Questions tagged [quantum-gate]

For questions regarding usage, performance, implementation, application or theory related to quantum gates.

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59 views

How does the graphical notation used to denote doubly-controlled gates work?

$\qquad$ $\qquad$ What is the difference between solid and hollow? How to express the corresponding matrix of these figures? In addition, if they are not adjacent, what should be done in the middle of ...
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Is there anything Quantikz can do that Tikz cannot do?

I am learning how to draw quantum circuits. I was checking the options available and I could see that Tikz and Quantikz are suitable for making circuits diagrams but I want to know if there are some ...
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How the simulator work?

Recently I focused on how to simulate in classical computer, and I found Qiskit offers qasmsimulator and statevector simulator. ...
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Applying a gate to all line qubits without explicitly listing them in Cirq

Say we have a custom gate CG, defined by a unitary matrix U, and line qubits qubits in Cirq. ...
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Visualizing custom gates in Cirq

I'm trying to visualize a custom gate in Cirq. I have through this page, which briefly mentions how to create custom gates in Cirq. However, I'm getting errors when trying to visualize it. My current ...
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Question About How Qiskit Reset Gate Affects Other Entangled Qubits

I am trying to understand how the reset gate in Qiskit affects qubits its entangled with. Consider the following circuit with qubits $q_0$ and $q_1$: Where circuit240 takes $|0\rangle$ to $a|0\rangle ...
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1answer
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How to prepare a quantum circuit for $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle+|10\rangle)$ starting from $|00\rangle$

How do I prepare a quantum circuit for $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle+|10\rangle)$ state starting from the $|00\rangle$ state? I have no clue how to do it. I tried with controlled Hadamard ...
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1answer
246 views

Quantum Circuit To Compute Any Inner Product

I'm currently reading the paper Classification with Quantum Neural Networks on Near Term Processors It shows a method to determine the following quantity: Where U is a unitary operator acting on $|z,...
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1answer
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Interconnection clarification?

I just want to clear what seems to be a bit confusing to me with quantum gates and their corresponding output. below are 3 scenarios implementing two hadamard gates two hadamard gates on one qubit ...
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1answer
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Grover's Algorithm on a Database with more than 50% matching entries

The Setup for Grover's Algorithm is the following: Given an oracle $f_O^{\pm}$ representing a Query on a Database with total $N$ entries $N$ of which $k$ are matching. Grover's Algorithm is used to ...
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1answer
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How do you embed a POVM matrix in a Unitary?

In QuantumKatas Measurement Task 2.3 - Peres-Wooter's Game, we are given 3 states A,B and C. We construct a POVM of these states. But how do we convert that POVM into a Unitary that we can apply. ...
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How can a half-wave plate affect the position qubit and not the polarization qubit of a photon?

I recently was watching these 2 videos on Coursera which show how to build a simple quantum computer that can implement the simplest case of the Deutsch-Jozsa algorithm (which uses only 2 qubits). ...
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Expectation value of an operator error: Composition is not defined over operators of different dimensions,

I am trying to calculate the expectation value of a customized operator on two similar but differently constructed states $\phi = \phi_2 =\frac{1}{\sqrt{2}}\left( |001⟩ + |011⟩\right)$ which consist ...
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What are some general concepts of how a classical computer would interface with a quantum computer?

Very general question so I'm not looking for an exact answer. I just want a basic description of certain ways it can be done and then if possible the names of those ways, so that I can look them up ...
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A question about how does the single qubit gate simulated in simulator?

I have found the procedure of simulation process as this picture : Image reference. So in the low-level compilers, all single-qubit gates are approximated by the universal gate set (CNOT, H, T, S). ...
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How to calculate destabilizer group of toric and other codes

Some papers use the "destabilizer group" for more efficient simulations; see for example (page 3): https://www.scottaaronson.com/showcase2/report/ted-yoder.pdf "In addition to ...
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Prove expressions for visibilities $\operatorname{Tr}(\rho_a^2\rho_b^2), \operatorname{Tr}[(\rho_a \rho_b)^2]$ in terms of SWAP operations

Given two states $\rho_a$ and $\rho_b$, and knowing that the SWAP gate swaps two qubits, how can one prove that visibilities $v_1=Tr[\rho_a^2 \rho_b^2] = Tr[S_{AB} S_{BC} S_{CD} \rho_a \otimes \rho_a \...
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Quantum operations as sparse matrices

What are examples of quantum operators or evolutions of quantum states that can be modeled as sparse matrices?
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What are the practical limitations of complementing quantum computations with memristors?

