Questions tagged [quantum-gate]

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

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Qiskit's PauliTrotterEvolution yields weird gates

I am trying to work with Qiskit's PauliTrotterEvolution() module, but the resulting circuits contain weird gates that I know nothing about. Here is a simple example: I want to implement the fermionic ...
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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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2 votes
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How can I initialize a state like, $|00\rangle$ or $|01\rangle$ or $|10\rangle$ or $|11\rangle$ in Qiskit?

Many thanks in advance for your help. I am a beginner in Qiskit. I want to implement a circuit that uses the position of an element/item, of the form (x,y) and I would like to represent it as a state $...
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6 votes
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Does the controlled Pauli Z gate cause entanglement?

I'm trying to understand the relationship between the factorability of a 2 qubit gate and that gate's ability to cause entanglement. I've begun by considering the controlled Pauli Z gate. After ...
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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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4 votes
1 answer
215 views

Does a photonic quantum computer control a single photon?

Does a photonic quantum computer control a single photon and use it to represent a single qubit? I think ion trapped quantum computers use a single ion to represent a qubit. I would like to know how a ...
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Implement a square root of Swap gate in using qiskit [closed]

Does the √SWAP gate have a ready-to-use function on the Qiskit circuit library? If not, how to implement it?
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2 answers
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Strange behaviour of IdentityGate IGate in IBM Q Composer

Can anyone explain the strange impact of the IGate in the enclosed quantum teleportation setup in view of the computational basis states? Any help is welcome!
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How to decompose square root SWAP gate in Mathematica

The Quantum Mathematica add-on package is a very good tool to implement quantum gates. It contains gates as shown in this figure. How to use these gates to decompose square root SWAP gate?
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Circuit including phase factor in $XY(\beta, \theta)$ gate

In Implementation of the XY interaction family with calibration of a single pulse, the $XY(\beta, \theta)$ gate is defined as $$ XY(\beta, \theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 &...
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Show that $\langle v,O(v)\rangle= \mathrm{tr}(O|v\rangle\langle v|)$ for $v \in V$

I have a question regarding this exercise: Let O be an observable on V. Show that $\langle v,O(v)\rangle= \mathrm{tr}(O|v\rangle\langle v|)$ for $v \in V$. I thought that this exercise is quite easy ...
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How to get half-way gate of a two-qubit quantum gate? [duplicate]

If I have a quantum gate, how can I get the gate that represents half-way of that gate? As an example of what I want: How do I derive $\sqrt {SWAP} $ gate $$\sqrt {SWAP} = \left( {\matrix{ 1 &...
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How to implement gate which is like Identity but multiplied on "i"

In my program I need a single qubit processing gate which implements logic like this: |0> ==> i*|0> |1> ==> i*|1> This is like Identity gate but multiplied on "i" I ...
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4 votes
1 answer
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Why is the function operator used in Simon's algorithm unitary?

From the Qiskit textbook I read about Simon's algorithm. There are two n-wide quantum registers, so the general state is given by $$|x\rangle_n|y\rangle_n$$ where x and y are the $2^n-1$ binary ...
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1 answer
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Silicon and Germanium semiconductors mixture in quantum computing

Can Silicon and Germanium semiconductors mixture (chemical reaction) with some other chemical elements (if required) assist in creating new and existing robust electronic components? Si + Ge + ? + ? = ...
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2 votes
1 answer
115 views

At what depth and for what architecture are random quantum circuits $1$-designs?

I was confused about something related to quantum $1$ designs. Let us recap two facts we know about random circuit ensembles that form a $1$ design. $1$ design, for a quantum circuit over $n$ qubits, ...
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1 vote
1 answer
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How many single and double qubit gates are required to create a uniform superposition of vertices of a Johnson Graph J(n,r)?

Can I in $\tilde{O}(r)$ number of gates (single and double qubit) create a uniform superposition of vertices of Johnson Graph $J(n,r)$? I would like to create a state $|\psi\rangle = \frac{1}{\sqrt{n \...
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1 vote
1 answer
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Prove $E(R_n(\alpha),R_n(\theta)^n)<\epsilon/3$ from $E\big(R_n(\alpha),R_n(\alpha+\beta)\big)=|1-\exp(i\beta/2)|$

where $E(U,V)=\max_{|\psi\rangle}||(U-V)|\psi\rangle ||=||U-V||$ is the error when $V$ is implemented instead of $U$. See page 196, Quantum Computation and Quantum Information by Nielsen and Chuang. I ...
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3 votes
2 answers
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Do we need ancillary qubits to implement orthogonal measurements?

