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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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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17 votes
1 answer
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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
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
6 votes
1 answer
1k views

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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5 votes
1 answer
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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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2 votes
2 answers
582 views

VQE Cirq example

Is my understanding correct that in this example the Hamiltonian measurement is not performed through measuring individual Pauli operators because all its terms are mutually commuting? So, for each ...
mavzolej's user avatar
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2 votes
1 answer
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In Variational Quantum Eigensolvers, what does "grouping Pauli operators into tensor products requiring the same post-rotations" mean?

In this paper (nature version), the authors state We group the Pauli operators into tensor product basis sets that require the same post-rotations. As a result, they have the table S2 in the suppl. ...
fagd's user avatar
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2 votes
1 answer
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VQE restart from a previous computation

I'm running VQE algorithm on ibmq-qasm-simulator. I'm trying to implement a restart mechanism in order to be able to start a new computation from the result of a ...
Valentina'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
1 answer
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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
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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1 answer
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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
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
3 votes
2 answers
828 views

How to express real matrices as linear combinations of unitaries?

I am working on using Variational Quantum Linear Solver (VQLS) for some tasks. Here, we need to represent matrix A as a linear combination of unitaries. $$ {\bf A} = \Sigma^n_{i=1} c_iA_i $$ My ...
Sajal's user avatar
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3 votes
2 answers
562 views

How to run VQE experiments on IBMQ Backends?

The VQE.run method only takes a quantum_instance of type QuantumInstance or BaseBackend and ...
MShakeG's user avatar
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2 votes
1 answer
137 views

How does this expression from the VQLS paper result in a CZ-gate?

I am reading the VQLS paper and equation C2 on page 10 they have: $ \delta_{ll'}^j = \beta_{ll'} + \langle0|V^\dagger A_{l'}^\dagger U(Z_j \otimes I_\bar{j}) U^\dagger A_lV|0\rangle $ Here they define ...
thespaceman's user avatar
2 votes
1 answer
504 views

How grouping of Pauli strings is handled in Qiskit when running VQE?

When performing a VQE algorithm, the electronic problem Hamiltonian of the physical system under study needs to be mapped to a qubit Hamiltonian written as a sum of tensor products of Pauli operators (...
Radu M.'s user avatar
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1 vote
1 answer
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An effective way to submit all the jobs for VQE/QAOA at a time to an IBMQ machine?

In Qiskit, I am solving a VRP for 5 nodes and it creates 20 variables for a QUBO. It runs in a 65 qubit machines (any machine below that many fails). Now, in such a typical solvers for optimization (...
Amitava Chakraborty's user avatar
1 vote
1 answer
220 views

Why is local qasm simulation taking so long for VQE?

I've successfully run the $LiH$ VQE simulation detailed in Simulating Molecules using VQE using the statevector_simulator, however when attempting to run the same ...
MShakeG's user avatar
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1 vote
1 answer
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Qiskit statevector_simulator returns different results

I'm running VQE algorithm from qiskit aqua on statevector_simulator and each time I run it I get different results which are sometimes correct and sometimes not. I'...
user10234's user avatar
0 votes
2 answers
665 views

Suppress deprecation warnings from Qiskit

I am running a standard VQE from the example shown in here https://qiskit.org/textbook/ch-applications/vqe-molecules.html, however I keep getting this output constantly (as many times the vqe runs ...
Akashkumar Patel's user avatar