Questions tagged [optimization]

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

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1answer
38 views

Pack Header Error when using QAOAProgram [closed]

I want to use QAOAProgram from Qiskit in the following way: ...
3
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0answers
27 views

What type of tasks it is possible to solve on a quantum simulator?

In this article, the author claimed that researches from Harvard and MIT created 256 qubits quantum simulator. However, we are not talking about piece of software on a classical computer but actual ...
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2answers
196 views

Complexity of $n$-Toffoli with phase difference

I'm interested in the $n$-Toffoli gates with phase differences. I found a quadratic technique in section 7.2 of this paper. Here's the front page of the paper. Here's an image of the section that I'm ...
5
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0answers
67 views

Solving linear system $Ax=b$ with exponential speed-up via binary optimization?

The main disadvantage of HHL algorithm for solving $A|x\rangle = |b\rangle$ is that exponential speed-up is reached only in case we are interested in value $\langle x|M|x\rangle$, where $M$ is a ...
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0answers
44 views

How to improve embedding process in D-Wave?

I am quite new to the quantum computing field. Currently, I am trying to solve a combinatorial optimization problem on a D-Wave system, which I successfully translated into QUBO form. I also managed ...
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0answers
42 views

Minmax theorem for optimization over isometries and states

I have the following minmax problem and I am wondering if the order of the minimum and maximum can be interchanged and if yes, why? Let $\|\cdot\|_1$ be the trace norm defined as $\|\rho\|_1 = \text{...
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0answers
36 views

Quantum annealing - studies showing empirical evidence for better performance in comparison with classical computers

Currently, it is not known wheter quantum anneling or algorithms like VQE and QAOA for general purpose quantum computers bring about any increase in computational power. However, there are some ...
3
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1answer
98 views

What explains my anomalously scaled up VQE?

I am trying to implement VQE from the Qiskit to obtain the ground state of a very specific Hamiltonian that has been generated via a docplex minimized quadratic ...
2
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0answers
15 views

Measurement on a specific basis and proof of circuit output

I am trying to understand a proof from Practical optimization for hybrid quantum-classical algorithms. In particular, I need clarifications on how do you perform the measurement on a different basis ...
2
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1answer
40 views

QAOA not returning solution for simple clustering problem

I am following University's of toronto QML course and there's a section where QAOA is applied to cluster a set of vectors by mapping the clustering problem into a Maxcut problem. Unfortunately qiskit'...
4
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2answers
123 views

Role of entanglement in a VQE ansatz for combinatorial problems

Variational Quantum Eigensolver is used in quantum chemistry and combinatorial optimization (CO). I'm interested in the latter. In the CO setting a Hamiltonian is a diagonal matrix with real entries ...
2
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1answer
176 views

What's the role of mixer in QAOA?

In QAOA algorithm, two terms are being discussed; 1) clause or cost (C) Hamiltonian and 2) mixer consisting of pauli X gates. What is the role of this mixer? Not clear why it comes after the C. ...
2
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1answer
71 views

Set the bounds for ansatz parameters in VQE

How can I make intervals for free parameters when I use VQE function? (https://qiskit.org/documentation/stubs/qiskit.algorithms.VQE.html) I have built a parametrized ($\theta_1,...,\theta_n$) circuit ...
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1answer
46 views

Qiskit Portfolio Optimization : Does the resulting matrix show the stock combination to select?

The IBM Qiskit Portfolio Optimization sample finally provides an array similar to [1,0,1,1] representing the 4 digits as the stocks. So does the ...
2
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0answers
43 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
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2answers
147 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 ...
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2answers
51 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
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2answers
180 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
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1answer
61 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 ...
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0answers
121 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 ...
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2answers
99 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.
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1answer
352 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. ...
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0answers
124 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
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1answer
83 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
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1answer
73 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 ...
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2answers
274 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
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1answer
70 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 $m$ ...
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1answer
76 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
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0answers
40 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
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1answer
165 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
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1answer
385 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
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1answer
148 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
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1answer
149 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: ...
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1answer
61 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
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1answer
107 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
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1answer
82 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 ...
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1answer
148 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
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1answer
136 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
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0answers
41 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 ...
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1answer
71 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
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1answer
77 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
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1answer
165 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. ...
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0answers
56 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 ...
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2answers
68 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 ...
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2answers
61 views

Layout Method in qiskit

Using transpile with optimization_level = 3, which is the layout method used by default?
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1answer
86 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 ...
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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 ...
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0answers
37 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
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1answer
838 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 ...
5
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1answer
203 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 ...