Questions tagged [optimization]

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

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78 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 ...
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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 ...
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1answer
41 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)^...
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1answer
49 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, \...
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1answer
52 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 ...
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84 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}}(...
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35 views

Code for a simple optimization problem in Criq

For a demonstration, I would like to code a simple optimization problem in Cirq. I don't care what the problem is, but I want it understandable to someone who has had only basic algebra. One idea is ...
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1answer
88 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 ...
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1answer
143 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 ...
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1answer
57 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 ...
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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 ...
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27 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 ...
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59 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 ...
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58 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. If ...
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1answer
71 views

How does the fact that the output of a quantum circuit cannot be efficiently simulated classically help for optimisation?

This question refers principally to the article where for a low-depth circuit QAOA, the output cannot be efficiently simulated classically. I am wondering how this kind of quantum supremacy matters ...
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172 views

How to implement NM Algorithm for Variational Quantum Eigensolver?

First of all: thanks for reading again. I appreciate the feedback I have gotten from this community the past weeks as I started to feel ready to ask questions about quantum computing topics. I am ...
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52 views

Illustrating limitations of quantum computing

Can you illustrate why even with a functioning quantum computing energy minimization in an Ising Model simulation, an NP-hard problem, cannot be solved?
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1answer
62 views

How to tell if the ground states of two Hamiltonians are solutions of the same optimization problem?

Let's say, that we have an optimization problem in the form: $$ \min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p, $$ where $f(x)$ is an objective function, $g_i(x)$ are ...
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155 views

Is there a general method of expressing optimization problem as a Hamiltonian?

Let's say, that we have an optimization problem in the form: $$ \min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p, $$ where $f(x)$ is an objective function, $g_i(x)$ are ...
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41 views

What does it mean to have 2000 qubits and 6016 couplers?

From official D-Wave docs: The D-Wave 2000Q QPU has up to 2048 qubits and 6016 couplers. For example, I have the optimization problem defined as the QUBO problem. If I want to solve it on D-Wave,...
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131 views

Genetic algorithm does not converge to exact solution

I'm trying to evolve quantum circuits using genetic algorithms as they did in this paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin &...
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1answer
142 views

Evolving a quantum circuit using a genetic algorithm

I've written a small quantum circuit simulator in python, so now I'm trying to evolve some circuits via genetic algorithms. My encoding is very simple, it's just a rectangular table of strings ...
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1answer
71 views

Optimise implementation of a quantum algorithm when an input is fixed

I need to implement a quantum comparator that, given a quantum register $a$ and a real number $b$ known at generation time (i.e. when the quantum circuit is generated), set a qubit $r$ to the boolean ...
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77 views

Optimal sampling strategy for VQE

In VQE we wish to minimize some cost function $F(\vec{x})$ that is dependent on a quantum state $\left| \psi_\vec{x} \right>$ which is prepared by a unitary $U(\vec{x})$ depending on some (...
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214 views

Resources on hybrid quantum-classical algorithms applied to combinatorial optimization problems

I am doing a thesis on "Metaheuristics and Quantum Computing", and was wondering if anyone could recommend some papers/pages to read talking about hybrid quantum/classical computing. (My idea is to ...
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1answer
115 views

Applying Group Leaders Optimization to Quantum Belief Systems

Context: I am particularly interested in quantum cognition & would like to use a tool like pyZX to perform the following types of optimizations. In Preparing a (quantum) belief system they "...
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1answer
295 views

Understanding the Group Leaders Optimization Algorithm

Context: I have been trying to understand the genetic algorithm discussed in the paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin &...
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3answers
440 views

How to run algorithms on IBMQ via Qiskit-Aqua?

I am trying to run an optimization problem on IBMQ. Running the same code on QASM simulator works fine. However, changing only the backend name to IBMQX takes long time. I am aware of the queues ...
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1answer
116 views

Minimum number of CNOTs for a 4-qubit increment on a planar grid

Recently I've been wondering how high NISQ machines will be able to "count". What I mean by that is, given the most optimized increment circuit you can make, how many times can you physically apply ...
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2answers
313 views

Minimum number of CNOTs for Toffoli with non-adjacent controls

I want to decompose a Toffoli gate into CNOTs and arbitrary single-qubit gates. I want to minimize the number of CNOTs. I have a locality constraint: because the Toffoli is occurring in a linear array,...
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85 views

Application of classical approximate optimization algorithm to bottlenecks of quantum computing

According to J. Gough, one of the bottlenecks in the current development of large-scale quantum computing may be the lack of our ability to simulate large scale quantum system, which is a NP-hard ...
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1answer
322 views

Barren plateaus in quantum neural network training landscapes

Here the authors argue that the efforts of creating a scalable quantum neural network using a set of parameterized gates are deemed to fail for a large number of qubits. This is due to the fact that, ...
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164 views

Devising “structured initial guesses” for random parametrized quantum circuits to avoid getting stuck in a flat plateau

The recent McClean et al. paper Barren plateaus in quantum neural network training landscapes shows that for a wide class of reasonable parameterized quantum circuits, the probability that the ...
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1answer
183 views

Is there any general statement about what kinds of problems can be approximated more efficiently using a quantum computer?

As the name already suggests, this question is a follow-up of this other. I was delighted with the quality of the answers, but I felt it would be immensely interesting if insights regarding ...
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1answer
1k views

What is the difference between QAOA and Quantum Annealing?

Edward Farhi's paper on the Quantum Approximate Optimization Algorithm introduces a way for gate model quantum computers to solve combinatorial optimization algorithms. However, D-Wave style quantum ...