Questions tagged [algorithm]

For questions about quantum algorithms, that is, sequences of quantum gates, operations, and measurements, whose purpose which achieve some goal. Standard examples are Shor's and Grover's algorithms.

Filter by
Sorted by
Tagged with
1 vote
0 answers
29 views

Quantum algortihm for SVD and eigendecompostion

In this paper by Rebentrost, Steffens, and Lloyd, it is stated that: Such tasks [eigen- and singular value decomposition of a matrix] could be performed efficiently via phase estimation on a ...
  • 11
0 votes
0 answers
24 views

Understanding Shor algorithm fo Elliptic Curves Demonstration

I was reading Shor's discrete logarithm quantum algorithm for elliptic curves. And i have two questions. In page 7 they say that $x = (x0 - dy) mod q$, where $x0$ is between 0 and q-1, but then they ...
1 vote
1 answer
34 views

Is there an alternative algorithm to extract a probability of states of qubit after measuring?

Let a simple quantum circuit consist of one qubit and one classical bit. Initially, a qubit has the $|0\rangle$-state and then goes through some sequence of quantum gates, see the circuit below. The ...
  • 111
0 votes
0 answers
14 views

An algorithm for solving LDEs: How find non-zero indices of Vs1 operator?

I am using qiskit to implement the second part of this algorithm which can be found on page 7: "$A$ is non-unitary" section of the appendix. Basically, it expands the solution of the ODE $x(...
  • 169
3 votes
2 answers
2k views

What is the fastest quantum computational algorithm by which quantum computer speed up than classic one?

What is the fastest quantum computational algorithm by which quantum computers speed up than classic one? Of course, those speedup algorithms have to be proven.
0 votes
0 answers
17 views

Confused how Jordan gradient algorithm would work

Jordan's gradient algorithm is a quantum algorithm to find the gradient vector of a function at a point. Here is the paper: https://arxiv.org/pdf/quant-ph/0405146.pdf So in the paper it says To ...
0 votes
1 answer
25 views

Grover's Algorithm - Diffusion Matrix [closed]

In the Grover's Algorithm, the diffusion matrix $D$ is defined as: $$\begin{cases} D_{ij}=\frac{2}{N} \quad \text{ if } i \neq j \\ D_{ii}=-1+\frac{2}{N} \end{cases}$$ And then it goes on to say &...
  • 135
0 votes
0 answers
34 views

How to obtain the inner product of the local registers for a superposition state?

For a superposition state $$|{{\Phi }^{+}}\rangle =\frac{1}{\sqrt{4}}\left( |0\rangle |{{U}_{1}}w_1,w_2\rangle +|1\rangle |{{U}_{2}}w_1,w_2\rangle +|2\rangle |w_1,{{U}_{1}}w_2\rangle +|3\rangle |w_1,{{...
  • 388
0 votes
0 answers
34 views

How to obtain the product of the amplitudes of arbitrary basis vectors in a superposition state without measuring?

Suppose there is a superposition state $|{{\Phi }^{+}}\rangle =\sum\limits_{i=0}^{15}{{{\alpha }_{i}}|i\rangle }$, I want to get ${{\alpha }_{i}}\times {{a}_{j}},i\ne j,i,j\in [0,15]$ without ...
  • 388
2 votes
0 answers
96 views

How to implement an unitary operator expressed as a linear combination of unitaries without qubits ancilla

Let's say that I know the decomposition of a unitary operator $\hat{A}$ in terms of other unitary operators $U_{k=0, \dots, M}$, i.e: $$ \hat{A} = \sum_k \alpha_k U_k$$ I know how to implement in ...
2 votes
1 answer
61 views

Encoding arbitrary quantum gates using qubits

Given an arbitrary 3-qubit state $\sum_{xyz} c_{xyz}|xyz\rangle$, is there a circuit (possibly with measurement) that creates the state $\sum_{xy} c_{xyy}|x\rangle$, up to a normalization constant? As ...
  • 123
1 vote
1 answer
106 views

What Adding Modulo To Register Means

I was reading about the Jordan gradient algorithm(https://arxiv.org/pdf/quant-ph/0405146.pdf) and I am a bit confused about one of the phrases: Next, use the blackbox to compute f and add it modulo $...
1 vote
2 answers
134 views

Quantum Computing Daily Practice / Quiz platform

I am looking for a platform where I can solve quizzes and programming / algorithmic challenges related to quantum computation and information. To be more specific, I am looking for a platform that is ...
21 votes
1 answer
3k views

An impossible quantum adder claimed by a journal article?

In Quantum adder of two states that are themselves superpositions, I asked: I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\...
  • 407
3 votes
1 answer
180 views

Quantum adder of two states that are themselves superpositions

I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\sum_{j=0}^ {N-1} |j\rangle|b_j\rangle$, with $i,j,a_i,b_j \in \mathbb{N}$. I ...
  • 407
4 votes
1 answer
91 views

If you had a 1000 qubit NISQ machine with arbitrary connectivity, what would you do?

Many current devices are constrained to nearest neighbor connectivity or small system sizes, but suppose that a NISQ machine with 99-99.5% level two-qubit gate fidelities and arbitrary connectivity ...
1 vote
0 answers
22 views

Can a Quantum computer simulate classical hack and exploit in a network ? Also how would it be any different from the classical computer [closed]

I'm trying to write a realistic story around Quantum computing and was wondering how different a network exploit/hack would look if a Quantum computer was to hack into a private network, instead of ...
9 votes
1 answer
521 views

Any simple description of a circuit for Yamakawa-Zhandry algorithm?

Recently, popular sources (including Aaranson's blog and Quanta Magazine) have made it look like the recent Yamakawa-Zhandry algorithm is akin to Shor's algorithm, in the sense that it could ...
  • 1,584
0 votes
2 answers
63 views

Post selection on Qiskit

I want to perform post-selection on IBM Qiskit and run on actual quantum computer. (What is post-selection) How can I perform it ? Can I use qiskit.circuit.QuantumCircuit.reset for it ? How to use it ?...
1 vote
1 answer
49 views

What is repeat until success strategy?

What is repeat until success strategy? Is it related to post-selection ?
12 votes
0 answers
224 views

Are all quantum algorithms hidden subgroup algorithms?

I am reading the paper "Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit" by Samuel Lomonaco and Louis Kauffman from the book, "Mathematics of Quantum Computation and Quantum ...
1 vote
1 answer
40 views

How to synthesize function $f(x)$ in amplitude encoding

In computational basis encoding, the way to encode $f(x)$ is known - a classical circuit is converted to a quantum circuit which takes $|x\rangle|0\rangle \to |x\rangle|f(x)\rangle $. I wonder how I ...
0 votes
1 answer
171 views

Kaye Exercise 6.4.2 Classical deutsch jozsa algorithm

Can anyone help with this problem from, An Introduction to Quantum Computing, Phillip Kaye, Raymond Laflamme, Michele Mosca Exercise 6.4.2: Show that a probabilistic classical algorithm that makes $O(...
1 vote
1 answer
88 views

Kaye Exercise 6.3.1, Deutsch algorithm modification

This exercise is worded as follows: In the Deutsch algorithm, when we consider $U_f$ as a single-qubit operator $\hat{U_{f(x)}}$, $\frac{|0\rangle - |1\rangle}{\sqrt{2}}$ is an eigenstate of $\hat{U_{...
1 vote
1 answer
72 views

QiskitError: 'Sum of amplitudes-squared does not equal one.'

I'm coding a 429 element length string to compare to other same length strings, but I keep getting that error. I used ljust to fill the string to a 512 element ...
  • 27
1 vote
0 answers
34 views

Amplitude Amplification applied to HHL Algorithm

I’m trying to understand and implement the amplitude amplification algorithm described in the HHL paper. I’m using the cirq implementation of the HHL algorithm as my starting point. I have a couple of ...
4 votes
1 answer
48 views

Are there some review papers of quantum combinatorical optimization problem and their application?

I'd like to get recommendations for review paper summarized for combinatorical optimization algorithm and application. Are there any papers that have been organized recently?
1 vote
1 answer
35 views

Questions about Quantum Phase Estimation [duplicate]

For https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html , what does it exactly mean by "to recover the state |2nθ⟩, apply an inverse Fourier transform on the auxiliary ...
  • 111
-1 votes
2 answers
43 views

Does this one qbit gate exist: [[2,0],[0,0.5]]?

I would like to know if this one qbit quantum gates exists: 2 0 0 0.5 Or any quantum gates with x and y such as : x>y>0 and x 0 0 y The first gate is reversible so i think it makes sense ...
2 votes
2 answers
132 views

Can a unitary with size not a power of 2 be used for Quantum Phase Estimation?

For Quantum Phase Estimation, we need a Unitary Matrix $ U $ such that $$ U~|\psi\rangle = e^{2 \pi i \theta}~|\psi\rangle $$ Using QPE, we can find the phase $\theta$. My question is about the size ...
3 votes
1 answer
56 views

Ansatz printing in Qiskit draws a single block

When I try to draw the quantum circuit it is shown in only one block and not the whole circuit. For example using the code: ...
  • 33
3 votes
1 answer
47 views

Implementing quantum swap operation such that $|x\rangle|f(x)\rangle$ changes to $|x\rangle|f(x+1)\rangle$

Suppose that a quantum state $|\psi\rangle$ in question is $|\psi\rangle \propto \sum_x |x\rangle|f(x)\rangle$. I want to implement a quantum swap operation such that computational basis $|x\rangle|f(...
  • 33
1 vote
1 answer
44 views

Qiskit: evaluating expectation value of S^2 operator

I am trying to obtain the expectation value of the S^2 operator with respect to VQE wave function in an older version of qiskit (0.26). To that end, I tried: ...
1 vote
1 answer
74 views

Applications of an efficient estimation of $\langle \psi | H | \psi \rangle$ for $H$ being the Heisenberg model, and $|\psi\rangle$ an arbitrary state

I consider that $H$ is an Hamiltonian acting on $n$ qubits. It is a sum containing $Poly(n)$ $n$-qubit Pauli operators $P_i^{(k)}$ for $i=1,2,3$, such that $P_i^{(k)}$ a tensor product of $\sigma_0=\...
1 vote
0 answers
23 views

Does QSVT/QSP require singular/eigen decomposition?

Basically the title says it all. Every construction I've seen for QSP and QSVT involves finding 1 and 2-dimensional invariant subspaces of the iterate, $O \equiv U_A \exp(i \pi/2 Z_\Pi)$, where $U_A$ ...
1 vote
1 answer
60 views

Can Quantum Computers (not simulators) solve a 4 node TSP?

I am currently researching the Traveling Salesman Problem, and it is known that Quantum Computers have a strong likelihood to increase the efficiency of TSPs in industry. I have mainly heard this in ...
  • 89
2 votes
1 answer
50 views

I am having problem in executing measurement based quantum computing circuit

This is the circuit I want to implement. But I am unable to do this. basically How I can tell qiskit that "if the qubit is in |+> state then operate H gate on qubit 2 or if the qubit is in|-&...
0 votes
0 answers
20 views

Why is extra information a problem for quantum data structures?

In the following paper: https://arxiv.org/abs/2204.13835 (Quantum Dictionaries without QRAM), it mentions "extra information is disastrous" , "[extra information should not] sneak into ...
  • 485
1 vote
1 answer
113 views

Why can quantum computing help in Portfolio Optimization?

Why is it said that Portfolio Optimization is a good case for quantum computing? Is it only speed? IF speed is the only benefit, why cant we build more powerful supercompuetrs?
1 vote
2 answers
79 views

How to deterministically add two integers on a quantum computer

I am new to the Quantum Computer world. I understand the basics of Quantum mechanics and I have watched a few lectures on Quantum computers, Quantum gates and played a bit on IBM QC. As far as I ...
0 votes
1 answer
33 views

Clarification about QTF proof regarding equality of QFT application and circuit application

I'm self learning quantum computing through IBM's Qiskit's learning section (which I really like), and I've stumbled across an inequality that I don't quite understand fully. This must be really easy, ...
0 votes
0 answers
43 views

Odd-dimensional matrix manipulation on quantum circuit

Just wondering if there is any work on dealing with odd-dimensional matrix, i.e. a matrix of which the dimension is N by N where N is an odd integer, and one could, for instance, solve the ...
0 votes
0 answers
50 views

Why do we start from the least significant bit in phase estimation algorithms?

I've been watching some videos and tutorials for quantum phase estimation. Here's a video I found helpful, which explains the phase estimation in general. I also learned the iterative phase estimation ...
  • 317
2 votes
3 answers
133 views

Definitions of a quantum circuit's depth and connectivity

The quantum circuit model of computation uses wires and gates. The information flows along the wires and gates attached to the wires modify the information and pass it further down the wires. In ...
  • 1,161
4 votes
0 answers
62 views

Role of physics in quantum computing [closed]

I am a physics graduate student and I am very interested in quantum computing, having taken two courses so far. My research advisor is a Materials Physicist and he says that there is really no role in ...
  • 41
0 votes
0 answers
15 views

determine degree of boolean polynomial given as black box

I searched a lot but couldn't find a good resource that addresses this question. Given a boolean polynomial with $n$ boolean variables as a black box, what is the most efficient way to compute its ...
1 vote
1 answer
98 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 ...
0 votes
0 answers
21 views

Extremal matrix elements in the Unitary Matrix corresponding to a Quantum Circuit

Quantum Circuits are represented as Unitary Matrices. Given the ability to implement the circuit for Unitary Matrix U, by what algorithmic procedure could one determine the smallest/largest matrix ...
  • 485
3 votes
2 answers
95 views

How to solve quadratic programming problems with continuous variables by using quantum algorithms?

I need to solve a quadratic programming problems with continuous variables, which is defined below: \begin{eqnarray} &&\min \, x^T \Sigma \, x - \mu^T x \nonumber\\ &&\mbox{subject ...
  • 136
4 votes
2 answers
109 views

What are the best-known lower bounds on the number of measurements required for quantum state tomography?

I'm very curious to know more about bounds of number of measurements (or number of independent copies of state) required to reconstruct full density matrix $\rho$ such that it is $\epsilon$-close (...
  • 173

1
2 3 4 5
19