Questions tagged [circuit-construction]
For questions about the construction of complex circuits using elementary quantum gates.
145
questions
2
votes
1answer
53 views
Understanding how control gates are written in tensor notation
I'm very confused about the tensor representation of Control gates. I had thought that all control gates were of the form $P_0 \otimes I+P_1\otimes \hat{A}$, where this does nothing to the first qubit ...
1
vote
1answer
18 views
Performing a measurement in the standard computational basis of a three qubit system on two qubits
I often see written "and then we perform measurement in the standard computational basis" but I'm a little fuzzy on what this means as it's never stated what type of measurement we're supposed to take....
2
votes
1answer
30 views
Circuit for controlled rotations conditioned on a $d$ bit precision estimate of $\theta$ for $O(d)$ gates
Suppose I have a $d$-bit estimate of $\theta \in (0, 2 \pi]$, say a register of qubits $|\tilde{\theta} \rangle = |z_1 \rangle \ldots |z_d \rangle$ for $|z_i \rangle \in \{|0 \rangle, |1 \rangle \}$ ...
3
votes
1answer
55 views
Reversible Circuit Simulation (for classical tests of quantum subroutines)
Problem: trying to implement and test quantum subroutines on quantum simulators I run into multiple challenges:
Quantum simulation is a very hard problem: a very low number of simulated qubits is ...
4
votes
1answer
26 views
Implementation of filter operation
If I want to implement the measurement operation corresponding to filtering, i.e.
$$
M_1=\left(\begin{array}{cc}1 & 0 \\ 0 & \alpha \end{array}\right)\qquad M_2=\left(\begin{array}{cc}0 & ...
5
votes
1answer
57 views
A basic question on circuits and matrix representation
I have several (rather basic) questions on matrix representation of circuits and I would be very grateful to anyone that could clear up my confusion, thank you in advance.
1) When reading circuit ...
2
votes
1answer
30 views
quantum circuit with feasible gates for state preparation
I have a classical vector of size $2^{n}$ (normalized) and I want to use this value as amplitude for my $n$ qbits, in the canonical basis $|00000\rangle$, $|00001\rangle$ etc.
I want to use real ...
5
votes
2answers
86 views
Is there a simple, formulaic way to construct a modular exponentiation circuit?
I'm a newcomer to quantum computing and circuit construction, and I've been struggling to understand how to make a modular exponentiation circuit. From what I know, there are several papers on the ...
0
votes
1answer
58 views
Measurements in Qiskit
What is the difference between 2 types of measurements depicted below?
At the end of unitary evolution, qubits are in superposition of states, and after measurement I get a set of probabilites ...
9
votes
2answers
253 views
How to create quantum circuits from scratch
I am doing self-study at the moment using primarily the book: Quantum Computing a Gentle Introduction by Eleanor Rieffel and Wolfgang Polak.
Getting through the earlier chapters and exercises went ...
3
votes
3answers
48 views
How to create an Ising coupling gate with Qiskit
I'm trying to apply a time evolution algorithm for a physical system I'm trying to simulate on QISkit, however, in order to do that, I need to use the so-called Ising coupling gate:
$I=\begin{pmatrix}...
1
vote
1answer
51 views
Is it possible to simulate any classical algorithm with the same efficiency on quantum computer?
Consider any data structure based on the binary search trees, e.g. set. Classical computers can make queries (insert, remove, test if element present), into this structure in $O(\log n)$ time, where $...
2
votes
1answer
27 views
Hamming with prefix oracle
I'm doing the Q# quantum katas and I'm stuck on an oracle in the Deutsch-Josza algorithm katas.
Let $|x\rangle=|x_0x_1\dots x_{n-1}\rangle$ be a qubit array and $r$ be bit string of $k\leq n$. The $...
0
votes
1answer
23 views
How is inner product addition performed?
The Swap test proof on page 8 of https://sites.cs.ucsb.edu/~vandam/teaching/S05_CS290/week9.pdf ends with this derivation:
How you add those inner products to get from $\frac{1}{4}(2 + \langle \Psi, \...
1
vote
0answers
15 views
Ansatz Techniques to Multi-Body Physics Problems
I have been reading this paper: https://arxiv.org/abs/1906.01563v1.
I am wondering: is it possible to use the idea behind quantum circuits to build classical Hamiltonians represented in the same way?...
3
votes
2answers
59 views
How do I get out 2 measurements from the same execution on Qiskit?
