Skip to main content
Share Your Experience: Take the 2024 Developer Survey
9 votes
Accepted

Number of Qubits Required for Simulation of Caffeine and Penicillin Molecules

I'm not sure if the 286 qubit estimate has ever been fully explained, but we can backwards reason about how to get to the figure. First off, accuracy of quantum chemistry simulations via ...
C. Kang's user avatar
  • 1,726
9 votes
Accepted

Roughly speaking, How many qubits will be needed to study (or simulate) a molecule such as: C29H31N7O?

My quick answer: something between 4 and 4000. ^_^ The number of qubits in an electronic structure calculation depends on at least three things: Your basis set. Your qubit mapping. Your algorithm. ...
jecado's user avatar
  • 1,186
8 votes
Accepted

If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?

Hint: Instead of using the BCH formula in the form usually presented, for example at the top of this Wikipedia page, use this consequence of Hadamard's Lemma: $$\tag{1} e^{iHt}\hat{a}e^{-iHt} = \hat{a}...
user1271772 No more free time's user avatar
6 votes

Developing quantum circuits for specific quantum chemistry configurations

Since Google is one of, if not the, industry leaders in molecular simulation with quantum computers, their published work is a reasonable benchmark for what's presently within reach. As you probably ...
Jonathan Trousdale's user avatar
6 votes
Accepted

Quantum chemistry: references

Have you read Towards quantum chemistry on a quantum computer (Nature Chemistry 2010, or here in the arXiv version)? They present "a photonic implementation for the smallest problem: obtaining the ...
agaitaarino's user avatar
  • 3,827
6 votes

If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?

Use the differential form of the time evolution, $$dO/dt=i[H, O]\ .$$
Norbert Schuch's user avatar
5 votes
Accepted

Why does joint ground state not change under action of beam splitting unitary operator?

Calculate $$ \begin{align} \hat{U}|00\rangle &= \exp\left(-igt(\hat{a}^\dagger_2\hat{a}_1+\hat{a}^\dagger_1\hat{a}_2)\right)|00\rangle \\ &= \sum_{k=0}^\infty \frac{(-igt)^k}{k!}(\hat{a}^\...
Adam Zalcman's user avatar
  • 22.9k
5 votes

Defining qubit operator from scratch

The question refers to the VQE, so let's start with this and Max_Cut; they can be built on the VQE. There used to be a vqe.ipynp but I can't find, look for an example. The VQE algorithm doesn't need ...
Bram's user avatar
  • 654
5 votes
Accepted

Do we know anything about the computational complexity of the exchange-correlation functional?

Computing the exchange-correlation functional to sufficiently high accuracy is QMA-hard, where QMA is the quantum version of NP. In particular, this means that in all likelihood, it will be hard even ...
Norbert Schuch's user avatar
5 votes
Accepted

What are some current applications of Quantum Computing in drug discovery? Are there any test examples of this?

There are several startups that have formed around QC-assisted drug discovery. The ones listed below have resources on their websites that you might find helpful. ProteinQure Qulab HQS Kuano For a ...
Jonathan Trousdale's user avatar
5 votes
Accepted

Molecular orbitals in Qiskit

The ActiveSpaceTransformer provided by Qiskit Nature allows you to specify a list of molecular orbital indices via its ...
mrossinek's user avatar
  • 346
4 votes
Accepted

No. of bits in 160 qubits computer

If you have $n$ bits you can combine them in $2^n$ different bit string (this come from combinatorics). Now take $n$ qubits. As any qubit can in superposition of two state, i.e. 0 and 1, $n$ qubits ...
Martin Vesely's user avatar
4 votes

Why does joint ground state not change under action of beam splitting unitary operator?

There's more than one way, and I'll suggest two of them here: Expand $\hat{U}$ using the formula for the Taylor series of an exponential ($e^\hat{A}$) centered around $\hat{A}=\hat{0}$, and then you ...
user1271772 No more free time's user avatar
4 votes
Accepted

Why does Parity mapping allow 2 qubit reduction?

There is a relatively intuitive way to understand 2-qubit reduction using the parity mapping. It uses that the number of $\alpha$ (spin up) and $\beta$ (spin down) electrons are conserved (because the ...
cheetah's user avatar
  • 433
3 votes
Accepted

How is the Hartree accuracy calculated between the exact and VQE results?