Considering the current state of research into quantum memristors, and the advantages/disadvantages of quantum and memristor driven computing architectures: Quantum Memristors Quantum Memristor ...
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Question about DIY Quantum Computer Prototype

I recently came across these 2 videos on Coursera which show how to build a simple quantum computer that can implement the simplest case of the Deutsch-Jozsa algorithm (which uses only 2 qubits). ...
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2answers
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What are generators for a “real” Clifford group?

I work with stabilizer codes using the real version of Pauli matrices: $X=((0,1),(1,0))$, $Z=((1,0),(0,-1))$, $Y=XZ$ (not $\imath XZ$). I know the encoders for these codes lie in the Clifford group ...
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50 views

Are quantum operations reversible?

If We perform some unitary operations on a Quantum State $|A\rangle$ after which it becomes$|A'\rangle$. Then if we perform the inverse of all those unitary operations on the state $|A'\rangle$ in ...
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Is there a quantum operation to change a phase $e^{(0.q_0 q_1 q_2 q_3)}$ into $e^{(0.q_1 q_2 q_3)}$?

Given a set of four qubits, say $q_{0},q_{1},q_{2},q_{3}$ which represent a $4$-bit binary number with $q_{0}$ as the MSB. After applying QFT on these qubits the phase of $q_{0}$using the concept of ...
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How do I encode a classical vector into the input qubits?

Does anyone know how to encode a classical vector into a quantum state? For instance, I would like to encoder a classical vector $(0, 0.1, 0.4, 0.9)$ into 2 qubits by adding some quantum gates on 2 $|...
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1answer
24 views

What is the shortest sequence of decomposition a given single-qubit unitary gate

Given a single-qubit unitary matrix, can we find the shortest sequence of Clifford + T gates that correspond to that unitary? According to Fast and efficient exact synthesis of single qubit unitaries ...
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How to solve these questions? [duplicate]

Link: v.ht/qhash. Here are some of the best questions available on the net, if anyone could code them in Q#, then it would be great. By solving you will gain experience on qubits, quantum gates, ...
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Is it possible to create a gate in Q# that is dictated by a matrix?

When observing the Hadamard gate it is simply a transformation matrix. I am wondering if there is functionality to hard code an arbitrary transformation matrix and its family members up till $m \times ...
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2answers
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How to find a circuit for the roots of QFT?

After reading about using quantum gates instead of ancillas, it asserts that every quantum circuit has a square root. Theoretically, they do, but is there a practical method to generate the quantum ...
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Difference between $Rz$ and $R1$ gate [closed]

You are given an operation that implements a single-qubit unitary transformation: either the Rz gate or the R1 gate. The operation will have Adjoint and Controlled variants defined. Your task is to ...
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1answer
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How to append an Instruction to a QuantumCircuit with variable length of QuantumRegisters as qargs?

I think it is a bug but I'm not really sure. Basically, what I'm trying to do is the following: I have an Oracle Instruction which I want to append to my QuantumCircuit, looks as follows: ...
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Is it possible to express u1(λ) through the gates rx, ry, rz while maintaining the phase? In Qiskit for example

Is it possible to express gate u1(λ) through the gates rx, ry, rz while maintaining the phase? Both in principle and in practice (in Qiskit for example)? The single gate rz(λ) is not suitable, because ...
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A question about a real programmable quantum computer

In the theory of universal quantum gates,I have known a common universal gate set is the Clifford + T gate set, which is composed of the CNOT, H, S and T gates. Then there is a concept called "...
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Question about the practical use of super dense coding in information transmission [duplicate]

Question about the practical use of super dense coding in information transmission: We know that by using super dense coding it is possible to transmit 2n classical bits transmitting n qubits, ...
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3answers
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How to spot the matrix representation of the quantum NOT operation

Applying the above construction to AND we get the map $(x1,x2,y) \rightarrow (x1,x2,y⊕(x1∧x2))$ for $x1,x2,y \in \{0,1\}$. The unitaryoperator which implements this is then simply the map $|x1〉|x2〉|y&...
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Show that a $CZ$ gate can be implemented using a $CNOT$ gate and Hadamard gates

Show that a $CZ$ gate can be implemented using a $CNOT$ gate and Hadamard gates and write down the corresponding circuit. Recall from Quantum Information Theory that $Z=HXH$. As $CNOT$ is a ...
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2answers
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Example of a quantum algorithm better than its classical counterpart which involves only $1$ qubit?

