Quantum Computing¶
MQS related projects¶
At MQS we are researching various aspects of quantum computing and will update this section as soon as we have integrated our quantum computing methods with the MQS API and SDK.
See the following MQS research papers for more information:
A joint optimization approach of parameterized quantum circuits with a tensor network
And here the current research projects MQS is taking part in or has completed:
PhotoQ Photonic quantum computing project involving measurement-based quantum computing and Gaussian boson sampling (GBS).
DLR Quantum Computing Initiative - QuantiCoM Project Advanced water simulations with classical and quantum computing.
Q-Chemion end to end quantum computing calculation pipeline with QEDMA, Oxford Ionics, Copenhagen University and the Technical University of Denmark (DTU).
MQS x Fraunhofer SCAI Benchmarking Framework In collaboration with Fraunhofer MQS has developed a quantum computing algorithms benchmarking framework to assess methods related to quantum computing enhanced quantum chemistry calculations.
In the following we are going to present all the different methods we are supporting in the Cebule SDK and are being released based on testing and validation results.
Mapping and measurement of electronic structure problems via gate-based quantum circuits¶
The MQS mapping method is a customized mapping method which excludes electronic states which violate specific constraints of an electronic structure problem. These constraints are defined by the particle number, spin multiplicity and spatial symmetries of a given molecular structure.
With our Cebule SDK you can run for example a VQE calculation together with our mapping method in the following way:
The MQS mapping task can be run via the Cebule SDK in the following way:
and the the results from the mapping task can be connected to a vqe task in the following way:
Important is to acknowledge that the measurement method also has a suitable measurement method which has been proposed in our paper [@] can be separated from each other in individual tasks.
For including the measurement method in the vqe task the following arguments have to be applied:
and in this way if only the mapping method but not the measurement method is applied in a vqe routine:
and vice versa:
Efficient quantum computing with parameterized tensor networks as matrix product states (MPS) and operators (MPO)¶
Tensor networks have shown that they can be applied to encode quantum chemistry problems in a highly efficient way to apply calculation routines for various molecular properties.
The TN-VQE method depicted in our paper [@] was the starting point for us to develop a highly tensor network based approach to leverage classical computing to perform as much computational effort for a quantum chemistry calculation as possible to only make the most crucial calculation run on a QPU.
You can apply a matrix product state encoding of a molecule in the following way with the Cebule SDK:
When the MPS encoding has completed you can again, as shown with the mapping and measurement methods above, run a VQE routine:
This also allows to combine the mapping, measurement and MPS encoding for the VQE routine with the following SDK task:
Active space selection methods¶
Correlation optimized virtual orbitals (COVO)¶
Active Space Finder (ASF) by HQS¶
Zero-noise Extrapolation for Variational Quantum Algorithms¶
Variational Quantum Algorithms (VQAs) like the Variational Quantum Eigensolver (VQE) are specifically designed to run effectively on near-term quantum computers, which lack quantum error correction. Consequently, there’s substantial interest in determining whether these algorithms can provide practical computational advantages. In chemistry, accurately predicting molecular energies with classical methods (such as Density Functional Theory, Coupled Cluster, and Full Configuration Interaction) can be extremely computationally expensive. Quantum computing, with its natural ability to represent quantum entanglement and correlations between particles, has the potential to significantly accelerate these calculations. Thus, enhancing VQAs through error mitigation methods such as Zero-noise Extrapolation (ZNE) is relevant to areas such as pharmaceuticals, energy, and catalysis – which together have a global market size of trillions of dollars – for molecular and material design both in industry and academic research.
ZNE works by intentionally increasing noise in quantum circuits via redundant gates, measuring the expectation value of a circuit with respect to some operator at different noise levels, and then extrapolating with a curve fit to estimate the zero-noise result.
MQS has systematically benchmarked different ZNE configurations – combinations of noise factors, noise amplification methods, and extrapolation techniques – to identify which configurations yield the most accurate and reliable improvements to VQE, as well as which configurations lead to unrealistic energy estimates.
We ran a series of experiments to benchmark various ZNE configurations for VQE using Qiskit and classical simulation with the IBM Brisbane noise model. From the experiments run, the best-performing ZNE configurations for the analyzed VQE cases in terms of stability and accuracy involve a large number of noise scalars (such as 12 factors between 1 and 6.5), two-qubit gate folding, and quadratic extrapolation. The cubic and exponential extrapolation methods can be prone to producing unphysical energies. By mapping which options consistently converge toward the noiseless energy and which diverge, a recipe for reliable error mitigation in VQE is provided.
ZNE can help one progress towards chemical accuracy with VQAs as shown in our results from the best-performing configuration. Note that this experiment was not tuned for chemical accuracy, it simply demonstrates how ZNE can take one closer to that target.