Here's my circuit, trying to checkout the effect of measurement on the IBM Q circuit. Here you can see I do 2 different measurement at different time, and I hope to be able to see both results. ...
4
votes
0answers
71 views
What implementation changes should be done in maxcut code using VQE?
In the paper, "Quantum algorithm implementations for beginners" in the section XVII. QUANTUM SIMULATION OF THE TRANSVERSE ISING MODEL (page 54-58), the authors have plotted energy $E$ vs magnetic ...
3
votes
0answers
88 views
Quantum Optimization via Quantum Label Classification in Quantum Circuits
I have been reading Farhi and Neven's paper on quantum neural networks on quantum circuits. I also found an example - albeit not ideal as pointed out by a couple of users - thank you - in here.
...
2
votes
1answer
64 views
Using Quantum Fourier Transform in adding two 2-bit numbers
I am trying to use Qiskit to write a code that uses QFT to add 2 numbers. I am referring to this paper:
https://iopscience.iop.org/article/10.1088/1742-6596/735/1/012083
I have a few questions:
1) Is ...
2
votes
1answer
44 views
Coding an oracle for Simon's algorithm
I am trying to implement Simon's algorithm which calls for a 2-to-1 mapping function that satisfies $f(x) = f(x⊕s)$.
I am looking for a simple way to code the oracle (using $H$, $Cx$, and $R$ gates), ...
3
votes
0answers
31 views
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 ...
2
votes
0answers
19 views
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, ...
2
votes
0answers
44 views
Measuring the expected energy of a quantum circuit
I implemented the following circuit:
I am interested in measuring the expected energy of the circuit. I am using Cirq. I am wondering what are the next steps. Sorry if the question seems very basic, ...
3
votes
1answer
74 views
N-Toffoli on Cirq
I am looking for guidance in more generally how to developed n-bit gates in Cirq.
I am working on a QNN paper and I need to develop a n-controlled gate to be able to measure the cost function of the ...
2
votes
0answers
23 views
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 ...
5
votes
0answers
54 views
How many two-qubit gates required for general N-qubit unitary?
Is there a known formula or a scaling behaviour for how many two-qubit gates are required to construct a general N-qubit unitary?
I suppose there are several cases to consider:
Exact representation ...
3
votes
1answer
90 views
Implementing a complex circuit for a Szegedy quantum walk in qiskit
Problem definition
I'm implementing a quantum circuit in qiskit for a Szegedy quantum walk, (reference, Fig 21.). It uses two registers of dimension $N$ ($N=3$) each one. The challenges I'm facing ...
6
votes
1answer
40 views
Simulating a 3-local Hamiltonian Term
This may be a fairly basic question, but in Nielsen & Chuang, the following circuit is given for simulating $\exp\left(-i\Delta t Z_1 \otimes Z_2 \otimes Z_3\right)$:
which uses an ancilla qubit ...
8
votes
2answers
152 views
How to program a controlled Hadamard-Hadamard gate?
I'm trying to program a controlled gate as the figure below in Qiskit. Should it be sufficient to separate and control individually the Hadamard gates?
4
votes
0answers
34 views
Can anybody explain or suggest a good reference on how to make a modular exponentiation circuit for N=15 with any coprime base?
I have read many papers related to it but in every paper, they just show the circuit of order finding algorithm for N=15, but did not explain what is the procedure to make it.
It will be great if ...
6
votes
0answers
40 views
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 ...
4
votes
1answer
85 views
Quantum Fourier Transform without SWAPs
The Quantum Fourier Transform from Nielsen and Chuang chapter 5 is pictured here:
In the textbook the author refers to "swap gates at the end of the circuit which reverse the order of the qubits".
...
4
votes
1answer
51 views
Quantum gate teleportation T gate
I am faced with the problem of teleporting certain gates using modified Bell states. For example, I have solved the problem with the $S$ gate, which is defined as following:
Alice and Bob share a ...
1
vote
0answers
22 views
Controlled controlled adder gates involved
Let's say I have a circuit that given in the figure
As we can see that this circuit consists of $2$-Toffoli gates and $4$ C-NOT gates, and to construct this entire circuit using only single qubit ...
3
votes
1answer
41 views
Primer for learning about quantum circuits simulating systems
I am interested in a couple of books or arXiv links to learn how to develop quantum circuits for the purpose of simulating quantum multi-body systems. Moreover, I am interested in learning how to ...
