/image-processing-frqi-neqr.html with the same circuit. Suppose I have the following image: and the flatten representation is [0 100 200 ...
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FRQI for 8x8 image

I read the paper A flexible representation of quantum images for polynomial preparation, image compression, and processing operations and found a scheme for 2x2 images which looks like this: I tried ...
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How to determine the basis state with maximum amplitude without measurement?

Suppose I have two quantum registers described respectively by the quantum states $| \psi_1 \rangle = \sum_i \alpha_i |i \rangle$ and $|\psi_2 \rangle = |0\rangle$. I would like to implement a CNOT ...
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Understanding Constant Multiplication Circuit for Binary Field - How to Construct Quantum Circuit from Linear Mapping

I was thinking to ask this on Math Stackexchange, but maybe here would be better since I also hope the answers also explain from quantum computation context. Problem So I was reading the paper "...
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Measuring in qiskit collapses onto the Z-Plane. Why do any rotations other than Y matter?

We have the situation where a 50/50 split between $|1\rangle$ and $|0\rangle$. This was done using a $H$-Gate. Now, when measuring in qiskit, if my understanding is ...
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Four-qubit error correction code

$\newcommand{\ket}[1]{\left|#1\right>}$ Consider the following 4-qubit code which allows you to detect a bitflip and/or a phaseflip. The logical 0 and 1 are encoded as: \begin{align*} \ket{0}_{...
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How to detect and correct swap errors in a quantum circuit?

Let's assume that I have a density matrix $\rho$ that consists of $N$ qubits. If this density matrix undergoes an error-channel that swaps any two qubits with an equal probability, i.e. $$ \mathcal{E}(...
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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 ...
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Working with higher energy states in Qiskit Experiments

I'm looking at the source code for the Qiskit Experiments module and see that the EFRabi class subclasses the Rabi class with the intent of calibrating rotations between the 1 and 2 states instead of ...
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Optimal decompositions of some standard multi-qubit gates

To have a concrete example in mind: 3-qubit Toffoli gate can be decomposed into 6 $CNOT$s as shown here I believe this is the most economic decomposition in terms of the number of $CNOT$s used. My ...
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How to create a quantum circuit to implement the same operations but acting on different qubits?

I want the draw the quantum circuit of the following Hamiltonian: $$H = - 4 \times X\otimes X\otimes X\otimes X - 4\times Z\otimes Z\otimes Z \otimes Z$$. I have been able to draw the circuits of $ - ...
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What is the relationship between cX gate and measurment?

I'm currently working with the cX gate but I have the question: This gate is a projection to sigmax axis on the bloch sphere if y partially trace the target qubit? Or i mean, what is the relationship ...
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How to analyze the following quantum circuit?

I'm trying to analyze the following quantum circuit The goal here is to analyze the final outputs at q3 & q4. For inputs, at q0 & q1, one of the Bell state $$|\psi\rangle = \frac{|01\rangle + ...
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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 to efficiently construct quantum circuits of oracles in multi-target quantum search?

In standard Grover's quantum search with only one target or its extension of multi-target quantum search, one of the two key parts is to quantize the boolean function $$f(x):\{0,1,\cdots,N-1\}\...
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Implementation of FANOUT using Toffoli gates

Consider the following implementation of FANOUT using Toffoli gates: I'm confused about the following statement: "the second bit being the input to the FANOUT and the other two bits standard ...
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Why isn't FANIN required to be able to simulate all other elements in a classical circuit

In Nielsen and Chuang, there's the following paragraph: The Toffoli gate can be used to simulate NAND gates and can also be used to do FANOUT. With these two operations, it becomes possible to ...
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Quantum Circuits for Time-Series Data

I am currently working with a dataset with autocorrelated features, i.e, x(t) affects the value of x(t+1) which affects the value of x(t+2). Suppose this is the circuit representing x(t): Does ...
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Can someone explain using H and T gates repeatedly?

The Qiskit textbook says it is used because $R_x$, $R_y$, and $R_z$ are not accurate single qubit rotations. Can someone elaborate what the repeated $H$ and $T$ gates actually do? In what scenario ...
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The use of modulo 2 in state representation after CNOT

The following circuit with a CNOT gate has the following effect on a computational basis state $|a, b\rangle$, where all additions are done modulo 2. Why is the state of the second qubit changed to $...
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Initial state preparation for Hadamard test

I thought I understood Hadamard test but it seems to be shaky. I understand that to get the expectation value $\langle\psi\ | V^\dagger|{\bf Q}|V|\psi\rangle$ we need to have gate $V$ (in blue) below ...
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Applying a projector or a general nonunitary gate in the middle of a circuit using qiskit

Is there a way to implement a projector gate in a middle of a circuit?. For instance, assuming I have a Bell state $|00\rangle+|11\rangle$, I'd like to apply a projector on the first qubit onto state $...
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Is there an efficient quantum circuit that create a random permuntation matrix?

Suppose we want to generate a random, random according to some probability distribution, unitary permutation matrix that is applied to an input of $n$ qubits. So is there an efficient polynomial time ...
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Getting exponential sequence of coefficients with not so many $T$-gates

Let $\Psi \in (\mathbb{C}^2)^{\otimes n}$ be a $n$-qubit quantum state. In the computational basis, we can write $\Psi$ as $$\Psi = \sum_{(i_1, \dots, i_n) \in \mathbb{F}_2^n} \Psi_{i_1, \dots, i_n} |...
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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 ...