Questions tagged [optimization]
For questions concerning how to improve quantum computers on different aspects like performance, efficiency or fault-tolerance.
151
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14
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scipy.optimize.minimize throwing error
I used minimize for optimizing the ansatz parameter. I wrote the line like
...
- 27
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1
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28
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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\...
- 13
4
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62
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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 $\{ \...
- 5,610
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25
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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-...
- 111
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2
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56
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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 ...
- 166
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2
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40
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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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43
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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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46
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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. ...
- 155
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2
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96
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Variational Quantum Algorithms and Quantum Advantage
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 ...
- 111
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73
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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 ...
- 11
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1
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65
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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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1
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44
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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 ...
- 25
3
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31
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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 ...
- 454
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38
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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 ...
- 11
3
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77
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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 ...
- 135
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21
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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:
<...
- 321
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99
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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}
...
- 71
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1
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59
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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 ...
- 12.9k
2
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0
answers
22
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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 ...
- 151
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57
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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 ...
- 151
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1
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53
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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 (...
4
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1
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62
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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?
- 41
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109
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Single Yang-Baxter reflection
Context and definitons
I want to study the evolution of a three qubit Heisenberg Hamiltonian:
$$H=(I\otimes X\otimes X)+(X\otimes X\otimes I)+(I\otimes Y\otimes Y)+(Y\otimes Y\otimes I)+(I\otimes Z\...
- 1,973
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83
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Grover Adaptive Search in Qiskit - why ancilla qubit is not used?
I am trying to solve some QUBO tasks with Grover Adaptive Search ("GAS"). For testing purposes, I use a simple task with quadratic part
$$
A = \begin{pmatrix}0 & -0.5 \\ -0.5 & 0\end{...
- 12.9k
4
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2
answers
151
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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} + ...
- 2,033
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answers
47
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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 ...
- 11
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0
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18
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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 ...
- 11
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22
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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 ...
- 2,033
1
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1
answer
174
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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 ...
1
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1
answer
72
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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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0
answers
30
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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
277
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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 ...
- 545
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168
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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
...
- 1,292
3
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2
answers
246
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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 ...
- 136
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0
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71
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Quantum AND† gate
In the paper Implementing Grover oracles for quantum key search on AES and LowMC, the authors use a different construction of AND gate and its adjoint rather than the Toffoli gate to decrease the T-...
- 117
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31
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Techniques to parallelize controlled-unitaries controlled by the same qubit but acting on different target qubits
I need to find a way to parallelize a set of controlled-unitaries that are all controlled by the same qubit and are targetting $n$ different qubits. The main constraint that I have is that I can only ...
- 1,340
4
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1
answer
121
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T-depth in Qiskit
How to find T-depth in Qiskit? Is there any inbuilt function or some method to find T-depth? I know that the .depth() function exists which returns circuit depth (i....
- 117
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1
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145
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What is the original paper introducing the Variational Quantum Eigensolver?
My question is very simple. I am looking for original paper where Variational Quantum Eigensolver (VQE) has been introduced. After some Googling I was able to find many applications of VQE and its ...
- 12.9k
4
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3
answers
472
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Cost of SWAP gate
We know that a SWAP gate needs three CNOT gates but I have seen papers which say that a SWAP gate can be achieved by necessary rewiring can are not counted towards the final quantum cost. I am ...
- 117
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votes
2
answers
221
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Solving Hamiltonian eigenvalue problem
I would like to solve an eigenvalue problem of a Hamiltonian. I was able to find the lowest eigenvalue by converting the Hamiltonian into a matrix and applying linear algebra eigenvalue techniques. ...
- 2,033
2
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0
answers
32
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The energy levels crossover problem in Quantum Annealing
How to avoid energy levels crossover in quantum annealing by Kibble-Zurek mechanism? Any detailed references?
- 31
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1
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284
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The relationship between max-cut and max independent set
I know that Max Independent set problems are not equivalent to Mac-Cut problems. The cost function of Max-Cut can be described by the classical Ising model
$
H = \frac{1}{2} \sum_{i,j\in E}(1 - Z_i ...
- 31
5
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1
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157
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Qiskit: QAOAnsatz circuit with custom Hamiltonian
I am trying to implement the Quantum Approximate Optimization Ansatz by creating a parametrized subcircuit
$$V (α) = e^{−iH_M α_1} e^{−iH_D b_1} ... e^{−iH_M α_n} e^{−iH_D b_n}$$
with the custom ...
- 321
2
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1
answer
116
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Quantum Annealing vs Quantum Monte Carlo: can QMC do all that QA can?
I'm working on an essay about quantum technology, and the connection between the annealing algorithm and quantum computing hardware is an important transition in the text. I'd like to know if there is ...
- 33
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1
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263
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How linear combination of unitaries gradient work (Qiskit, PennyLane)?
I'm trying to implement linear combination of unitaries(LCU) gradient from Qiskit Gradient Framework
but on PennyLane.
First, i looked through the source code in Qiskit.
In Qiskit LCU gradient if we ...
1
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0
answers
83
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qutip.sesolve and qutip.optimize_pulse_unitary produce different results
I'm currently trying out some things with qutip in the field of optimal control (state-to-state transfer) and have some trouble to reproduce my results from the optimization process with sesolve.
My ...
5
votes
2
answers
151
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maximization of trace between two operators with respect to different norm constraints
I want to maximize $\text{Tr}(XY)$ over $X$ for fixed $Y$, where $X$ and $Y$ are both hermitian (but doesn't necessarily positive) operators, and $X$ is constrained by its p-norm bounded by $1$, i.e. $...
- 413
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109
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Is No Free Lunch Theorem generalizable to Quantum Computation?
The "No Free Lunch Theorem" says: that when averaged across all possible problems, any two strategies have equivalent performance. However it uses Bayesian reasoning to arrive at this ...
- 377
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1
answer
198
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Closest quantum state with a fixed marginal: Analytical solution?
Let $\rho_{AB}$ be a bipartite state and let $\sigma_{B}$ be another state. What state $\tilde{\rho}_{AB}$ is closest to $\rho_{AB}$ and satisfies $\tilde{\rho}_B = \sigma_B$? We can define closeness ...
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