I was reading over the proof of the Deutsch-Jozsa algorithm, which in its simplest case, involves at least 2 qubits. Is there an example of a quantum algorithm that is better than it's classical ...
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1answer
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The effect of available information on random quantum channels

This question is about the effect of available information on random quantum channels. Suppose there are two black box devices. Device 1. We have a black box device with a single qubit in it. Once ...
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1answer
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Do all physical architectures for quantum computers use the same universal gate sets?

Now I have understood that physical implementation of quantum computer need a universal quantum gate set like Clifford+T to realize any unitary quantum gate. However, I don't know if it is all the ...
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Is it possible to create a quantum computer with a double-slit or Stern-Gerlach apparatus?

If we choose double-slit, can we put multiple "slits" and create calculation for just one algorithm (problem, solution...)? Not general purpose quantum CPU, just for one. Same question for Stern-...
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1answer
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Is $e^{i\beta} R_Z(-2\beta)$ equivalent to $U_1(2\beta)$?

As far as I know the single qubit gate $$ e^{i\beta\sigma_z} = \begin{bmatrix} e^{i\beta} & 0 \\ 0 & e^{-i\beta} \end{bmatrix} = e^{i\beta} \begin{bmatrix} 1 & 0 \\ 0 & e^{-i2\beta} \...
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a question about quantum gate decomposition on simulator or emulator

I have read a paper about "approximated decomposition" of a unitary single gate (Solovay-Kitaev algorithm) which told us a any unitary single gate can be decomposed into {Hadamard, Phase} with any ...
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1answer
52 views

How to decompose unitary quantum gate in current simulator or emulator?

I have a question about how to decompose a unitary quantum gate in a currently existing simulator or emulator. I have read some papers about SK algorithm and other algorithms which aim to decompose ...
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1answer
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Understanding the length of the sequence obtained via Solovay-Kitaev decomposition

I have downloaded two codes of SK algorithm from GitHub and try to understand how to decompose a unitary single qubit gate. These code are https://github.com/DEBARGHYA4469/Quantum-Compiler and https:/...
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What do coupling coefficients mean in terms of Pauli gates, and why are they time dependent?

Hi I am reading this error mitigation paper by the IBM team and I am slightly confused about the meaning of "coupling coefficients" when describing multi-qubit Hamiltonian. I have only seen coupling ...
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122 views

How to decompose a unitary single qubit gate by universal quantum gate set?

How to decompose a unitary single qubit gate? I have read some paper or books, which told me a unitary single qubit gate could be decomposed by universal quantum gates set. For example {phase gate, ...
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1answer
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Are these two circuits equivalent (using swap gates with control qubits)?

Hi. I'm trying to make a circuit including some Toffoli gates in Qiskit. The problem is that, because of connectivity between qubits, some gates should be modified to satisfy it. I've read this ...
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2answers
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How can I code a Conditional phase shift transform?

I am interested in implementing a operation in Q#. The operation should follow the algorithm below: When $A=0$ it is quite easy to see that the algorithm states if the qubitt is in nullspace apply a ...
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2answers
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What are the possible qubit states?

For a quantum state on the form $$|\psi \rangle = \alpha |0 \rangle + \beta |1 \rangle$$ which possible qubit states can you construct from this? I know that $\alpha$ and $\beta$ must satisfy $$|\...
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1answer
54 views

quantum gates hamiltonian [closed]

How could we construct a circuit with quantum gates for desired time-dependent hamiltonian? For example I think we can have 3 steps : a simple hamiltonian :$ 2\sigma_x+ 3 \sigma_z$ a time ...
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1answer
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Quantum NOR Gate

How to implement NOR gate functionality within a quantum circuit? Having $3$ input bits $f(x) \rightarrow y$, I would like to achieve $y=1$ every time when $x=?00$ is on input ($x=000$ or $x=100$).

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