Consider an $n$ qubit state $|\psi\rangle$. Let's say I want to implement an $m$ outcome orthogonal measurement on $|\psi\rangle$, where $m \neq n$. Denote the set of $m$ orthogonal measurement ...
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1 answer
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How is transformation for measurement in an arbitrary basis derived?

I started with Qiskit today and find it very exciting. As a first question I want to understand how to measure an arbitrary state $|\Psi\rangle$ not in the basis of ...
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Decomposition of U1 gate $U_1(\lambda)$ , Phase Shift gate $\phi(\delta) $, and Swap gate [closed]

Can we express U1 gate $U_1(\lambda)$ , Phase Shift gate $\phi(\delta) $, and Swap gate $$ U_1(\lambda) = \begin{pmatrix}1 & 0 \\ 0 & e^{i\lambda}\end{pmatrix}$$ $$ \phi(\delta) = \begin{...
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1 answer
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how to know the appropriate time to know the SWAP gate operation in dipole interaction

Consider dipole-dipole interaction between two qubits,$H_{int} = g \boldsymbol\sigma_{1}\cdot\boldsymbol\sigma_{2}=g(X_1X_2+Y_1Y_2+Z_1Z_2)$. How can I show that by turning on this interaction for an ...
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3 votes
1 answer
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Conditional lower bound on approximate stabilizer rank of magic states

I am currently reading about the approximate stabilizer rank and properties of the same. I will quote the definitions from this paper. The stabilizer rank of a quantum state $|\psi\rangle$ is the ...
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1 answer
170 views

Measurement of single qubit operator $U$ which is both Hermitian and unitary with eigenvalues $±1$

Suppose we have a single qubit operator $U$ with eigenvalues $±1$, so that $U$ is both Hermitian and unitary, so it can be regarded both as an observable and a quantum gate. Suppose we wish to measure ...
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3 votes
2 answers
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What is the name of this "ancilla based" process to implement gates

I just want to know if there is a specific name for the implementation of a gate on the top qubit with the help of the bottom qubit, represented on this image: It looks like gate teleportation but it ...
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4 votes
1 answer
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Where does the "correction" in quantum error correction occur, specifically when using repetition codes?

I'm reading the part of the qiskit textbook that deals with this (https://qiskit.org/textbook/ch-quantum-hardware/error-correction-repetition-code.html) and so far it seems as though they're just ...
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1 vote
1 answer
156 views

Getting non-Clifford after performing several Clifford gates in qiskit

I'm trying to test Clifford gates in qiskit according to the table in Fault-tolerant SQ, page 101. I tried 4 Cliffords in the test $$-X/2 - X -X/2,Y/2,X/2 - -X/2,Y/2,-X/2$$ using the following code <...
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1 answer
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Why can the Hamiltonian $H=P_x(t)X+P_y(t)Y$ make an arbitrary unitary $U=R_x(b)R_y(c)R_x(d)$?

p.281 of Nielsen and Chuang's book says that A single spin might evolve under the Hamiltonian $H = P_x(t)X + P_y(t)Y$, where $P_{\{xy\}}$ are classically controllable parameters. From Exercise 4.10, ...
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1 answer
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Equivalent matrix for operators in qiskit

What is eqivalent matrix to qc.rx(np.pi, 0): ...
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6 votes
2 answers
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When can pairs of states be transformed into other pairs of states via unitary mapping?

The states $|+\rangle, |-\rangle$ can be mapped to $|0\rangle, |1\rangle$ by a simple rotation. But if I now have other states ($|\psi_0\rangle, |\psi_1\rangle$) which are not orthogonal, does a ...
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1 vote
1 answer
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Is it possible to perform $z$ rotation in Qiskit with just $x$ and $y$ rotations?

Is it possible to perform $z$ rotation in Qiskit with just $x$ and $y$ rotations? I tried the following: ...
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2 votes
1 answer
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Is the CNOT in the standard three-qubit circuit for the GHZ state necessary?