7
votes
0answers
44 views
Summation of amplitudes [duplicate]
I was wondering how to create generalized entangled superpositions of qubits when I came to need of an algorithm to generate the following:
Suppose we have two $n$ qubit states, $$|\psi\rangle = \...
2
votes
0answers
47 views
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\...
3
votes
1answer
94 views
2-qubit QFT in IBMQ: controlled phase rotation
I've started getting into quantum computing in the last few days.
As part of the learning, I've figured it would be fun to implement some circuits on IBMQ Experience as I learn. So now I'm stuck with ...
2
votes
0answers
54 views
Tensorial notation for this quantum XOR circuit
Suppose I have this quantum XOR circuit; this is a quantum circuit for the classical XOR operation $$\begin{eqnarray*}
x_1'= x_1\oplus x_2\oplus x_3\oplus x_4,\\
x_2'=x_2\oplus x_3\oplus x_4\oplus x_5,...
2
votes
1answer
60 views
Quantum operation in blocks
I have $n$ states in superposition $|A\rangle=\dfrac{1}{2^{l/2}}\sum_{i=0}^{2^l-1}\sum_{j=0}^{2^l-1}|0\rangle^{\otimes q}|i\rangle^{\otimes l}|j\rangle^{\otimes l}$. Now I have to apply the transform ...
1
vote
0answers
56 views
Quantum operation involving permutation
Suppose I have the state $\frac{1}{2^l/2}\sum_{i=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |i\rangle^{\otimes}|0\rangle_i^{\otimes l}$.
I perform some unitary transformation between the registers $|i\...
3
votes
1answer
800 views
Can someone walk us through Nielsen's proof on a circuit for quantum teleportation?
Michael Nielsen posted on Twitter about a proof on a circuit for quantum teleportation.
Had some fun this afternoon re-analyzing the circuit for quantum teleportation. Here's a proof I found that ...
5
votes
1answer
82 views
Most efficient way for general state generation
Assume we are given an $n$-qubit system and complex numbers $a_0, \ldots, a_{m-1}$ with $m = 2^n$. Assume further we start with the initial state $|0 \ldots 0\rangle$ and want to make the ...
5
votes
1answer
77 views
How to encode MNIST data set on a quantum circuit to study supervised learning with QNN?
I am trying to implement arXiv:1802.06002†. I do not understand how to take the data set from MNIST and apply it to a quantum circuit.
[†]: Classification with Quantum Neural Networks on Near Term ...
2
votes
1answer
159 views
Circuit construction and Dirac notation of the following operation
I have a state $$ |\tilde{\Phi_2}\rangle =\dfrac{1}{2^{3l/2}}\sum_{x=0}^{2^l-1}\sum_{y=0}^{2^l-1}\sum_{z=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |x\rangle^{\otimes l}\otimes |y\rangle^{\otimes l}\...
4
votes
1answer
85 views
Circuit construction for execution of conditional statements using least significant bit
Suppose I have integers and encode them as binary strings for example: $$|0\rangle=|00\rangle,|1\rangle= |01\rangle,|2\rangle=|10\rangle,|3\rangle=|11\rangle.$$
Now an $n$ bit integer, say $x$, is ...
1
vote
1answer
135 views
How do I translate a quantum circuit for computing x + y mod 8 into a program?
I have made the above quantum circuit that gives the mod $8=2^3$
operation between $|x\rangle$ and $|y\rangle$. Now I want to write its corresponding program using some language. Where can I do that i....
1
vote
1answer
58 views
Implementing a controlled sum operation
I want to implement a controlled operation that involves the following: we have the following qubits: $|x_0\rangle,|x_1\rangle,|0\rangle,|1\rangle,|z_0\rangle,|z_1\rangle$. I want to add the first ...
1
vote
0answers
27 views
Implementing conditional operators in a quantum circuit
I have 4 states say $|00\rangle, |01\rangle,|10\rangle, |11\rangle$. I want to add the states in a manner such that
$|a\rangle=|00\rangle\otimes|01\rangle\to |00\rangle\otimes|01\rangle$
and
$|b\...
1
vote
1answer
49 views
Implementing piecewise functions on a quantum computer
I am curious about how to do implement functions like $$f(x)=\begin{cases}
2x &\text{if} &0\leq x <0.5 \\
x/2 &\text{if} &0.5\leq x<1
\end{cases}$$
Do we implement this like ...
