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Questions tagged [circuit-construction]

For questions about the construction of complex circuits using elementary quantum gates.

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How to build a quantum circuit representing the Ising Model?

Can someone explain to me how to build a quantum circuit representing the Ising Model? I just want to understand how to represent the Ising Model for the purposes of quantum state label classification....
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How is it possible to implement unitary operator when its size is exponential in inputs?

A quantum circuit can use any unitary operator. Its matrix is exponential in the number of input bits. In practice how can this ever be possible (aside from operators which are tensor products), i.e. ...
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What is the physics behind a quantum classifier for labeling quantum states? [on hold]

I am trying to understand what physics is found behind labeling quantum states on the Ising Model.
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How to superpose two composite qubit states?

Assuming we have two sets of $n$ qubits. The first set of $n$ qubits is in state $|a\rangle$ and second set in $|b\rangle$. Is there a fixed procedure that generates a superposed state of the two $|a\...
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1answer
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Quantum addition and modulo operation using gates

I have a matrix equation $X_{\text{new}}=AX_{\text{old}}$, where $A=\begin{bmatrix}1 & 1 & 1\\ 2 & 3 &2\\ 3&4&4 \end{bmatrix}\bmod 64$, and $X_{\text{old, new}}\in \{1,2,...64\}...
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Given a decomposition for a unitary $U$, how do you decompose the corresponding controlled unitary gate $C(U)$?

Suppose we have a circuit decomposition of a unitary $U$ using some universal gate set (for example CNOT-gates and single qubit unitaries). Is there a direct way to write down the circuit of the ...
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How to construct a quantum circuit for the following state transformation?

I have a certain transformations that goes as follows: Given $A=|abc\rangle$, $B=|xyz\rangle$, now I have cases as: $$\text{if }c=1,z=1, b\oplus y=1 \implies \text{flip}(x)$$ $$\text{if }c=1, z=1 \...
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How to complete this teleportation circuit? How to create a copy of $|\psi〉$?

This is a quantum circuit. M represents the act of making a measurement on the first two qubits. The circuit is supposed to transfer the state $|\psi\rangle = a |0\rangle + b |1\rangle$ ($a, b \in \...
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Understanding the Group Leaders Optimization Algorithm

Context: I have been trying to understand the genetic algorithm discussed in the paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin &...
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1answer
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Evolving a quantum circuit using a genetic algorithm

I've written a small quantum circuit simulator in python, so now I'm trying to evolve some circuits via genetic algorithms. My encoding is very simple, it's just a rectangular table of strings ...
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Constructing a circuit which performs the transformation $|x,y\rangle \to |x, x + y \bmod 4\rangle$

When faced with exercises like these, I find it hard to know how to construct the circuits due to the amount of input one needs to account for. I have seen the solution provided here however, I don't ...
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1answer
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Understanding quantum circuit diagrams: a circuit that compares two states $|YX\rangle$ and $|AB\rangle$

I have a quantum circuit which I would like to understand, which compares two standard basis states $|YX\rangle$ and $|AB\rangle$. It operates on the corresponding bits in each of the two states: i.e.,...
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1answer
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Deutsch–Jozsa algorithm: why is $f$ constant?

I'm trying to understand how the Deutsch–Jozsa algorithm works with the following circuit: Circuit in Quirk Since we have the top 2 wires measuring $|0\rangle$ with 100% probability, it means $U_f$ ...
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How to calculate circuit depth properly?

Is the circuit depth the longest sequence of gates applied on one of the qubits? Or is it something more complicated?
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N&C quantum circuit for Grover's algorithm

In the chapter about the Grover algorithm, it is suggested that the gate which executes the phase shift is given in the following form: Now I have looked at this gate in detail and come to the ...
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3answers
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Summing states of two qubit registers

I'm addressing the implementation with gates of an algorithm where there is the need of creating a qubit register $|\Psi\rangle$ starting from two input qubit registers $|a\rangle$ and $|b\rangle$, ...
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How do I add 1+1 using a quantum computer?

