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Questions tagged [circuit-construction]

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

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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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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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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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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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How to decompose 4 qubits Toffoli-gate into two-qubits CNOT gate?

Can I decompose a 4-qubit Toffoli gate into two qubit CNOT gate without ancillary state?
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Multiple random coin flips without measurements

The question is similar to this one. As suggested in the answer, I can easily do this with just one qubit: I repeatedly Hadamard it and measure in order to have a fair coin flip at every point. The ...
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qiskit - Is there any way to discard the results of a measurement?

I have a circuit composed by n qubits, plus a single one which is an ancilla. I'm making multiple measurements on the ancilla at different stages of the circuit, ...
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How to get all combinations of given input?

I'm stuck with a very specific problem that I'm not sure on how to implement using quantum gates. Suppose I have an n qubit circuit and that I want in output a ...
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Why are these circuits not producing the same output?

I am simulating the phase shift algorithm on the Quirk platform. Even when the endian-ness of the built-in inverse QFT gate is corrected for, the circuits still output different results. Shouldn't the ...
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Implementation of inverse QFT?

When implementing the inverse quantum Fourier transform, in addition to reversing the circuit, does one need to take the conjugate transpose of the phase shift gates in the circuit as well?
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Why are these circuits not producing the expected output?

This circuit was created on the Quirk platform. I'm trying to implement a basic case of phase estimation. For some reason, I'm getting this strange result. When the Inverse QFT is broken down, it ...
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A quantum circuit with entanglement with Eve

I'm trying to work through a self-made exercise, which may be ill formed as a question. Any general advice in dealing with these types of problems is also much appreciated! I'm looking at a quantum ...
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How to analyze highly entangled quantum circuits?

I came across a quantum circuit very similar to the phase estimation circuit, which is shown below: In the ...
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List of known circuits and their expected output

I've written an API which takes in a circuit scaffold, according to some specifications, and outputs the results of simulating the circuit. The circuit constraints are that the measurements are ...
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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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How to you encode a network as an adjacency-list in the quantum-gate model?

I have a network problem that I believe would be represented as an adjacency-list on a quantum circuit. Typically, the list is up for traversing from various perspectives (e.g., shortest-path between ...
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Reversible computation without inverting the circuit

I know that if you have a circuit $U$ that transforms $A → B$, it's possible to construct an inverse, ${U\dagger}(B) → A$. Is it also possible to transform the states with $T_{i,o}$ so that I can use ...
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Can we do adiabatic quantum computing with a quantum circuit model and how?

This is a question that must be asked a lot but is it possible? And if in theory possible, what are the challenges to do it, and what are the drawbacks?
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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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Mapping Algebraic Normal Form of Exclusive Sum of Products to Toffoli Network

How does one map an ANF to a toffoli network? Is there a straight-forward procedure for doing this? For example, given the ANF for the Sum function of an adder: $$S = A \oplus B \oplus C \oplus ABC$$ ...
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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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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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Solving a circuit implementing a two-level unitary operation

The circuit below implements the following two-level unitary transformation: $\tilde{U}$ is a unitary matrix: $\tilde{U} = \left[\begin{matrix} a & c \\ b & d \end{matrix}\right]$ where $a, ...
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Applying Group Leaders Optimization to Quantum Belief Systems

Context: I am particularly interested in quantum cognition & would like to use a tool like pyZX to perform the following types of optimizations. In Preparing a (quantum) belief system they "...
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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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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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$R_z$ gate representations

Why is the $R_z$ gate sometimes written as: $$ R_{z}\left(\theta\right)=\begin{pmatrix}1 & 0\\ 0 & e^{i\theta} \end{pmatrix}, $$ while other times it is written as: $$ R_{z}\left(\theta\...
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Simulating Read only QRAM (constructing an oracle) [closed]

In many algorithms an array that stores a classical data or quantum data is crucial. The QRAM (quantum random access memory) that stores classical data in the circuit has been done. My question ...
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Is there a general method to implement a 'greater than' quantum circuit?

I am interesting in finding a circuit to implement the operation $f(x) > y$ for an arbitrary value of $y$. Below is the circuit I would like to build: I use the first three qubits to encode $|x⟩$, ...
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Fault tolerant quantum measurement: how is implemented the “majority vote”

As a fundamental component for a quantum computation, the measurement needs to be implemented in a fault tolerant way. As indicated in Chuang and Nielsen Quantum Computation and Quantum Information, ...
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How to create a condition on only one classical bit when we have a total of 2 classic bits in the system

I am trying to make a quantum circuit with one qubit and 2 classical bits for each measurment in the system below: I want to make condition on the first bit: if the first collapse to zero so x ...
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Decomposition of arbitrary 2 qubit operator

As you know, universal quantum computing is the ability to construct a circuit from a finite set of operations that can approximate to arbitrary accuracy any unitary operation. There also exist some ...
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Generalization for $n$ quantum teleportations

In Breaking Down the Quantum Swap, it is stated: Thanks to the CNOT, we can implement a xor-swap on a quantum computer. All we need to do is chain three CNOTs back and forth. In a comment to a ...
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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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What is the smallest quantum circuit to produce two-qubit state (a,b,b,b)?

How can I synthesis a two-qubit quantum state of the state vector (a,b,b,b) using basic quantum-gate circuit (arbitrary single-qubit rotation and controlled $Z$ gate)? And further, can I know a given ...
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Automatic compilation of quantum circuits

A recent question here asked how to compile the 4-qubit gate CCCZ (controlled-controlled-controlled-Z) into simple 1-qubit and 2-qubit gates, and the only answer given so far requires 63 gates! The ...
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How to re-create the following circuit image?

What would be the best way to re-create the following image of the HHL quantum circuit without compromising on image quality (the image is from this review paper)? Using qasm2circ I can create the ...
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Why do we need a Classical Register for carrying out Quantum Computations?

I've just started to mess about with QISKit on Python and one thing is confusing me a fair bit. Given that we are building Quantum Circuits what is the need for a classical register ? Is it because ...
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Minimum number of CNOTs for Toffoli with non-adjacent controls

I want to decompose a Toffoli gate into CNOTs and arbitrary single-qubit gates. I want to minimize the number of CNOTs. I have a locality constraint: because the Toffoli is occurring in a linear array,...
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Topological Circuit Simulator

Does something like Quirk exist for topological (eg. braided) circuits? Alternatively, any ideas on how @CraigGidney is getting these circuits (or something similar)?
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Showing the equivalence of two simple {NOT, CNOT} circuits

As a beginner, for exercise purpose, I’ve studied this two quantum circuits. They are equivalent, and for 2 qubits it’s easy to write the unitary transformation matrix. Looking for another method I ...
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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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SWAP gate(s) in the $R(\lambda^{-1})$ step of the HHL circuit for $4\times 4$ systems

Context: On the 5th page of the paper Quantum circuit design for solving linear systems of equations (Cao et al, 2012) there's this circuit: Schematic: A brief schematic of what's actually ...
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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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Photonic Circuit Idea (Does this already exist?)

I have had a few ideas for circuits that I would like to get feedback on (do such things already exist, what utility they serve, etc). Any suggestions on how I might graphically render these? ...
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Quantum Arithmetic

I'm looking at this paper and try to implement the Quantum adders they define myself. Suppose we have a number $b=b_{n-1}\dots b_1b_0$ and they want to add a constant number $a=a_{n-1}\dots a_1a_0$. ...
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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 can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ ...