Questions tagged [optimization]

For questions concerning how to improve quantum computers on different aspects like performance, efficiency or fault-tolerance.

Filter by
Sorted by
Tagged with
2
votes
0answers
39 views

Is there a general proof of convergence of variational quantum eigensolvers (VQEs) to the minimum eigenvalue?

For QAOA it is known that in the large $p$ limit, the algorithm finds the minimum/maximum (see article A Quantum Approximate Optimization Algorithm). Is there in general a proof for VQE starting ...
2
votes
2answers
110 views

What exactly happening in QAOA in a general way?

So I know that in QAOA we have the two hamiltonians. Mixer and Cost Hamiltonian. Lets start: First we have our Qubits which get in the Superposition if we add the Hadamard Gate. Then we have the both ...
1
vote
2answers
49 views

In quantum adiabatic simulation, is the $s$ in $(1-\frac{s}{T})H_{in}+\frac{s}{T} H_{cl}$ related to the $t$ in $e^{-iHt}$?

I just want to do a whole adiabatic calculation on quantum circuit. To prepare two Hamiltonian of $H_{initial}$ and $H_{classical}$ and solve $H_{classical}$ using adiabatic calc like quantum ...
4
votes
2answers
68 views

From QUBO matrix to Ising model in Qiskit

Given a general QUBO matrix $Q$ for a quadratic minimization problem, is there a Qiskit way to obtain the Pauli gate list or the Ising model for it? A related question is Qiskit: Taking a QUBO matrix ...
2
votes
1answer
50 views

Vertex Cover mappings from QUBO to Ising and vice versa

According to paper Ising formulations of many NP problems, Vertex Cover problem has the following Ising formulation: $$\underset{x}{\text{min }} f(x) = a\sum_{(i,j) \in E}(1-x_i)(1-x_j) + b\sum_{i \in ...
4
votes
0answers
85 views

Solving higher-order (unconstrained) binary optimization problems with QAOA without quadratization

I am aware that it's possible to use QAOA to solve QUBO problems. However, I've recently seen some sources mentioning the possibility of solving HOBO/HUBO problems using QAOA as well [1][3]. While I ...
3
votes
2answers
95 views

Question on practical quantum computing programming code [duplicate]

Has anyone tried any quantum computing programming code that shows or demonstrates the advantage of a quantum computer over classical computers? Thanks a lot.
8
votes
1answer
249 views

Comparing method of differentiation in variational quantum circuit

Training of variational circuits needs to calculate the derivative to be optimized. Several methods were proposed (1), the most famous ones being the finite difference and the parameter shift rule. ...
3
votes
0answers
117 views

Implemented QAOA returns wrong result

I try to apply QAOA algorithm to find minimal energy state of the Hamiltonian: $H_A = \frac{1}{2}\sigma_z^1 + \frac{1}{2}\sigma_z^1\sigma_z^2$ It is expected that with p=2 my variational should ...
5
votes
1answer
71 views

Why QAOA with $p \rightarrow \infty $ gives the optimal solution?

In the QAOA paper, it is shown that the optimal value of the p-ansatz $M_p$ converges to $\max_z C(z)$ as $p \rightarrow \infty$ on page 10. The proof is to relate to QAOA by considering the time-...
3
votes
1answer
62 views

Can QAOA solve a constraint optimization problem?

Can QAOA solve a constraint binary optimization problem? QAOA is short for Quantum Approximate Optimization Algorithm. I read the information https://qiskit.org/textbook/ch-applications/qaoa.html. But ...
3
votes
2answers
256 views

Does the Qiskit ADMM optimizer really run on quantum computers?

I read Qiskit quantum admm on this website. I doubt whether this Qiskit ADMM algorithm can run on a quantum computer. The code did import packages from Qiskit, but it doesn't create any quantum ...
2
votes
1answer
47 views

To find the best angles in QAOA why we do not optimize over a maximum ofall shots instead of a mean?

When finding the best angles for QAOA we optimize over $F_{p}(\beta , \gamma) = \langle \psi_p(\gamma,\beta)|C|\psi_p(\gamma,\beta)\rangle $. In each optimization step we simulate the circuit $m$ ...
0
votes
1answer
71 views

Is there a quantum circuit to find the maximum of two inputs?

Is there a quantum circuit (preferably on Quirk as an example) that will enable me to find the maximum from two inputs? Example input A: 11011 input B: 11100 Expected output: 11100
2
votes
0answers
36 views

How to implement the Maximum or Minimum Searching Algorithm (QUMMSA) circuit in Quirk?

I am Java and Python programmer who started self-learning Quantum Computing a couple of months back. The journey has been thus far very tough. I have been using QisKit and Quirk to learn by in ...
2
votes
1answer
142 views

How to solve QUBO problems in Q#?

Short version: I'm trying to solve a traveling salesman problem very similar to the traveling Santa example here: http://quantumalgorithmzoo.org/traveling_santa/, which is also included in the samples ...
4
votes
1answer
236 views

QUBO, Ising Hamiltonians and VQA

I understand that usually the combinatorial optimisation problems are turned into QUBO, which has a very simple mapping to Ising Hamiltonians. Ising Hamiltonians in turn have the desired properties of ...
3
votes
1answer
116 views

Can QAOA be considered as simulation of a quantum annealer on a gate-based quantum computer?

Quantum annealers are single purpose machines allowing to solve quadratic unconstrained binary optimization (QUBO) problems. QUBO problems have following objective function: $$ F=-\sum_{i<j}J_{ij}...
3
votes
1answer
120 views

How does the classical optimization of the angles $\gamma$ and $\beta$ in QAOA work?

I have been trying to implement QAOA with classical optimization of the angles $\gamma$ and $\beta$, but I I'm failing at the classical part. In paper Quantum Approximate Optimization Algorithm: ...
1
vote
1answer
55 views

Qiskit: Error when importing libraries for ADMM optimizer

I would like to try and ADMM optimizer as shown in Qiskit Tutorial in Quantum Lab. Firstly, I imported necessary libraries (copy/paste from the Tutorial): ...
2
votes
1answer
73 views

Quadratic optimization in Qiskit: Error when QuadraticProgram with quadratic constraint converted to QUBO

I prepared a quadratic optimization task with binary and integer variables and linear and quadratic constraints. I fed it into QuadraticProgram in Qiskit. After ...
2
votes
1answer
74 views

Quantum Circuit Optimization with Machine Learning [closed]

I read some paper about Quantum Circuit Optimization but I am on a low level. And have some experience in ML. But what I don't understand is it possible that ML can help to optimize Quantum Circuits ...
-1
votes
1answer
144 views

Implementing a circuit that returns $|01\rangle$ and $|10\rangle$ with equal probability

Using Python how can I implement a quantum circuit that returns $|01\rangle$ or $|10\rangle$ using only $CX$, $RX$ and $RY$ gates, starting with random parametric gates as parameters and optimizing it ...
2
votes
1answer
117 views

Qiskit sample - Portfolio optimization

I've recently tried to run this sample from Qiskit (Portfolio Optimization) I was able to change RandomDataProvider to YahooDataProvider and able to run it on real stock prices. However, there is one ...
3
votes
0answers
33 views

What is the query complexity of the QUBO algorithm?

What is the complexity of the quantum unconstrained binary optimization (QUBO) algorithm in the number of queries to the quantum processor? To clarify, I'm asking about the complexity on quantum ...
1
vote
1answer
65 views

Optimization using Quantum Logics

Is it possible to solve the following kind of optimization using Quantum Computing? Minimize 5*x1 - 7*x2 binary x1 x2 If yes, is it possible to have a sample code ...
2
votes
1answer
69 views

How can I solve the problem of optimisation the quantum computer?

I am trying to solve the problem of optimization (VRP) with genetic algorithm and quantum computing in the platform IBM Q Experience. But I am unable to advance on this. How can I do it? According to ...
5
votes
1answer
134 views

Qiskit Portfolio Optimization Application

I recently got flung into the world of quantum computing and I'm a beginner at coding. I was assigned to do the Portfolio Optimization tutorial of the Qiskit Finance Tutorials and input real data. ...
5
votes
0answers
54 views

Computing the expectation values of a Hamiltonian constructed from a cost functions in combinatorial optimization

One of the main steps in Hybrid Quantum algorithms for solving Combinatorial Optimization problems is the calculation of the expected value of a hermitian operator $H = \sum{H_i}$ (where $H_i$ are ...
0
votes
2answers
55 views

How to stop optimization of a circuit during transpiling in web-interface of IBM Q?

I was playing with approximation of gates with Clifford+T group on IBM Q. Everything works well on simulator, however, when I tried to run my circuit on actual quantum processor, a transpiler ...
1
vote
2answers
43 views

Layout Method in qiskit

Using transpile with optimization_level = 3, which is the layout method used by default?
1
vote
1answer
79 views

SPSA max_trials

I'm using SPSA as an optimizer in VQE algorithm. The code runs on ibmq-qasm-simulator. I've set SPSA max_trials parameter to 500, but, when I run the code, it makes ...
1
vote
0answers
40 views

van Dam's proof for adiabatic optimization and graph diameter

My question concerns a proof in https://people.eecs.berkeley.edu/~vazirani/pubs/qao.pdf, "Limits on Quantum Adiabatic Optimization - Warning: Rough Manuscript!" by Wim van Dam and Umesh Vazirani. It ...
1
vote
0answers
35 views

Is there a limit to the size of problems that your simulators can run on Qiskit Aqua?

I'm trying to solve QUBO problems using Qiskit QAOA and VQE solvers. However, I have the experience that I can only solve small problems. I tried with both QAOA and VQE and both experience the same ...
2
votes
1answer
559 views

How to convert QUBO problem to Ising Hamiltonian?

According to paper Ising formulations of many NP problems an unconstrained quadratic programming problem $$ f(x_1, x_2,\dots, x_n) = \sum_{i}^N h_ix_i + \sum_{i < j} J_ix_ix_j $$ can be expressed ...
4
votes
1answer
141 views

What are the differences between the different transpiler optimization levels in qiskit

I am currently running a simple algorithm using Qiskit and I am running it for various transpiler optimization levels (0-3). I wish to know what exactly occurs differently when for example I run the ...
0
votes
2answers
162 views

What is Ising Hamiltonian ? What its role in Portfolio Diversification?

I am asking this question with reference to this https://github.com/Qiskit/qiskit-iqx-tutorials/blob/master/qiskit/advanced/aqua/finance/optimization/portfolio_diversification.ipynb Happy to know new ...
1
vote
2answers
169 views

What is the risk factor on IBM's portfolio optimization notebook?

In the notebook "portfolio optimization" on IBM's platform the goal is to calculate the optimal stock selection using a classical and a quantum algorithm (VQE). A random portfolio is generated and ...
2
votes
0answers
127 views

How can I implement partial transpose on a variable in Picos (Python, trying to solve an SDP)?

I try to optimise a quantity via an SDP. I optimise over all PPT measurement operators and hence have the constraints $\Pi_k^{T_B} \succeq 0$ (PPT) for my measurement operators. The part of the code ...
2
votes
1answer
63 views

Quantum Annealing - Job Shop Problem

using this paper, I want to implement a solution for the Job Shop Problem on a D-Wave machine. One of the constraints mentioned in the paper, is $$ h_3(\bar{x}) = \sum_i \left(\sum_t x_{i,t}-1 \right)^...
3
votes
1answer
191 views

QAOA for MaxCut - Algorithm motivation

In the QAOA algorithm for MaxCut, the authors construct a very specific scheme where the qubits (corresponding to the vertices of the graph) are transformed using a sequence of unitaries $$|\gamma, \...
0
votes
1answer
88 views

Quantum algorithm for binary assignment problem

Based on the properties of the qubit, how could I solve this problem: I have 3 person A B C and 2 taxis T1 and T2 A and B are friends B and C hate each other A and C hate each other How could I ...
3
votes
0answers
94 views

Forbidden/allowed outputs of a quantum channel

The coherent information of a channel $\mathcal{E}_{A'\rightarrow B}$ is defined as the maximum value obtained by the following function where the maximization is over all input states $$I_{\rm{coh}}(...
3
votes
1answer
114 views

Optimizing over quantum channels

I am given fixed quantum states $\rho_X$ and $\sigma_Y$ and some function of the form $\text{Tr}(N_{X\rightarrow Y}(\rho_X)\sigma_Y)$. I would like to maximize this function over all completely ...
6
votes
1answer
602 views

Travelling salesman problem on quantum computer

Recently a pre-print of article Efficient quantum algorithm for solving travelling salesman problem: An IBM quantum experience appeared. The authors use a phase estimation as a core for their ...
4
votes
1answer
66 views

How to explain that I get a value lower than the smallest possible through minimization procedure in VQE?

As far as I know after minimization I have to obtain a value $E_{0}\le \frac{\langle \psi (\theta)|H|\psi (\theta)\rangle}{\langle \psi (\theta)|\psi (\theta)\rangle}$, where $E_{0}$ - eigenvalue of ...
1
vote
0answers
26 views

Entanglement and teleportation in quantum annealing and parallel computation

In classical optimization problems, some objective function's surface serves as a landscape for finding its minimum through minimization algorithms. Instead of your typical U-shaped objective ...
2
votes
0answers
51 views

Quantum Optimization algorithms

The Harrow-Hassidim-Lloyd (HHL) algorithm for quantum matrix inversion (linear algebra) bridges classical math to quantum math and has been adopted for quantumizing many classical applications, such ...
3
votes
0answers
91 views

Quantum algorithms, combinatorial optimization, and approximation bounds

Recently, I saw this article, Classical and Quantum Bounded Depth Approximation Algorithms where the author discusses the limitations of QAOA relative to classical approaches. In particular, they ...
4
votes
0answers
125 views

General mixed integer linear programming problem with quantum computers

I was wondering if anyone had a sample code for running a general MILP problem. I saw some coding for some very specific problems and I thought they were kind of far away from what we needed. $$ \text{...