I think you may have misread the section - the document says: When noise mitigation is enabled, even though the result does not fall within chemical accuracy (defined as being within 0.0016 Hartree ...
C. Kang's user avatar
  • 1,726
3 votes
Accepted

Fermionic occupation operator and nearest neighbor Fermionic hopping interaction as a qubit operator

The oldest and most commonly known way is the Jordan-Wigner transformation. The qubit operators will be $\mathcal{O}(N)$-local for $N$ occupiable orbitals. A significantly more complicated way is the ...
user1271772 No more free time's user avatar
3 votes
Accepted

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

Let's start with some problems Two big problems we're interested in for drug discovery where quantum computers may do well are high accuracy prediction of receptor-ligand binding affinities and ...
Greenstick's user avatar
  • 1,086
3 votes

From general Hamiltonian to Ising Hamiltonian

One way to do it would be to use a transformation, such as this one: \begin{align} X_i &= \frac{1 - Z_{i,j}Z_{i,k}}{2}\textrm{sgn}(j)\textrm{sgn}(k)\tag{1}\\ Y_i &= \textrm{i}\frac{Z_{i,k}-Z_{...
user1271772 No more free time's user avatar
3 votes

Jordan-Wigner map for ionic molecule H_2^+

This error is telling you, that the construction of the molecule within PySCF (the classical computing backend used to perform the initial HF calculation) is failing. The reason for this, is that by ...
mrossinek's user avatar
  • 346
3 votes

Efficiently compute $\langle 0^{\otimes n} | e^{iA} H e^{-iB} |0^{\otimes n} \rangle$ in Qiskit

You can use swap test to calculate $\langle 0^{\otimes n} | e^{iA} P_j e^{-iB} |0^{\otimes n} \rangle$ for each term $P_j$ in Pauli decomposition of $H$, then do the weighted sum classically:
Egretta.Thula's user avatar
2 votes

Quantum Chemistry and Quantum Computing

You may be referring to works like Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator (arXiv version). However, I'd say that in general the prediction of reaction ...
agaitaarino's user avatar
  • 3,827
2 votes
Accepted

What set of quantum logical operations can one use to benchmark spin Hamiltonians?

The answer arguably depends on the problem you wish to solve with your computation. More specifically, are you wanting to optimize near-term applications in the NISQ era, or are you wanting to build a ...
James Wootton's user avatar
2 votes
Accepted

Primer for learning about quantum circuits simulating systems

Here's a fairly thorough overview: https://arxiv.org/abs/1308.6253 For completeness I'll include the paper from the comment: https://arxiv.org/abs/quant-ph/0108146
bRost03's user avatar
  • 579
2 votes

Why does joint ground state not change under action of beam splitting unitary operator?

Let $|\psi\rangle$ be an eigenstate of an operator $A$, $A|\psi\rangle=\lambda|\psi\rangle$. Then $$e^A |\psi\rangle = \sum_{k=0}^\infty \frac{A^k}{k!}|\psi\rangle = \sum_{k=0}^\infty \frac{\lambda^k}{...
glS's user avatar
  • 25.3k
2 votes

If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?

Note that $$[(a^\dagger)^n,a] = -n(a^{\dagger})^{n-1}, \qquad [(a^\dagger)^n a^m,a] = -n (a^\dagger)^{n-1}a^m, \qquad [a^n,a]=0.$$ Consider an arbitrary function of the mode operators, that we assume ...
glS's user avatar
  • 25.3k
2 votes

Fermionic occupation operator and nearest neighbor Fermionic hopping interaction as a qubit operator

Use the Jordan-Wigner transformation. For a 1D chain with NN interaction it will yield a spin Hamiltonian with NN interaction (specifically, the hopping will map to a XX term and the on-site term to a ...
Norbert Schuch's user avatar
2 votes
Accepted

Fermionic commutation relation using Jordan-Wigner transformation

Based on my answer to this: Fermionic occupation operator and nearest neighbor Fermionic hopping interaction as a qubit operator, you can see that we have: \begin{align} \hat{a}_i &= \frac{1}{2} ...
user1271772 No more free time's user avatar
2 votes
Accepted

Getting the current variational parameters in Qiskit

What I would do here is get back the raw results of your res, and there are stocked the parameters of the Ansatz you are looking for : ...
Lena's user avatar
  • 2,597
2 votes

How to calculate the Hartree-Fock energy in Qiskit?

As you are asking specifically for the evaluation of the energy only, I will be brief. I will assume that you have a init_state (a quantum circuit) that produces ...
Mauricio's user avatar
  • 2,326

Only top scored, non community-wiki answers of a minimum length are eligible