IonQ has published a new paper in a peer-reviewed journal describing a new technique that uses a hybrid classical/quantum computing approach to improve the accuracy of quantum circuits without increasing circuit depth or computational cost for quantum chemistry problems.
IonQ’s trapped-ion quantum computers were used, together with an efficient variational quantum eigensolver (VQE) algorithm, to simulate molecular bond dissociations. The VQE algorithm used had low circuit depth and a constant measurement overhead, which makes it suitable to run on near-term quantum devices. By using orbital optimization, we fully leveraged the capabilities of hybrid quantum-classical computing to improve prediction accuracy. It was observed that the predicted relative energies on quantum computers are in excellent agreement with the predictions of noiseless quantum simulators.
In short, we have developed a very efficient VQE algorithm that takes advantage of hybrid quantum-classical computation and can be run on state-of-the-art trapped ion systems with promising results.
This technique is a significant step towards solving real-world chemistry problems via quantum computers; one of the most promising potential real-world applications currently being explored is building computational models of the reactions in lithium batteries.
Running quantum circuits more efficiently
You have two considerations when building a quantum circuit to simulate chemical reactions. You can make it deep, and it will make accurate predictions but won’t be very efficient, or, you can make it shallow (efficient) but at the cost of accuracy. This need to strike a balance between circuit depth and accuracy is currently one of the largest limiting factors in the ability of quantum computers to solve meaningful quantum chemistry problems.
To decrease the impact of this tradeoff, we used a VQE ansatz called the unitary pair coupled cluster doubles (uPCCD). Instead of directly mapping individual electrons to qubits, we map electron pairs to qubits. Crucially, we can entangle pairs of qubits arbitrarily, meaning we did not limit entanglement to the ‘nearest neighbor’ of any given qubit. These long-range entanglements can be done very efficiently on trapped-ion systems. This contrasts with superconducting systems, which would need to use more gates to accomplish the same effect.
Overall, uPCCD offers several advantages:
You immediately reduce the number of qubits required by a factor of two, compared with mapping electrons directly to qubits.
You get very efficient circuits. If you don’t do this kind of paired approximation you will end up with a circuit whose depth scales quartically in the number of qubits. To put this in perspective, every time you double the qubits, the circuit must perform 16x more operations. But if you do the pair approximation, the same circuit only scales quadratically – only 4x as many operations when you double the qubits.
The all-to-all connectivity of IonQ’s trapped ion systems allows highly efficient implementation, as all-to-all connectivity obviates the distinction between “nearest-neighbor” and “long-range” entanglement.
Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers as envisioned by Midjourney AI
Additional Optimizations
In addition to the uPCCD ansatz, we improved the results further with an additional pioneering technique called “orbital optimization”. In orbital optimization, the goal is to further improve the accuracy of VQE by incorporating additional data from the ansatz back into the solution, thereby tailoring the orbitals to the specific problem at hand. In our work, we show how the orbital optimization process can be performed classically using data obtained from the quantum computer, thereby eliminating the need for additional quantum overhead.
We do this by measuring certain properties of the circuit on the quantum computer, putting those measurements into a classical computation routine, and then feeding the results back into the quantum circuit. This significantly improves the accuracy of the algorithm, without increasing its circuit depth or the computational burden on the quantum system.
Overall Takeaway
When using this new technique on small molecule dissociations, we found that this optimization technique really improves accuracy—without increasing circuit depth. This means we have developed a more accurate method with the same quantum computational requirements.
Of particular interest to note is that the difference between this and the other ways of using hybrid quantum/classical computational resources is that with this technique, both the quantum and classical parts are significant contributors to the overall result—they are equal partners. While this won’t change the way people develop algorithms on quantum computers, it does show you need to take advantage of both quantum and classical hybrid computation to get the most performance out of a quantum computer.
Overall, this technique represents an important advance in quantum chemistry methodology in quantum computing. Ultimately it paves the way for increases in speed and accuracy–allowing us to run deeper quantum circuits with fewer errors and zero additional computational costs.