Questions tagged [optimization]
For questions concerning how to improve quantum computers on different aspects like performance, efficiency or fault-tolerance.
166
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Question about entanglement forging
For circuit knitting (entanglement forging), do anyone understand the mechanism behind equation (3) which halves the amount of qubits required for a circuit ?
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How to add a circuit layer after computing QAOA layer
I have used the Qiskit-based QAOA function to solve a combinatorial problem tsp, and I want to append a circuit after the QAOA layer, is there any way to do that?
Qaoa
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When is a quantum algorithm considered to have a significantly superior performance over another quantum algorithm?
Suppose we have two heuristic quantum algorithms $A$ and $B$ that attempt to solve a certain class of optimization problems. Let's suppose that the benchmarking metric is Time To Solution (TTS), which ...
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How to use Warm-Start QAOA in QisKit to solve non-convex QUBO problem?
I have a non-convex QUBO problem that I'd like to solve by warm-starting QAOA with a solution obtained from a continuous relaxation solution obtained by a classical algorithm. The specifics of the ...
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Recent experimental demonstrations of variational quantum algorithms?
I am interested in the recent experimental demonstrations of variational quantum algorithms.
Can someone please provide me with a list of references of recent experimental demonstrations of ...
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1
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25
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Portfolio optimization via quantum Zeno dynamics in Qiskit
Recently, I came across paper Portfolio Optimization via Quantum Zeno Dynamics on a Quantum Processor. In the paper, a new approach to optimization with QAOA is introduced. Instead of employing a ...
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45
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How to sanity check QAOA cost Hamiltonian?
I'm trying to learn QAOA and how to apply it to a complex combinatorial problem. But for the purpose of this question I'll use the common example
MaxCut.
I'd like to know if I've set up my cost ...
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85
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Does QAOA require that the problem Hamiltonian be an Ising Hamiltonian as a quadratic function of the spin variables?
In the context of QAOA, I often see the problem Hamiltonian being called an "Ising Hamiltonian", and shortly after, I that the Hamiltonian is a quadratic function of the spin variables.
Is ...
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49
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Inequality constraint to QUBO penalty
I am trying to formulate a problem as QUBO problem and am not able to transform the inequality constraint.
$$ \sum_i^N x_i \geq 1 $$ into a suitable penalty function. For N = 2, the penalty term can ...
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2
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2
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111
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Does the gradient commute with the partial trace?
Suppose I have a parameterized quantum state: $\rho(\theta) = U(\theta) \rho U^\dagger(\theta)$. I am curious to know whether the following holds:
$\frac{\partial \text{Tr}_A (\rho(\theta))}{\partial \...
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Why is a large quantum annealer likely to leave its ground state?
For problems of significant size in quantum annealing, I have read that even for slow transitions, the annealer is likely to leave its ground state. I have not fully grasped the meaning of why exactly ...
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Extracting a QUBO matrix from pyqubo
I am benchmarking different QUBO solvers for a very simple instance of the knapsack problem.
Some of these solvers require the matrix, Q, and offset, b, from the equation:
$$
\begin{equation}
x^{\...
3
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1
answer
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Does QAO Ansatz have any better performance guarantees than QAOA?
QAOA is a well-known heuristic for solving optimization problems, and it has the desirable property that as p -> infinity, the true minimum objective function value is reached.
There is a ...
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41
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Can pyqubo and qiskit be used together?
I used Pyqubo to create an optimisation problem with an objective function and some constraints, but I want to use Qiskit to run QAOA/VQE on my model. Is it possible to call my Pyqubo model into ...
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SPSA: maxiter (int) – The maximum number of iterations. Note that this is not the maximal number of function evaluations
This is from classical optimization algo. used for VQE. May I know what is the difference between maxiter and the number of function evaluation difference?
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37
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scipy.optimize.minimize throwing error
I used minimize for optimizing the ansatz parameter. I wrote the line like
...
