Questions tagged [quantum-gate]

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

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Hadamard Overlap Test

I am trying to understand a test called Hadamard Overlap Test, which consists of a destructive swap test (section IV of swap test and Hong-Ou-Mandel effect are equivalent) right after a Hadamard test. ...
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Sequential circuit using quantum gates

Without feedback/loop how can we build a sequential circuit? The basic feature of sequential circuit is that is depends not only on the current inputs but also on the previous inputs/outputs. I've ...
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Postselection and hardness of estimating amplitudes

Let $A$ be a class of quantum circuits such that \begin{equation} \text{Post}A = \text{Post}BQP, \end{equation} where $\text{Post}$ indicates post-selection. Is only this amount of information ...
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How many qubits and how many gates, are required for finding the eigenvalues of a matrix?

Say I have an $N \times N$ matrix and I want to know the eigenvalues to a precision of $\pm \epsilon$. How many qubits and how many gates do I need?
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How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?

This is a sequel to How are two different registers being used as "control"? I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
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What is the difference between quantum control and quantum optimal control?

In the context of quantum control theory, it is common to see references to both quantum control and quantum optimal control (e.g. 0910.2350 or the guide on qutip quantrum control functions). ...
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Given a non-Clifford quantum circuit $U$, is it possible to construct a commuting Clifford circuit $C$?

Given a non-Clifford circuit $U$, say $U = \prod_{i=1}^k e^{i \theta_i P_i} $ for $P_i \in \{ I,X,Y,Z\}^{\otimes n} $ and $\theta_i \in \mathbb{R}$. Is it possible to construct a non-trivial Clifford ...
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Two qubit gate decomposition in using Qiskit

I am writing some python code to be able to optimise the total error in two qubit gate decomposition. I am using the Qiskit module qiskit.quantum_info.synthesis.two_qubit_decompose My question relates ...
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How do we realise photonic gates?

I am interested in photonic computing, and I am curious how the gates work. I once saw a picture of a photonic CNOT gate that used just mirrors and polarizers. I have not been able to find any ...
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Is the universality of a qubit based quantum computer different from the universality of a continuous-variable quantum computer?

I understand that a quantum computer is universal if it can compute anything that a quantum Turing machine can. Another way to think about universality is that any unitary transformation on, e.g., a ...
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Equivalence checking of quantum circuits up to error

Suppose you are given two circuit descriptions $A$ and $B$ where by a circuit description I mean a sequence of gates (in the order they are applied) and the qubits they are applied on. (For the sake ...
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Exact functions of a single-iteration Grover Search Algorithm's operators

I'm doing a practice assignment where I'm asked to identify specific features of the Grover Search Algorithm's second operator (picture in post, further on "$Us$"), which mirrors the system relative ...
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There exists an efficient gate that swaps values of different superposition kets?

Is there an efficient gate that swaps values of different superposition kets? Let $ \alpha_i, \beta_i $ be string in $ \{0,1\}^n$, I'm wondering if there are a known results about the existence of ...
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Is the Eastin-Knill Theorem incorrect?

I am reading through this paper (the Eastin-Knill Theorem) and there is a step in the proof of the main theorem that I do not understand. Let $Q$ be a composite quantum system supporting a quantum ...
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Solovay-Kitaev Balanced Group Commutators in SU(2) Implementation

I am currently looking into quantum compilation and came across Dawson and Nielsen's paper on the Solovay-Kitaev Algorithm, which seems like a good starting point as it is referenced in a many of the ...
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Universality for reversible classical computation

Is there any way to check whether a set of gates (for example, take the set comprising of the CNOT gate and the Hadamard gate) is universal for reversible classical computation? I can think of trial ...
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Extract the Crosstalk noise of a circuit in Qiskit

I'm new to Quantum Computing. How to extract the cross-talk noise of a quantum circuit using qiskit? Can someone provide an example code for this?
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An algorithm to perform Gram-Schmidt orthogonalization of linearly independent state vectors

In the first paragraph of the 2nd section of this article, it is stated that given a set of linearly independent $n$-qubit state vectors, Alice can perform the Gram-Schmidt procedure to obtain ...
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Good resources for seeing qubit control pulse shapes (Transmon qubits)

I'm looking for resources which can show the pulse shapes for various single-qubit and two-qubit gates. More specifically, is there any resource which can show me calibrated pulse shapes so that I can ...
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Which codes can implement transversal non-Clifford gates

A paper Three-dimensional surface codes: Transversal gates and fault-tolerant architectures discusses 3D surface codes and shows that CZ and CCZ gates are transversal in [these] codes. They give a ...
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What is the thought process for circuit making after seeing input and output of a matrix?

Here is an exercise (4.27) from Nielsen and Chuang and I found the answer (given in the figure below) online without any explanation. The question was to construct a circuit by seeing a matrix (given ...
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How can I express controlled unitary operation in QPE of this implementation of HHL?

I have found this implementation of HHL, and I don't understand why the controlled unitary operation is expressed in the form of $\exp(i t_0 A/2)$ and $\exp(i t_0 A/4)$. The rotation of $\pi$ and $\...
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What is the correct name of this quantum gate? Possibly state control gate

Let $\vec v \in \mathbb{C}^2 $ be the following quantum state: $$ \vec v = \frac{1}{\sqrt{2}}\begin{bmatrix} v_{1} \\ v_{2} \\ \end{bmatrix},\space \lvert v_1 \rvert = 1,...
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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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Is there a way to directly construct controlled gates in continuous variable (CV) quantum computation?

