Fault-tolerant Coded Quantum Chemical Distributed Calculation

Kai Yuan, Shuai Zhou, Ning Li +4 more

Easy and effective usage of computational resources is crucial for scientific calculations. Following our recent work of machine-learning (ML) assisted scheduling optimization [J. Comput. Chem. 2023, 44, 1174], we further propose (1) the improved ML models for the better predictions of computational loads, and as such, more elaborate load-balancing calculations can be expected; (2) the idea of coded computation, that is, the integration of gradient coding, in order to introduce fault tolerance during the distributed calculations; and (3) their applications together with re-normalized exciton model with time-dependent density functional theory (REM-TDDFT) for calculating the excited states. Illustrated benchmark calculations include P38 protein, and solvent model with one or several excitable centers. The results show that the improved ML-assisted coded calculations can further improve the load-balancing and cluster utilization, owing primarily profit in fault tolerance that aims at the automated quantum chemical calculations for both ground and excited states.

Ivan Kassal

Miroslav Urbánek, Benjamin Philip Nachman, Wibe Albert de Jong

A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that, even without achieving full fault tolerance, quantum error detection is already useful on the current generation of quantum hardware. We demonstrate this experimentally by executing an end-to-end chemical calculation for the hydrogen molecule encoded in the [[4, 2, 2]] quantum error-detecting code. The encoded calculation with logical qubits significantly improves the accuracy of the molecular ground-state energy.

Nitish Kumar Chandra, Eneet Kaur, Kaushik P. Seshadreesan

Fault tolerant quantum computation over distributed quantum computing (DQC) platforms requires careful evaluation of resource requirements and noise thresholds. As quantum hardware advances toward modular and networked architectures, various fault tolerant DQC schemes have been proposed, which can be broadly categorized into three architectural types. Type 1 architectures consist of small quantum nodes connected via Greenberger-Horne-Zeilinger (GHZ) states, enabling nonlocal stabilizer measurements. Type 2 architectures distribute a large error correcting code block across multiple modules, with most stabilizer measurements remaining local, except for a small subset at patch boundaries that are performed using nonlocal CNOT gates. Type 3 architectures assign code blocks to distinct modules and can perform fault tolerant operations such as transversal gates, lattice surgery, and teleportation to implement logical operations between code blocks. Using the planar surface code and toric code as representative examples, we analyze how the resource requirements, particularly the number of Bell pairs and the average number of generation attempts, scale with increasing code distance across different architectural designs. This analysis provides valuable insights for identifying architectures well suited to fault tolerant distributed quantum computation under near term hardware and resource constraints.

Mollie E. Schwartz, Danna Rosenberg, David K. Kim +6 more

Aparna Kanungo

Quantum error correcting codes have been introduced to encode the data bits\nin extra redundant bits in order to accommodate errors and correct them. However,\ndue to the delicate nature of the quantum states or faulty gate operations, there is\na possibility of catastrophic spread of errors which might render the error correction\ntechniques ineffective. Hence, in this thesis we concentrate on how various operations\ncan be carried out fault-tolerantly so that the errors are not propagated in the same\nblock. We prove universal fault-tolerance for nonbinary CSS codes. This thesis is\nfocussed only on nonbinary quantum codes and all the results pertain to nonbinary\ncodes.\nEfficient error detection and correction techniques using fault-tolerant techniques\ncan help as long as we ensure that the gate error probability is below a certain\nthreshold. The calculation of this threshold is therefore important to see if quantum\ncomputations are realizable or not, even with fault-tolerant operations. We derive an\nexpression to compute the gate error threshold for nonbinary quantum codes and test\nthis result for different classes of codes, to get codes with best threshold results.