This is a very basic question about the GHZ state. I know the standard construction: A Hadamard on one qubit, and then CNOT gates with targets on all the other ones. However, why can't I just have $n$...
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3 votes
1 answer
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How to apply Euler's formula to $Z$ rotations such as $e^{i\pi/8 Z}$?

I was following the Qiskit textbook and wanted to show that $R_z (\pi/4) = e^{i \pi/8 Z}$. Plugging $\pi/4$ in for $\theta$ in the matrix from this page $ \begin{bmatrix} e^{-i \pi/8} & 0 \\ 0 &...
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1 vote
1 answer
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Decomposition of the multi-controlled gate in tensorflow quantum

In TensorFlow Quantum 0.5.0, the support for Cirq gates that have arbitrary control via the gate.controlled_by function is added. I would like to know which kind of ...
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2 votes
1 answer
74 views

What is "gate length" in quantum computing?

I am working on adding a new provider to Qiskit, and I have to specify the properties of the backend. What is "gate length" (in ns) referring to?
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1 vote
1 answer
96 views

Definition of Deutsch gate and meaning of $\theta$

I'm trying to understand the definition of a Deutsch gate. In particular what does $\theta$ mean in its presentation? Is it derived from the coefficients of the input state or a free parameter or ...
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3 votes
0 answers
53 views

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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3 votes
1 answer
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Is the square-root-of-SWAP for a pair of 4-dimensional qudits isomorphic to two square-root-of-SWAPS for two pairs of qubits?

This may be a very naïve question indicative of a lot of confusion, but I am trying to understand more about Hamiltonian simulation. I'm starting to intuit that the $n^{th}$-root-of-SWAP acting on a ...
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3 votes
1 answer
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Applying $R^{'\dagger}_{xz}$ in gate teleportation

In figure 4 of the paper Quantum Teleportation is a Universal Computational Primitive, the authors show a circuit for applying a unitary $U$ fault-tolerantly via teleportation. I'll paste the figure ...
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2 votes
2 answers
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Are composite gates within superconducting hardware implemented as a single pulse or as a series of pulses?

If we have for example a gate $U^{\otimes2}$, then within superconducting hardware, is the $U$ applied onto the first qubit and then the second or is a pulse corresponding to a composite gate (tensor ...
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1 answer
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What are the "higher moments" of the gate fidelity?

Reading the paper Gate fidelity fluctuations and quantum process invariants I came across the concept of higher moments of the gate fidelity, for example in the following excerpt from the introduction:...
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6 votes
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What is the set of generators for the qutrit Clifford group?

According to this article, any Clifford gate, acting on $n$ qubits, can be generated by Hadamard, CNOT, and S gates. What are the set of generators for qutrit Cliffords?
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1 answer
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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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4 votes
1 answer
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Qutrit analogues of controlled Z and cc-Z gates

I am trying to look for the qutrit analogues of a controlled-Z, and a cc-Z (Z gate with two controls) for qubits. There is a previous answer that gives a qutrit analogue of a CNOT gate, but does not ...
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4 votes
1 answer
143 views

Cliffordness of the qutrit Hadamard gate

Consider a simple generalization of the Hadamard gate to qutrits, defined as follows. \begin{equation} \begin{pmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0\\ \frac{1}{\sqrt{2}} &...
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2 votes
3 answers
479 views

Are these two circuits equivalent in performing controlled time-evolution?

I want to perform the controlled time-evolution of some 2 or 3-qubit Hamiltonian. Say we have this example: $$ H= Z_0\otimes Z_1 + Z_1\otimes Z_2 $$ The circuit performing the time-evolution ...
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1 vote
1 answer
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Can we do error correction for entangled particles?

There are several quantum error correction techniques, such as 3-qubit bit-flip code, and Shor’s 9-qubit code. 3-qubit bit-flip code is a straightforward technique for correcting a single error (...
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-1 votes
1 answer
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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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1 answer
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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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2 votes
1 answer
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Different statevectors with different quantity of complex numbers for same single-qubit states in Qiskit

I have several questions, but before ask, I want to write some theoretical. As we know, we can represent any single-qubit quantum state by the next representation: $$ |\psi\rangle=c_0|0\rangle+c_1|1\...
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