Questions tagged [vqe]

For questions about the Variational Quantum Eigensolver, a quantum/classical hybrid algorithm that can be used to find eigenvalues of a (often large) matrix H. When this algorithm is used in quantum simulations, H is typically the Hamiltonian of some system. In this hybrid algorithm, a quantum subroutine is run inside of a classical optimization loop.

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Is VQE a class of algorithms or a specific algorithm?

Is VQE a class of algorithms or a specific algorithm? For example, is QAOA a VQE or is VQE an algorithm distinct from QAOA that solves the same class of problems? If VQE is a specific algorithm, what ...
Malcolm Regan's user avatar
14 votes
3 answers
6k views

How to calculate an Expected Value of some operator acting on qubits?

I'm trying to implement the Variational Quantum Eigensolver in Qiskit. Suppose, I have an operator $A = \sigma_1^z\sigma_2^z$ acting on some two-qubit state $|\psi\rangle$. After a measurement I get ...
C-Roux's user avatar
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14 votes
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Why exactly are variational algorithms considered promising?

There is obviously a great deal of work happening at the moment on variational quantum algorithms. However, I'm struggling to understand why exactly are they considered promising? Looking through some ...
Nikita Nemkov's user avatar
12 votes
1 answer
426 views

What does the paper "Training Variational Quantum Algorithms Is NP-Hard (Phys. Rev. Lett. 127, 120502)" mean?

I have seen the recent paper "Training Variational Quantum Algorithms Is NP-Hard (Phys. Rev. Lett. 127, 120502)" and the authors stated that training the classical optimization in ...
Chao-Hua Yu's user avatar
11 votes
1 answer
848 views

What is the complexity of estimating the expectation value of an observable?

The average value of an operator $O$ in the state $\left.|\psi\right>$ is $$\overline{O}=\left<\psi|O|\psi\right>$$ Now for simplicity let $\left.|\psi\right>=\left.|0\right>^n$ and ...
Nikita Nemkov's user avatar
9 votes
2 answers
568 views

Decomposing Hamiltonian into qubit model representation

One of the main applications of VQE is its application to find the approximation to the ground state energy (smallest eigenvalue of the Hamiltonian) for a particular molecule through an iterative ...
KAJ226's user avatar
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9 votes
1 answer
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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 ...
karolyzz's user avatar
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8 votes
1 answer
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List of problems that can be reduced to finding the ground state of a Hamiltonian

I'm doing some reading into Variational Quantum Eigensolvers (VQEs), Quantum Approximate Optimization Algorithms (QAOAs), and other similar algorithms. I know that the point is to find the ground ...
johndont's user avatar
8 votes
1 answer
1k views

Circuit for VQE Expectation Value Finding

I'm looking into the circuit for the VQE, but am stumped at how we can identify the expectation value of the Pauli series. Essentially, how do we find: $$ \langle \psi | H_i | \psi \rangle $$ Given $...
C. Kang's user avatar
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8 votes
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Is there a mistake in the VQE Ansatz in Cirq's tutorial?

I have been going through Cirq's VQE background tutorial and after examining the Ansatz it seems to me that the only layer that actually affects the final measurement is the rot_x_layer. The other ...
dncolomer's user avatar
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1 answer
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Intuition behind the construction of an ansatz circuit

I'm learning about the VQE algorithm. When I looked at the declaration in Qiskit I saw you need to pass an ansatz which prepares the state. I looked at some commonly used ansatz functions, e.g. ...
user14092875's user avatar
7 votes
1 answer
521 views

What's the point of VQE if classical computers can solve for eigenvalues easily?

From a few VQE tutorials online I see that they normally start with something like: VQE is a way of getting a good estimate for the upper bound of the ground state of a quantum system's Hamiltonian....
Alexander Soare's user avatar
7 votes
1 answer
512 views

Why am I able to simulate such high qubit numbers on my laptop?

Recently I've been working on a VQE-related project, for which I'm using Qiskit's TwoLocal variational form (qiskit version 0.34.2). I noticed that I was able to simulate this circuit up to ...
Matthias's user avatar
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1 answer
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How to prepare Unitary Coupled Cluster ansatz for VQE in a circuit?

