Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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.

269 questions
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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 are its defining features that distinguish it…
Malcolm Regan
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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 a set of probabilities corresponding to states…
C-Roux
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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 papers and review articles (such as this one…
Nikita Nemkov
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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 variational quantum algorithms is NP-Hard. Does it mean we cannot…
Chao-Hua Yu
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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 assume we have a circuit that prepares $O$. How many times one has…
Nikita Nemkov
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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. EfficientSU2 of Qiskit, and I saw many of them use…
user14092875
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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 being diagonal in computational basis and the…
karolyzz
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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 $H_i$ can be decomposed into Paulis? The first…
C. Kang
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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 method. To be able to do this, we first need to write…
KAJ226
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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 state of a Hamiltonian. I'm interested in…
johndont
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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. $$ | \psi_{\rm{UCC}} \rangle = U(\theta)|\mathrm{HF}\rangle $$ Here, $U(\theta) = \exp[ T(\theta) -…
Ashy
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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 layers simply act on the phases and therefore seem…
dncolomer
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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 surprisingly high qubit numbers on my laptop, so I wanted…
Matthias
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How is the ground state of a Hamiltonian defined?

I'm studying VQE, but there is something I don't get. We know (I think) that for a given Hamiltonian the minimum eigenvalue is associated with the ground state. But if we take the Hamiltonian to be Pauli Z, then it has two eigenvalues: 1 associated…
Sorin Bolos
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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 Instance. But this doesn't seem to work. Here is the…
Tom
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