We know that a universal gate set for CV quantum computation is that of squeezing, beam splitters, and some nonlinear gate (e.g. this answer). We also know from Knill, Laflamme, and Milburn that ...
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Reducing an ansatz to a shallower circuit

Given a very general hardware efficient ansatz as in Figure: and say that you already know all the rotation parameter for the gates in the red box, is there any way to build a gate sequence that ...
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How does Spin Measurement correspond to quantum NOT gate?

Newbie in quantum computing (and stack overflow) here. I am confused regarding the relation between spin measurement in quantum mechanics and the quantum NOT gate. I have a Bloch sphere picture of a ...
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Calculating length of code words in quantum information(compression)

I was studying this article by Boestrom and Felbinger. We define the significant length of the codewords in the preparation of the communication protocol : $$L_c(w_i) = \lceil log_k(i) \rceil$$ We ...
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When writing data into qRAM, can I do it in a superposition state?

In general, quantum algorithms are said to be hybrid algorithms. Especially when storing data in qRAM, it seems to be done through classical calculations. Is it possible to write this part directly to ...
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Implementing controlled $U_3$ gate from $R_{\hat{n}}$ with given parameters

This is a follow-up question to solve for parameters of a controlled $U_3$ gate. Suppose I have the unit vector $\hat{n} = (n_x,n_y,n_z)$ and an angle $\xi$ (assume we know both of them). Then, we ...
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Implementation of the "Quantum Verification of Matrix Products" algorithm

I would like to implement a Quantum Verification of Matrix Products, using Ambainis OR Burhman algorithm but I don't know how to start. There isn't much documentation about it, and no circuit in the ...
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Fowler Distance in Solovay-Kitaev Algorithm

I have been using this code to implement the Solovay-Kitaev algorithm for approximating arbitrary single qubit gates. One measure of success it gives is the 'Fowler distance'. I cant find a definition ...
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IBM QE - Parameters that differentiate the various backends

I'm doing a university thesis using IBM's quantum backends. In my analysis I am making some considerations on what differentiates one backend from another other than the number of qubits and quantum ...
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What are the possible gates that I can use to vary input states before CNOT?

We know that the noise of the $\text{CNOT}$ gate varies depending on the input state before it. What are the gates that I can put in the place of the 4 identity gates above to change the input state ...
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What is the elementary gate set for ion-trap quantum computers?

I asked earlier Which quantum gates can we use in terms of depth?. In the question, I asked I want to measure the depth of a circuit, but I do not know which quantum gates should be used when the ...
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What is known about the quantum version of Schoening's algorithm for 3SAT?

Schoening's algorithm for 3SAT can be converted to a quantum algorithm.  The classical circuit representing a 3SAT expression in CNF form can be converted to a quantum version involving reversible ...
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Are there already hypothetical durations of how long a continuous-variable gate would take on a continuous-variable quantum computer?

I've heard that you run up against the very large constant factors when comparing run times of quantum and classical computers -- things simply take much longer in a carefully controlled quantum setup ...
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Preparation of states that correspond to efficiently integrable probability distributions

I have been trying to implement methods from paper Creating superpositions that correspond to efficiently integrable probability distributions by Grover and Rudolph. It is stated that there exists an ...
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What is the explicit action of the non-linear gate in CV quantum computing on the quadratures?

In this excellently answered question 'How are gates implemented in a continuous-variable quantum computer?' the typical gates for CV quantum computing were listed and described. In particular for ...
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Why are two qubits gates more noisy?

I would like to understand why two qubit gates are generally more noisy. If I am interested in single qubit gates, I can have an effective modelling as a master equation: $$\dot{\rho}=\frac{1}{i \...
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Gate times for different qubit technologies

Different qubit technologies exist and for each, operations are implemented differently. My question is what the typical times are for the standard gates (single qubit rotations, Hadamard, CNOT, T, ...
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Understanding shared Bell states from quantum entanglement

I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3) I have several things about this process that I don't understand, and I was hoping someone could ...
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Identity Gate Timing Discrepancy

I have been examining problems where gate timing is important. When implementing an identity gate, the issue of timing has resulted in a few verification experiments to compare the gate time to that ...
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How to derive a circuit from given equations?

I was reading a paper on Quantum Neural Networks where the authors discussed a new back propagation algorithm. They shared a schematic of the circuit. However, I am unable to understand how the ...
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There seems to be a problem with the implementation of identity gates on Qiskit as compared to the circuit composer

I have been experimenting with slowing down the decay of qubits, and as a control, I implemented a circuit with just identity gates for comparison. However, when I implement such circuits in Qiskit, ...
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How to perform quantum logic gates on plasmons?

In the link provided researches utilize strong two-plasmon absorption in graphene nanoribbons to create a “square-root-of-swap”, could such a device be utilized to perform other quantum logic gates? ...
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Understanding CNOT gate for indirect measurement

I am trying to write a simple circuit to understand the process of finding the set of parameters such that the cost function of that circuit in question is minimized. For that I understand one has to ...
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Restoring an initial state after computation

Let me first tell my problem statement. Suppose I have a uniform superposition of states $$|A\rangle=\dfrac{1}{2^{9}}\sum_{i,j,k=0}^{2^6-1}|0\rangle^{\otimes 8}|i\rangle|j\rangle|k\rangle,$$ where $|0\...
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Tensorial notation for this quantum XOR circuit

Suppose I have this quantum XOR circuit; this is a quantum circuit for the classical XOR operation $$\begin{eqnarray*} x_1'= x_1\oplus x_2\oplus x_3\oplus x_4,\\ x_2'=x_2\oplus x_3\oplus x_4\oplus x_5,...
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Why does state preparation of 'off the shelf' qubits not follow from the Born rule (Mermin)?

In Mermin's Quantum Computer Science, section 1.10 (Measurement gates and state preparation), Mermin writes that: This role of measurement gates in state preparation follows from the Born rule if ...
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