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34
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Find min of a quantum state L2 norm
I have a problem minimizing this norm with respect to $\alpha$:
$\min_{\alpha}||e^{i\alpha}|\psi\rangle-|\phi\rangle ||^2$ (1)
The result is that this achieves min when $\alpha=-\measuredangle \langle\...
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Numerical optimization over separable measurements
For a set of bipartite density operators $\{\rho_a\}_{a=1}^m \subset D(\mathcal{X} \otimes \mathcal{Y})$ each associated with a probability $p(a)$, an optimal separable measurement is a POVM $\{ \...
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Variational Quantum Algorithms for Graph Traversal
I have a combinatorial optimization problem which on a first pass I think boils down to finding a path with a maximal score. The score for a path is computed by an auxiliary function.
Are there near-...
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How are the parameters in a variational circuit optimized?
I'm quite new to QML and I don't understand how the parameters in a variational circuit are optimized.
I read about the parameter shift rule but what happens after the gradient is calculated ? How do ...
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Solving a linear optimization problem with inequality constraints in qiskit? is it possible?
This is an easy optimization problem that can be classically solved. My question is that, in qiskit, how can we solve this optimization problem using IBM real machines? Is it even possible to do that?
...
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47
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Using BFGS for MAXCUT
In the original Qiskit QAOA implementation, the sample uses COBYLA as the classical optimizer in the following code segment:
...
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1
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55
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GRAPE with Python?
I want to do some quick GRAPE calculations in Python. The qutip implementation is handy but I can't modify the fidelity function. However, I need to use my own fidelity function to evaluate fidelity. ...
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2
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129
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How to derive quantum advantages for VQAs, if the underlying classical optimization is hard to solve?
This is probably a dumb question but here it goes:
Variational Quantum Algorithms (VQAs) are the leading proposal to derive quantum advantage use NISQ devices. VQAs employ classical optimization ...
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qiskit.algorithms.optimizers callback function for all optimizers
I am aware that VQE and VQC factory supports callback functions which can allow us to store intermediate values during optimization through callbacks in its arguments. However my loss function is ...
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95
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Implementation of QAOA to solve version of knapsack problem
Say I want to fill a knapsack with as many things as possible. I don't care about what they are, simply the number. But I don't want the total weight to exceed a set limit.
[https://qiskit.org/...
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Frequency range of superconducting qubit
What are the reasons/considerations for setting the transmon qubit frequency between around 3-6 GHz? What undesirable consequences will result if the frequency is out of the range?
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Does pytket have an optimization pass that removes gate-inverse pairs & identity rotations & redundant gates and/or merges rotations?
For the following sample circuit I want to reduce the number of gates in pytket:
for example, I know:
Adjacent Rx gates can be merged
CZ is self-inverse and cancels itself out because any Hermitian ...
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34
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How to compare Quantum Annealing and Adiabatic Quantum Computing?
I'm still unsure on the difference between adiabatic quantum computing (AQC) and quantum annealing (QA). Please critique these interpretations:
AQC: Define a Hamiltonian with an easy-to-prepare ...
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46
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Solving TSP on real hardware
I'm trying to solve the traveling salesman problem using Qiskit. Following the relevant tutorial, I end up with an algorithm that uses $n^2$ qubits. This grows rapidly enough that I couldn't possibly ...
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Understanding of the transverse-field Ising model
I want to make sure whether I do understand the transverse Ising model correctly or not. The classical Ising model describes the interaction between spins in a grid and the state of spins can be ...
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Qiskit: efficient way to create bound circuits?
I am running an optimization problem whose objective function $F(a)$ requires measuring N variational circuits $V_i(a)$ at each evaluation.
So, roughly, I have created N parametric circuits and I do:
<...
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102
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Lowest energy problem with additional constraints
Consider the following minimization problem:
\begin{align}
&\min_{\rho} \mathrm{Tr}[\rho H] \\
\text{such that:}& \\
&Tr[\rho A_i] \leq 0 \ \ \forall A_i, \ i \in \{1,2,3,...\}
\end{align}
...