I have read the following paper by Dumitrescu et al. To make a Unitary Coupled Cluster (UCC) ansatz, one prepares with the following equation. $$ | \psi_{\rm{UCC}} \rangle = U(\theta)|\mathrm{HF}\...
Ashy's user avatar
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7 votes
2 answers
184 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 ...
Martin Vesely's user avatar
7 votes
1 answer
807 views

How can I run a VQE on one of IBMQ's Quantum Computers

I have implemented a VQE based on Qiskit's VQE function and want to run that on an actual quantum computer. My understanding was, that an IBMQ backend can be passed into the function as a Quantum ...
Tom's user avatar
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0 answers
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Run VQE for parametrized quantum circuit with ancilla qubits

Let's say we have the following circuit (picture and code shown below), and now the $q_0$ is an ancilla qubit. If the system of interest has only two qubits, Is there a way to use only $q_{1,2}$ as my ...
fagd's user avatar
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6 votes
1 answer
2k views

How to show mathematically the equivalency between Ising Model and QUBO?

It is said that the Ising Model using spin variables $s ∈ \{−1, 1\}$ $$H(s)=\sum_{i}h_is_i+\sum_{i<j}J_{ij}s_is_j,$$ and a Quadratic Unconstrained Binary Optimization (QUBO) problem with binary ...
26118in's user avatar
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1 answer
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VQE - How to get from expectation value to eigenvalue?

In VQE, for a single-qubit Hamiltonian, I can use a standard ansatz to make a state $\psi$ and use two products to compute the expectation value $\langle\psi|{\cal H}|\psi\rangle$. As I vary the ...
rhundt's user avatar
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How to add several parameters in qiskit circuit?

I want to construct an ansatz circuit in Qiskit, so I need some parameters to act on the gates (e.g. RX(a), RY(b)). In the Qiskit tutorials I find a way to implement a parameter: ...
wu Peter's user avatar
6 votes
1 answer
305 views

What is the physical unit of the energy calculated using VQE on Qiskit?

Suppose there is any arbitrary ansatz producing variational energy for any arbitrary Hamiltonian. What is the physical unit corresponding to the energy? Since numerical algorithms only output a ...
quantum's user avatar
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6 votes
1 answer
366 views

Use one_body_integrals to know which orbitals to freeze in ElectronicStructureProblem

In exercise 5 of the this year's IBM Quantum Challenge, you need to use the FreezeCoreTransformer (along two_qubit_reduction and ...
epelaez's user avatar
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5 votes
2 answers
174 views

Why is it hard to prove complexity bounds for variational algorithms?

I'm not very familiar with variational algorithms, but I've heard people say that they're "heuristic" and it's difficult to measure their performance via complexity analysis. Why is this the ...
confusion's user avatar
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5 votes
2 answers
461 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 ...
MonteNero's user avatar
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5 votes
1 answer
242 views

Is VQE or one of its variations enough to help with medicine development?

One of the reasons quantum computing is often hyped in media is because of how it'll help with vaccine and medicine development. For example, this article in Financial Express and this other in ...
epelaez's user avatar
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5 votes
1 answer
962 views

How does the performance of QAOA and VQE compare to Grover's?

I believe finding the optimal solution is guaranteed for Grover's Algorithm along with quadratic speed-up according to Nielsen and Chuang's book. I wonder if there is any statement regarding QAOA and ...
John Parker's user avatar
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5 votes
1 answer
120 views

gradient estimations on variational quantum algorithms

Other than the two famous parameter-shift rule and finite difference method, is there any other (perhaps simple) methods to estimate gradients of a cost function in variational quantum algorithms?
Jon Megan's user avatar
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1 answer
951 views

What are the main differences between the "unitary coupled cluster" and the "hardware efficient" ansatzes in VQE?

There are two popular initial states, in general, for VQEs: the unitary coupled cluster ansatz and the hardware efficient ansatz (for details, see here: https://quantaggle.com/algorithms/ansatz/). ...
BlackHat18's user avatar
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5 votes
1 answer
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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 ...
Soumik Adhikary's user avatar
5 votes
1 answer
328 views

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 ...
consthatza's user avatar
5 votes
1 answer
653 views

Simulation of a helium molecule using Qiskit

I am trying to compute the ground state energy of He-He using VQE. For this purpose I have utilized Qiskit and have written the following script: ...
user14660's user avatar
4 votes
2 answers
218 views

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 \...
Jon Megan's user avatar
  • 497
4 votes
3 answers
326 views

Generally, could VQE be used to prepare the highest energy state?

