Quantum Advantage computational capability in NISQ era; is it even possible?
Introduction:
To create this content, I spent plenty of time researching, sifting through many online documents (links included), and watching a few video clips ( the link is included). I am glad I spent the time learning about this new advancement because someday soon, I may be able to put it to work in solving ground state energy in quantum chemistry and material design projects.
Most ground energy state calculations are done on classical computer simulation systems, although I have noticed ion trapping systems such as IonQ working on similar projects. Currently, I am looking for some Python code to examine its structure. So, let's talk about this.
PS: My research on this topic will continue.
A new clever solution....
Researchers at Columbia university and Google Quantum AI center have been busy developing newly-minted computational algorithm that uses the most quantum bits to date to calculate Ground State Energy, the lowest-energy state in a quantum mechanical system. The discovery will help make it easier to design new materials - that's big news.
David Reichman and Joonho Lee of Columbia University propose a scalable, noise-resilient quantum-classical hybrid algorithm that seamlessly embeds a special-purpose quantum primitive into an accurate quantum computational many-body method, namely QMC. (Fermionic quantum Monte Carlo (QMC) methods).
The quantum many-body problem is one of the complex problems of complexity theory: A direct solution requires computational resources that grow exponentially with the size of the problem to be solved. We need new optimized and benchmarking sophisticated algorithms to make the many-body problem tractable and use the solutions to predict the behavior of materials and molecules of scientific and technological interest. While researching the work of David Reichman and Joonho Lee of Columbia University, I learned about the Simons foundation and CCQ products, related to this post, but I will do a post on it next describing the connection.
Let's break this work down to simple English and find out the details and at the end we can see the outcome for material science using a hybrid quantum and classical system. We need to have more hybrid systems for intractable financial and optimization problem solving tasks. In near future, perhaps this approach can be adapted to speed up calculations benefiting different industries. As we add more error-resilient qubits, this calculation method can be extremely useful.
- A novel use of quantum and classical computers solving chemistry problems - Pic: Credit to Columbia University. If you are solving chemistry and material science problems on quantum computers of today (the NISQ Era,) you have a new promising tool to reduce the statistical errors, or noise, produced by quantum bits, or qubits, in crunching chemistry equations.
Google's Quantum Chips
David and Joonho Lee, and Google Quantum AI teaming together, developed the algorithm that uses up to 16 Sycamore qubits (Google Quantum Computer has 53-qubit system last I checked), to calculate the ground State energy, the lowest energy state of molecule.
“These are the largest quantum chemistry calculations that have ever been done on a real quantum device,” David Reichman said. The ability to accurately calculate ground state energy, will enable chemists to develop new materials, said Joonho Lee, who is also a visiting researcher at Google Quantum AI. The algorithm could be used to design materials to speed up both nitrogen fixation for farming and hydrolysis for making clean energy, among other sustainability goals, he said.
The research team used a quantum Monte Carlo probabilities calculation algorithm to determine the ground state energy of three molecules: Heliocide (H4), using eight qubits for the calculation; Molecular Nitrogen (N2), using 12 qubits; and Solid Diamond, using 16 qubits.
The Monte Carlo algorithm uses a system of methods for calculating probabilities when there are a large number of random, unknown variables present - it is similar to a game of roulette. Variables such as the number of electrons in a molecule, the direction in which they spin, and the paths they take as they orbit a nucleus influence the ground state energy. Using the Schrodinger equation the electronic state then encoded. Usually, solving such an equation on a super computer (classical computers) is extremely challenging often impossible to solve, because as the molecules get bigger, the calculation of ground state become exponentially harder and at some point it becomes intractable. So using this new novel method we may have a new way to circumvent the exponential scaling problem.
We know that the Qubits, the computational mechanism of Quantum computer are fragile and error-prone: the more qubits used, the less accurate the final answer. Dr. Lee’s algorithm harnesses the combined power of classical and quantum computers to solve chemistry equations more efficiently while minimizing the quantum computer’s mistakes - that is very promising. "It’s the best of both worlds,” Dr. Lee said. “We leveraged tools that we already had as well as tools that are considered state-of-the-art in quantum information science to refine quantum computational chemistry.”
How does it work?
Here is the best I can understand. So, the system entails a classical computer working in concert with a quantum computer, a suitable classical computer that can handle most of Dr. Lee’s quantum Monte Carlo simulation. Sycamore (Google's 53 Qbit Quantum computer) plays a role at some point when , most computationally complex calculation occur. The overlap calculation between a trial wave function (a guess at the mathematical description of the ground state energy that can be implemented by the quantum computer) and a sample wave function (part of the Monte Carlo’s statistical process. ) sets the stage for the next step.
The overlap information then provides a set of constraints, known as the Boundary Condition, to the Monte Carlo sampling, which ensures the statistical efficiency of the calculation.
Wow! - So what do we gain?
It's interesting to know that the prior record for solving ground state energy used 12 qubits and a method called the variational quantum eigensolver, or VQE. But, worth mention that the VQE method ignored the effects of interacting electrons, an essential variable in calculating ground state energy that is included in the Dr. Lee’s quantum Monte Carlo algorithm.
Here is the best part:
Adding virtual correlation techniques from classic computers could help chemists tackle even larger molecules, Lee said.
👍So, we now have a new way to calculate the ground state energy much more accurately, thanks to quantum computing's current state of the art.
End Post
Additional reading and online video on the topic:
"It’s the best of both worlds,” said Joonho Lee. “We leveraged tools that we already had as well as tools that are considered state-of-the-art in quantum information science to refine quantum computational chemistry.” --------------------------
"The convergence to the self-consistency in the dynamical mean-field theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are used as the input to the impurity solver."
Unbiasing fermionic quantum Monte Carlo with a quantum computer
What is Ground state?
The ground state of an electron, the energy level it normally occupies, is the state of lowest energy for that electron. There is also a maximum energy that each electron can have and still be part of its atom.
You can calculate the ground state energy using The Bohr Model
Explanation:
A simple expression for the energy of an electron in the hydrogen atom is: E=−13.6n2 where the energy is in electron volts n is the principle quantum number.
This gives rise to the familiar electron energy level diagram where they converge and coalesce.
So for an electron in n=1:
E=−13.6eV
To convert to joules you can x this by 1.6×10 to the power of −19
For many - electron atoms quite complicated approximate methods can be used which take into account factors such as electron interactions and screening effects.
Ground State example:
Consider a carbon atom whose electron configuration is the following. The total energy of the electrons in this carbon atom can not be lowered by transferring one or more electrons to different orbitals. Therefore, this carbon atom is a ground-state atom.
NISQ Era:
Noisy intermediate-scale quantum era
In the noisy intermediate-scale quantum era the leading quantum processors contain about 50 to a few hundred qubits, but are not advanced enough to reach fault-tolerance nor large enough to profit sustainably from quantum supremacy. The term was coined by John Preskill in 2018.
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