This can be seen as the software complement to How does a quantum computer do basic math at the hardware level? The question was asked by a member of the audience at the 4th network of the Spanish ...
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1answer
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Estimation of Z in the quantum Euclidean algorithm

In this paper there is a quantum algorithm that can estimate the distance between a given vector U and a set of vectors V (by taking the mean). In some part of the algorithm, we need to find the sum ...
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1answer
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Implementing an oracle

Suppose $x$ is an $N=2^n$ elements database. Let's define a $2N$-bit database with $y \in \{0,1\}^{2N}$ indexed by $(n+1)$-bit strings $j=j_1\ldots j_n j_{n+1}$, where \begin{align} y_j=\begin{cases}...
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How can I invert the least significant bit of a certain term of a superposed state?

Say I have $$\dfrac{1}{\sqrt{2}}\bigl(|1\rangle|221\rangle|0\rangle + |3\rangle|73\rangle|2\rangle\bigr).$$ How can I change that into $$\dfrac{1}{\sqrt{2}}\bigl(|1\rangle|221\rangle|1\rangle + |...
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How can the state $\lvert0\rangle+M^{-1/2}\sum_{j=1}^M\lvert j\rangle$ be generated?

I was wondering if anybody to help me to generate the following state. It would be preferable if you use only Hadamard, CNOT and T-gates, on $\lceil\log_2(M+1)\rceil$ qubits: $$|\psi\rangle = \frac{1}{...
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1answer
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Building an N-qubit Controlled S Gate

I've been beating my head against this problem for three days now and I just can't seem to crack it. To construct an N-qubit controlled Unitary gate, I can do something like this (note I'm using ...
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How to simulate a simple circuit to add two numbers in Quirk?

I am new and I don't understand where I should give the input and where I should get the output. Please explain with an example of a circuit run on the Quirk simulator. How to add two numbers?
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Is there any method of adding two operators in a circuit?

I am trying to reconstruct the time evolution of a Hamiltonian on the quantum computing simulator, quirk. Ideally I would like to generalise this to any simulator. The unitary matrix is $$U(t)=e^{-...
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How is the oracle in Grover's search algorithm implemented?

Grover's search algorithm provides a provable quadratic speed-up for unsorted database search. The algorithm is usually expressed by the following quantum circuit: In most representations, a crucial ...
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POVM three-qubit circuit for symmetric quantum states

I have been reading this paper but don't yet understand how to implement a circuit to determine in which state the qubit is not for a cyclic POVM. More specifically, I want to implement a cyclic POVM ...
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Circuit construction for Hamiltonian simulation

I would like to know how to design a quantum circuit that given a Hermitian matrix $\hat{H}$ and time $t$, maps $|\psi\rangle$ to $e^{i\hat{H}t} |\psi\rangle$. Thank you for your answer.
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What circuit or operation corresponds to the tensor product?

What Clifford gate circuit operating on states $|\psi_1\rangle$ and $|\psi_2\rangle$ prepares the state $|\Psi\rangle=|\psi_1\rangle \otimes |\psi_2\rangle$ ?
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1answer
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Garbage-Free Reversible Binary-To-Unary Decoder Construction

In designing reversible circuits one of the useful circuits is the decoder. The operation of a decoder is naturally reversible, so it makes sense to be able to create one with no garbage outputs. ...
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1answer
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Decompose a general two-qubit gate into general controlled-qubit gates

We often seek to decompose multi-qubit unitaries into single-qubit rotations and controlled-rotations, minimising the latter or restricting to gates like CNOTs. I'm interested in expressing a general ...
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SWAP test inputs

I'm using the SWAP test circuit for implementing a qubit registers comparison From the documentation I could find I've understood it can be applied to input qubits |$\alpha\rangle$ and |$\beta\...
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1answer
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Forming states of the form $\sqrt{p}\vert 0\rangle+\sqrt{1-p}\vert 1\rangle$

I'm curious about how to form arbitrary-sized uniform superpositions, i.e., $$\frac{1}{\sqrt{N}}\sum_{x=0}^{N-1}\vert x\rangle$$ for $N$ that is not a power of 2. If this is possible, then one can ...
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1answer
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How to construct a quantum circuit (QIP system) for the graph non-isomorphism problem?

