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.
...
- 1,086
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:
$$\tag{1}
e^{iHt}\hat{a}e^{-iHt} = \hat{a}...
- 13.5k
7
votes
Accepted
Number of Qubits Required for Simulation of Caffeine and Penicillin Molecules
I'm not sure if the 286 qubit estimate has ever been fully explained, but we can backwards reason about how to get to the figure.
First off, accuracy of quantum chemistry simulations via ...
- 1,684
6
votes
Developing quantum circuits for specific quantum chemistry configurations
Since Google is one of, if not the, industry leaders in molecular simulation with quantum computers, their published work is a reasonable benchmark for what's presently within reach. As you probably ...
- 3,352
6
votes
If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?
Use the differential form of the time evolution,
$$dO/dt=i[H, O]\ .$$
- 5,647
5
votes
Accepted
Why does joint ground state not change under action of beam splitting unitary operator?
Calculate
$$
\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}^\...
- 20.8k
5
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 ...
- 3,777
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 ...
- 544
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 ...
- 3,352
4
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 ...
- 5,647
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 ...
- 13.6k
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 ...
- 13.5k
4
votes
Molecular orbitals in Qiskit
The ActiveSpaceTransformer provided by Qiskit Nature allows you to specify a list of molecular orbital indices via its ...
- 321
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 ...
- 1,684
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 ...
- 13.5k
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 ...
- 1,046
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_{...
- 13.5k
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 ...
- 321
3
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 ...
- 413
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:
- 9,097
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
- 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
$$e^A |\psi\rangle = \sum_{k=0}^\infty \frac{A^k}{k!}|\psi\rangle = \sum_{k=0}^\infty \frac{\lambda^k}{...
glS♦
- 23.4k
2
votes
If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?
Note that
$$[(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♦
- 23.4k
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 ...
- 11.2k
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 ...
- 5,647
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} ...
- 13.5k
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 :
...
- 2,552
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 ...
- 2,202
2
votes
Logical vs Physical Qubits for Quantum Chemistry DFT
The number of physical qubits needed for each logical qubit, depends on the error rate. For example, Table II in this paper shows that the number of physical qubits per logical qubit for various ...
- 13.5k
Only top scored, non community-wiki answers of a minimum length are eligible