# Questions tagged [circuit-construction]

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

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### Faithful description of a photonic setting with the circuit model

The above picture comes from this paper. The circuit on the left and the one on the right are equivalent (up to the basis). However, there is an important difference: the circuit makes the input -- i....
55 views

### Can a polynomial-sized superposition of computational basis states be prepared with a polynomial-sized quantum circuit?

Suppose I am working with a class of states which consist of a superposition of $O(\text{poly}(N))$ computational basis states on $N$ qubits. Examples of this would be the subspace of states of fixed ...
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### Parallelizing a circuit with repetitive blocks on permuted qubits

Assume one has access to the following oracle: $$O |i\rangle|z\rangle = |i\rangle|z\oplus f(i_{N-1},i_{N-2},\ldots i_{1},i_{0})\rangle$$ where $|i\rangle =|i_{N-1}i_{N-2}\ldots i_{1}i_{0}\rangle$...
1 vote
41 views

### Hadamard gate in Grover algorithm

What is the need to apply the Hadamard gate as the first step while designing the diffuser circuit in the implementation of Grover's algorithm? I know what the gate does but I cannot understand what ...
1 vote
75 views

### Is it possible to implement an in-place multiplication quantum circuit?

How can a reversible multiplication quantum circuit be implemented? By "reversible" I mean one that performs a *= b on the inputs a and b of the ...
1 vote
31 views

### Implementing Readout Error in my circuit seems to have no effect whatsoever

I am trying to perform a simulation using Qasm in order to see how the readout error actually affects my circuit. The circuit I am implementing is a trivial one, the three qubit one that implements ...
55 views

### Raising Pauli Gate to power gives TypeError: unsupported operand type(s) for ** or pow(): 'complex' and 'ParameterVectorElement'

I am trying to implement a parameterised circuit in qiskit. Part of the circuit includes the operation $(X \otimes X)^\alpha$ where $X$ is the standard Pauli-X gate, $\otimes$ is the tensor product, ...
1 vote
61 views

### Qiskit: Mismatch between run_config.parameter_binds and all circuit parameters

I am trying to run the following circuit: ...
1 vote
29 views

### Raise tensor product to float power in qiskit

I am trying to implement the gate $(X \otimes X)^\alpha$ where $X$ is the standard Pauli-X gate, $\otimes$ is the tensor product and $\alpha$ is a real number. Is there a way to implement this in a ...
32 views

### Circuits acting on subsets of qubits in other circuits

I am trying to figure out what is the best way of dealing with registers while constructing circuits from abstract blocks. Consider the following subcircuit: \begin{equation} U|x\rangle|y\rangle|z\...
24 views

### Techniques to parallelize controlled-unitaries controlled by the same qubit but acting on different target qubits

I need to find a way to parallelize a set of controlled-unitaries that are all controlled by the same qubit and are targetting $n$ different qubits. The main constraint that I have is that I can only ...
21 views

### What are the differences between discrete-time quantum walks between dimensions?

When working with quantum walks in other dimensions (1D – 2D – 3D...) do your results tend to be different from what is proposed in theory with the probability density? The results obtained in the ...
75 views

### Qiskit: How to implement a classical function?

I'm quite lost, I have to implement the following function with qiskit $$f(x,y,z) = (\lnot x \land y \land z) \lor (x \land \lnot y \land z)$$ but how can we do that ? I don't understand how to do ...
36 views

Assume one is given two oracle circuits providing access to matrices $A_{ij}$ and $B_{ij}$ as follows (see eq. (6.2) here): \begin{equation} O_A |0\rangle|i\rangle|j\rangle=\left(A_{ij}|0\rangle+\sqrt{...
1 vote
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### Qiskit: QAOAnsatz circuit with custom Hamiltonian

I am trying to implement the Quantum Approximate Optimization Ansatz by creating a parametrized subcircuit $$V (α) = e^{−iH_M α_1} e^{−iH_D b_1} ... e^{−iH_M α_n} e^{−iH_D b_n}$$ with the custom ...
64 views

### 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 ...
132 views

### Is it essential to apply Quantum Singular Value transformation twice for Hamiltonian simulation?

I have been reading the paper A Grand Unification of Quantum Algorithms and I need clarification on the Hamiltonian simulation algorithm provided in the paper on page 23. . In procedure part point 2 ...
101 views

1 vote
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### Implementation for a Translationally Invariant Algorithm

I'm working on inserting an item into a sorted list https://arxiv.org/pdf/quant-ph/9901059.pdf. I would like to know how to implement this formula with Qiskit or just the circuit representing it : ...
127 views

### What is wrong with my circuit for the fourth-root of $X$?

For learning purposes I would like to hand-craft my own circuit for the fourth-root of $X$, using $S$, $T$, and $\sqrt X$ gates. Note that $\sqrtX$ is of order four, and will need two ancillas to ...
56 views

### Group of commuting Pauli matrices doesn't permit synthesis

I am working on learning grouped measurement and I began by reading this paper by a group out of UChicago showing a method for the synthesis of circuits for the grouped measurement of a set of ...
19 views

### How to simulate these Floquet and Rotation operators for kicked top model?

In this and other papers relating to the kicked top model, it is mentioned that spin coherent states can be expressed as: $$\left|\theta,\phi\right>=R(\theta,\phi)\left|j,j\right>$$ for given ...
1 vote
39 views

### Is there a construction and/or term for the following 'sandwich' measurement?

Suppose we have two projective measurements with elements $E_i$, $i=1...m$, and $F_j$, $j=1...n$. So we know $F_j^2=F_j$ and $E_i^2=E_i$ and $\sum_i E_i = \sum_j F_j = \mathbb{I}$. Then it is easy to ...
136 views

### If $A^4=B^4=AB=I$, what is a good circuit for $\sqrt A\sqrt B$?

TL/DR What is a good circuit for: \frac{1}{2}\begin{pmatrix} -i & i & 1 & 1 \\ 1 & 1 & -i & i \\ i & -i & 1 & 1 \\ 1 & 1 & i & -i\end{...
This is probably a pretty basic linear algebra question, but suppose we have two unitary operators $A$ and $B$, acting on the same $n$ qubits of $|\psi\rangle$, with $[A,B]=0$ - that is, $A$ and $B$ ...
I've been going over Nielsen and Chuang's Quantum Computation and Quantum Information and I ran into Exercise 4.22, which says, Prove that a $C^{2}(U)$ gate (for any single qubit unitary $U$) can be ...