IBM doubles the size of quantum simulations
In recently published research, an IBM team has demonstrated "entanglement forging", a technique that can simulate the ground state energy of water molecules very accurately, successfully representing 10 spin orbitals on five quantum bits of a 27-qubit Falcon quantum processor.
IBM has made great strides in using quantum hardware to simulate complex physical systems, with powerful new tools and notable achievements in quantum simulation almost every year. But despite these advances, today's quantum computers are still too small and too noisy to show the full quantum benefits.
IBM is always looking for a new way to advance quantum simulation technology, but its goal is not to enhance the hardware itself. They are developing new techniques that combine quantum and classical computing resources to solve simulation problems that are too difficult for today's noisy quantum hardware. The results of these efforts are an important step in the pursuit of quantum superiority.
This is not the first time that researchers have considered integrating classical computing resources in quantum simulations. In fact, classical computing power is a widely used technique in many of today's quantum simulations, including variable quantum instanton solvers (VQE) methods and error mitigation methods. a new IBM paper published in PRX Quantum on 14 January [1] introduces a new approach to a quantum simulation called "entanglement forging A new method of a quantum simulation called "entanglement forging" enables researchers to simulate a given quantum system on a quantum computer using only half of the quantum bits.
In their paper, the IBM team created a very accurate simulation of the ground state energy of a water molecule by using entanglement forging, successfully representing 10 spin orbitals on five quantum bits of IBM's 27-qubit Falcon quantum processor. Given its scalability and wide application to a variety of problem structures, the method can significantly extend the computational power of quantum systems, especially when combined with new programming models such as IBM's Quantum Serverless programming model - a new programming model that exploits both quantum and classical resources.
In general, if researchers want to simulate the 10 spin orbitals of a water molecule, they need to use a quantum computer with at least 10 quantum bits to do so. This is because most quantum simulation techniques require one quantum bit for each relevant "feature" of the system they are simulating.
With entanglement forging, IBM was able to effectively split the problem in two. This means that the researchers divided the 10 spin orbitals into two groups of five and then treated each group with just five quantum bits.
Andrew Eddins, an IBM Quantum researcher and first author of the latest paper, said: "We have shown a way that in many cases allows you to run larger problems on a quantum processor than would normally be possible. entanglement forging provides an efficient way to use classical computing resources for quantum problems, which can, in a way, double your power. It effectively triples the number of quantum bits you have, which is pretty significant."
Using problem structure to improve quantum computing
According to Sarah Sheldon, an IBM Quantum researcher and co-author of the paper, entanglement forging is an important addition to IBM's "circuit braiding" quantum computing technology. Sheldon says, "entanglement forging is a particularly scalable approach, at least for problems with such structures that are weakly entangled." In fact, the structure of the system or problem plays a crucial role in implementing the entanglement forging technique, which essentially works by splitting the system into two weakly entangled parts, modeling each part separately on a quantum computer, and then using classical resources to calculate the degree of entanglement between them.
Here, the term "weakly entangled" simply means that there is relatively little correlation between the two halves of the original system. This makes entanglement forging a natural fit for the task of modeling molecular systems in the presence of finite entanglement between spin-up and spin-down orbits.
According to Eddins and Sheldon, the uses of entanglement forging may extend far beyond chemical simulations. "It's not at all limited to the chemical setting we're looking at in this paper - the VQE problem, molecular Hamiltonian quantities, etc."
"There may be other systems - for example, spatial partitioning in a lattice model - where there is a natural partition that you can use to easily split the system into two weakly entangled parts. You can also apply entanglement forging to non-weakly entangled systems. At this point, we just need to do more calculations on a classical computer, and therefore need to determine how best to partition the system, or represent the correlation between the two parts."
How does "entanglement forging" works?
In order to understand why entanglement forging might have a beneficial effect in quantum simulations, it is necessary to take a step-by-step approach to understand how it works.
First, suppose we want to simulate a quantum state called ψ (in this case the state of a molecular system, such as water H2O), prepare the state on a quantum computer, and then make measurements to understand some of the properties of the state - that is, to measure the observable of the state, such as its energy. Splitting this state into two natural parts, they may have some entanglement.
As shown in the diagram below, for the molecular system of H2O (or other weakly entangled molecules) we split the system into two parts, corresponding to the spin-up and spin-down parts of the molecule. We, therefore, use arrows pointing in the appropriate direction to mark these two parts.
For the H2O molecular system (or other weakly entangled molecules), the two parts will correspond to the spin-up and spin-down parts of the molecule - marked using arrows pointing in the appropriate direction.
Entanglement forging takes a generic circuit that operates on a combined system of spin-up and spin-down parts and splits it into smaller circuits that run only half at a time. In other words, the entanglement forging technique takes a circuit that runs on 2N quantum bits and splits that circuit in half, i.e. N quantum bits.
The researchers then combine the results of these circuits into a sum weighted by a series of values that determine the entanglement structure of the original system, i.e. the correlation between the two parts.
This is where classical computing resources come into play. The classical computer represents the entanglement structure between the two parts by keeping track of the list of values mentioned earlier, and these values then determine the smaller experiments that the quantum computer must run to understand the properties of the entire state.
Weak entanglement leads to lower costs
Entanglement forging may greatly ease the burden on quantum computers when researchers represent entanglement between two parts of a given system, but it still has its own set of potentially huge computational costs, especially on the classical side. Classical computers must maintain a list of values representing the entanglement structure, and that list can be very large. The classical computer uses this list to tell the quantum computer which states it needs to prepare and measure in order to calculate the sum. The sum gives the total energy of the system.
Furthermore, the number of these measurements that must be made can have a large overhead cost. If the entanglement is weak, however, the sum will be almost equal to the first few terms and the remaining terms will be relatively small, thus reducing these overhead costs considerably.
To demonstrate their technique, the researchers ran a unique experimental version of a conventional VQE that simulated a 10-spin orbital model of a water molecule using only five quantum bits. Normally, 10 quantum bits are required to simulate spin-up and spin-down electrons in each orbital, but with the entanglement forging technique, the researchers were able to simply run the two halves of the molecular system separately.
Repeating the experiment for a range of molecular geometries, the study shows that entanglement forging produces highly accurate results on the order of 1-10 millihartree.
Ultimately, using only five quantum bits, the researchers were able to calculate the energy of the full 10-bit quantum system. Repeating the experiment for a range of molecular geometries, as shown above, the study showed that the technique produced highly accurate results on the order of 1-10 millihartree in the near-equilibrium region of primary interest.
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