I'm having some trouble understanding quantum interactive proof systems (QIP systems) and the related circuit constructions. Interactive proof systems model these type of situations: Interactive ...
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1answer
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Measurement of a qubit and storage of the information on a bit

Suppose we have the quantum circuit below with a quantum register of 2 qubits and a classical register of 2 bits. The Hadamard gates and CNOT gate are not important for the question. When we measure a ...
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What's my computational basis if I want to define a unitary operator that implements a function such as $f(i) = 2^{i+1} \text{mod 21}$?

I know I must define $U_f$, the unitary operator, on the computational basis. But what's my computational basis here?
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What's an example of building a circuit $U_f$ that implements a simple function $f$?

I'd like to be able to program simple functions into simulators such as QCL. I read that any function $f$ can be implemented, but I don't know how to get say a unitary matrix that implements $f$. $\...
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1answer
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Status of software packages for quantum compiling

By "quantum compiling", what I mean is classical algorithms to solve the following problem: given a $SU(D)$ matrix $U$ (the goal) and a set of $SU(D)$ unitary matrices $V_1 \cdots V_N$ (the gates), ...
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Implement a circuit as a matrix in ProjectQ

Suppose a have a circuit coded up in ProjectQ, suppose also it is that large to be hard enough to write it down as a unitary matrix by hands (e.g. order-finding, which is rather standard, but turns ...
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Programming quantum half adder

While computing the carry bit [C=0 XOR (AB)] I am unable to compute that AB in Qiskit. I don't whether Toffoli gate is available in Qiskit. So does anyone know how to perform AB, which is basically ...
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Correspondence between the Topological model and Quantum Circuit model

For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa. From the literature developed, it seems ...
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1answer
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Problem with approximating adiabatic evolution with quantum circuit

I am reading on how to approximate adiabatic evolution with quantum circuit and I had some trouble following the arguments given in the early papers which proves this results. I am mainly following ...
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Why is it important to eliminate the garbage qubits?

Most reversible quantum algorithms use standard gates like Toffoli gate (CCNOT) or Fredkin gate (CSWAP). Since some operations require a constant $\left|0\right>$ as input and the number ...
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1answer
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How to avoid error when applying certain combinations of degree of freedom rotations using a quantum circuit?

When applying each of the six degree of freedom rotations (or certain combinations of them) in an SO(4) using quantum gates, the results I expected are produced. For example, the following circuit in ...
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How are two different registers being used as “control”?

On page 2 of the paper Quantum Circuit Design for Solving Linear Systems of Equations (Cao et al.,2012) there's this circuit: It further says: After the inverse Fourier transform is executed on ...
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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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Error: Simulation of “Quantum algorithm for linear systems of equations” for $4\times 4$ systems on Quirk (without SWAP) - Global phase

Following @DaftWullie's answer I tried to simulate the circuit given in Fig. 4 of the paper (arXiv pre-print): Quantum circuit design for solving linear systems of equations (Cao et al, 2012), on ...
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1answer
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Classical XOR gate in Quantum Circuit

Can we use classical XOR gate in a quantum circuit? Or are there any alternatives for XOR gate?
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Is it better to use fewer gates or fewer working qubits? [closed]

I have a script that takes a while to simulate. I can modify it in such a way where I can use fewer qubits at a time, but it will require more iterations of manipulation. I believe this will cut down ...
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How to prevent future loops using a control qubit?

I am trying to construct a quantum multiplier using the method described here: https://arxiv.org/abs/quant-ph/0403048. However, it seems that the control qubit would only disable the following gates ...
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Do multi-qubit measurements make a difference in quantum circuits?

Consider the unitary circuit model of quantum computation. If we need to generate entanglement between the input qubits with the circuit, it must have multi-qubit gates such as CNOT, as entanglement ...