When I learned about the variational method in quantum mechanics and the variational quantum eigensolver (VQE), I was told that this method is used to prepare the ground state of a quantum system. I ...
ZR-'s user avatar
  • 2,388
4 votes
3 answers
2k views

Creating a parameterized Operator in Qiskit

I'm trying to run a VQE for a specific custom Anzats. The Anzats is built up of an unitary matrix $U_H$, which I'm trying to created in this way: ...
Paco Bontenbal's user avatar
4 votes
1 answer
568 views

Ansatz explanation for VQE

I have found quite a bit of information on the UCC ansatz, but I cannot really find basic explanations for the Ry and RyRz ansatzs... Are they just applying these gates to a circuit? If anyone has ...
bbbb's user avatar
  • 265
4 votes
1 answer
319 views

What is the expectation value for the ground state of $ H = \sum_i Z_i Z_{i+1} + \sum_i X_i $?

What is the expectation value for the ground state of $ H = \sum_i Z_i Z_{i+1} + \sum_i X_i $ ? In Eq. 15b this provides a solution in k space. The minimum would be reached for $E = -4$. But for ...
user18722294's user avatar
4 votes
1 answer
147 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 ...
C-Roux's user avatar
  • 888
4 votes
2 answers
132 views

Is there a way I can create an ansatz such that the number of 1 is same in all the superposition states? [duplicate]

So I am working with a variational quantum algorithm and I realised that it would be very beneficial if I could create an ansatz where all the states in the superposition have same numbers of 1s. For ...
Cheshta Joshi's user avatar
4 votes
1 answer
736 views

What exactly makes VQE faster than classical optimization?

I have been trying to understand Variational Quantum Eigensolver (VQE), particularly from the non-linear binary programming perspective. But after reading a few resources I'm still confused about ...
user113988's user avatar
4 votes
1 answer
452 views

TypeError: 'NumPyMinimumEigensolver' object is not subscriptable

I'm trying to implement the same Jupyter notebook Jin-Sung Kim gave in his YouTube video The Variational Quantum Eigensolver — Programming on Quantum Computers — Coding with Qiskit S2E4; however, I'm ...
Bruno Ambrozio's user avatar
4 votes
1 answer
158 views

In which type of Hamiltonian does the ansatz need an entangler in VQE?

I would like to prepare an ansatz for VQE. I know UCC ansatz is one of the most useful ansatz, but I would like to reduce the number of CNOT. From the matrix of a given Hamiltonian, can we know the ...
Ashy's user avatar
  • 375
4 votes
1 answer
301 views

Variational Quantum Linear Solver (Hadamard test): circuit question

Trying to understand the circuit/algorithm for VQLS and I found this diagram to show the high-level idea of doing the Hadamard test in this tutorial. But I am not quite sure why we need the two ...
John Parker's user avatar
  • 1,091
4 votes
1 answer
344 views

Expected value in a VQE qiskit

I'm learning VQE(variational quantum eigensolver) of qiskit, but I have a question about how it measures the expected value of the energy ($\left \langle H \right \rangle$). I saw in other question ...
Nicolas Parra Avila's user avatar
4 votes
1 answer
132 views

Resource recommendation on quantum simulations

I would like to know more about quantum simulations, so as to start on a few standard physical models (maybe particle in a box, harmonic oscillator, etc.) and then build up on more complex things. But ...
Bidon's user avatar
  • 818
4 votes
2 answers
331 views

How do I identify a VQE job run in real hardware?

I am running a VQEUCCFactory for H2 on a real hardware device. ...
bjail66's user avatar
  • 155
4 votes
0 answers
118 views

Variational Quantum Eigensolver (VQE) by scipy minimize in cirq does not work

I tried to make a cirq program calculating an eigenvalue of the observable by VQE. Inspired by the qulacs VQE tutorial, I defined a cost function from the expectation value of the observable with ...
Weongyu Lee's user avatar
4 votes
0 answers
66 views

Ansatz for VQE demonstrating Quantum Advantage

What would be a possible ansatz quantum state in VQE (variational quantum eigensolver [1]) that would demonstrate the quantum advantage of VQE over classic computers? More specifically, I see that VQE ...
user20374's user avatar
4 votes
0 answers
67 views

Difference between Qiskit and Openfermion two body integrals

I am struggling with understanding the differences between OpenFermion and Qiskit libraries when it comes to Molecular Data, two body integrals. For example, I am working with the following ...
Eugen's user avatar
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4 votes
0 answers
78 views

How is this Variational Quantum Singular Value Decomposition paper efficient in any way?

Link to paper here. This algorithm seems neat but the unitary decomposition of the matrix M generally takes an exponential number of Pauli basis elements in the number of qubits $N$, therefore an ...
JoJo's user avatar
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4 votes
0 answers
118 views

How to optimise QAOA

I have a similarly naive question about the classical part of the optimisation in the Quantum Approximate Optimization Algorithm. Specifically, the cost function is given prescribed as \begin{align} ...
user39726's user avatar

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