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Using entropy quantum computing for solving optimization problems
I would like to follow up on this question (What is Entropy Quantum Computing?).
Company Quantum Computing Inc. announced that they made their quantum computer aimed at solving binary optimization ...
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Absolute value of a BQM: how to substitute it with constraint?
I need to build an expression for the objective to be minimized which is based on the L1-norm. For doing this, I need to take the absolute value of a BQM, which is not possible, at least at the moment ...
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How to convert equality/inequality constraint to a BQM?
I need to submit a BQM to DWaveSampler. Since my problem has both objective and constraints, my understanding is that I need to add the latter as bqm to a composite BQM, which is then sent to the ...
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Calculating state fidelity and space complexity of Minimum Eigen Optimizers (VQE, QAOA and Grover Optimizer) in qiskit
I'm a beginner in using Qiskit and my Computer Science background is not extensive. But I understand the Quantum Physics aspects of it relatively well.
I solved a QUBO problem in Qiskit using VQE (...
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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?
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Single Yang-Baxter reflection
Context and definitons
I want to study the evolution of a three qubit Heisenberg Hamiltonian:
$$H=(I\otimes X\otimes X)+(X\otimes X\otimes I)+(I\otimes Y\otimes Y)+(Y\otimes Y\otimes I)+(I\otimes Z\...
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Grover Adaptive Search in Qiskit - why ancilla qubit is not used?
I am trying to solve some QUBO tasks with Grover Adaptive Search ("GAS"). For testing purposes, I use a simple task with quadratic part
$$
A = \begin{pmatrix}0 & -0.5 \\ -0.5 & 0\end{...
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Under what conditions the minimum eigengap is non-zero?
I would like to know sufficient conditions for a non-zero eigengap of a time-dependent Hamiltonian.
Suppose we have a time-dependent Hamiltonian $H(t)$ defined as follows:
$$H(t) = (1-s(t))H_{init} + ...
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Difference between using CircuitSampler vs Execute methods on obtaining expectation value
For a hybrid, VQE-type optimization in qiskit, in order to compute the expectation value of a Hamiltonian, we can use CircuitSampler on some Pauli sum operators, as well as Execute method on a list of ...
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SPSA optimizer picking up previous iterations evaluations
I would like to write a modified SPSA which takes up an optimization history of a previous VQE simulation. Is it something that can be done? The purpose of this is to cut down the amount of time and ...
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Error analysis on the approximation of an adiabatic evolution operator by a QAOA circuit
I would like to know what would be the approximation error of a QAOA circuit.
Suppose we have time-dependent Hamiltonian $H(t) = (1 - s(t))H_{init} + s(t)H_{prob}$ where $H_{init}$ in an initial ...
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Qiskit optimization_level values
Is there a clear explaination of how exactly optimization_level choice in qiskit's transpile() method affects on circuit? I expected to see some mathematical operations with the gates that similifies ...
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1
answer
88
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How to declare non-binary decision variables in an optimization problem?
I am working on a logistics problem which require me to find the optimum quantity of product to be manufactured and also to be shipped to satisfy the customer demand. I have made a decision variable $...
2
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How can I evaluate the weights of different shares in a portfolio optimization problem?
I'm trying to do a comparison between the classical way to do portfolio selection with Markovitz and the quantum counterpart. With Markovitz I'm able to generate an output representing the best ...
2
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1
answer
330
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Choosing a different optimizer when running QAOA in qiskit
I am trying to reproduce the QAOA example from https://qiskit.org/textbook/ch-applications/qaoa.html and learn how to opt for a different optimizer.
The relevant block in the example is (towards the ...
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Categories and types of quantum inspired algorithms
I have a question concerning "quantum-inspired" algorithms. There seem to be several types of algorithms that fall into this category. Some examples are:
Ewin's dequantized algorithms
...
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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 ...
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