Quantum Calculations Become 100 Times More Efficient with New Technique

A new algorithm, SQD-AA, computes the ground and excited states of complex Hamiltonians, a key step in modelling molecular behaviour and materials science. Nina Stockinger and colleagues at the Department of Physics, in collaboration with Max Planck Institute for the Science of Light, combine sample-based quantum diagonalization with amplitude amplification to overcome limitations in obtaining representative samples. The algorithm reduces query complexity by a factor exceeding 100 for specific model distributions and offers a quadratic advantage for exponentially decaying distributions. Evaluations on real molecules suggest SQD-AA requires fewer T-gates and shallower circuits than iterative quantum phase estimation, potentially enabling feasible computations in early fault-tolerant quantum computers where deeper circuits remain challenging.

Strategic quantum state detection dramatically reduces computational cost for molecular modelling

A factor exceeding 100 reduction in total query complexity was achieved for algebraically and exponentially decaying model distributions using the new SQD-AA algorithm. This breakthrough surpasses a vital threshold, enabling calculations previously impossible due to the exponential growth in resources needed for accurate molecular modelling. Traditionally, determining the ground state energy of a molecule requires solving the time-independent Schrödinger equation, a computationally intensive task that scales exponentially with the number of electrons and atomic nuclei. Methods like Hartree-Fock and Density Functional Theory offer approximations, but often lack the precision needed for complex systems. Quantum computing offers a potential solution, but even quantum algorithms face significant hurdles. Obtaining sufficient samples of rare but important quantum states previously demanded impractically large computational effort, a limitation circumvented by SQD-AA through deliberate manipulation of measured state probabilities. Sample-based quantum diagonalization (SQD) classically diagonalizes a Hamiltonian within a subspace defined by samples obtained from a quantum computer, but it inherently struggles when crucial basis states are sampled infrequently. This is because the accuracy of the diagonalization is directly tied to the completeness of the sampled basis. SQD-AA addresses this ‘sampling problem’ by employing amplitude amplification, a technique borrowed from Grover’s search algorithm, to selectively boost the probability of measuring these rare, yet significant, states. This amplification doesn’t change the underlying quantum state, but rather increases the likelihood of observing it during measurement, effectively enriching the sample set.

Circuits required for the SQD-AA algorithm are three to four orders of magnitude shallower than those needed for iterative quantum phase estimation (iQPE), representing a significant advantage for implementation on early fault-tolerant quantum computers. Real molecule analysis revealed the lowest total number of T-gates, a key metric for quantum computation, were achieved using SQD-AA, alongside a saving of two orders of magnitude in total runtime compared to standard SQD methods. This improvement stems from a reduction in the number of shots needed by up to a factor of 65, proving particularly beneficial for quantum computers utilising trapped-ion or neutral atom technologies where numerous measurements are time-intensive. The number of T-gates is critical because they are relatively slow and error-prone operations on many quantum computing platforms. Reducing the T-gate count directly translates to faster and more reliable computations. Furthermore, the reduction in ‘shots’, the number of times the quantum circuit must be run to obtain statistically meaningful results, is crucial. Each shot is susceptible to errors, so minimising the number of shots needed to achieve a desired level of accuracy is paramount. The performance gains were demonstrated on several small molecules, including hydrogen (H₂) and lithium hydride (LiH), showcasing the algorithm’s potential for tackling realistic chemical systems. The researchers carefully benchmarked SQD-AA against iQPE, a widely used quantum algorithm for energy estimation, demonstrating a clear advantage in both circuit depth and runtime. The shallower circuits are less vulnerable to decoherence, the loss of quantum information due to environmental noise, which is a major obstacle in building practical quantum computers.

Near-term quantum advantage and scalability limitations for molecular simulations

SQD-AA demonstrably reduces the computational burden for molecular energy calculations, but its current validation relies heavily on “early fault-tolerant scenarios”. This presents a tension, as the algorithm’s performance gains haven’t been fully established on the more complex, noisy quantum hardware expected in the coming years. The authors acknowledge limitations for highly accurate calculations or larger molecules, raising questions about scalability, despite SQD-AA’s current advantage in circuit depth. Shallower circuits are inherently less susceptible to errors, a critical factor for near-term quantum devices. The concept of ‘early fault-tolerance’ refers to quantum computers that have some error mitigation capabilities, but are not yet fully protected against errors. These machines are expected to become available in the next few years, and SQD-AA is designed to be particularly well-suited for them. However, as quantum computers become more powerful and complex, the nature of errors will likely change, and it is unclear whether the advantages of SQD-AA will persist. The scalability of SQD-AA is also an open question. While the algorithm reduces the computational cost for each individual calculation, the overall cost still grows with the size of the molecule. For very large molecules, the number of qubits and quantum gates required may still be prohibitive. The researchers are currently exploring techniques to further improve the scalability of SQD-AA, such as using more efficient data structures and algorithms. The new algorithm establishes a pathway towards more efficient molecular simulations by addressing a key limitation of sample-based quantum diagonalization: the infrequent measurement of important quantum states. Combining quantum sampling with amplitude amplification demonstrably reduces the computational effort required for accurate energy calculations, and the substantial reduction in circuit depth suggests potential feasibility on early, less stable quantum computers, opening avenues for exploring more complex molecular systems as quantum technology advances. Future work will focus on extending the algorithm to larger molecules and exploring its application to other areas of quantum chemistry, such as the calculation of reaction rates and excited-state properties.

The researchers developed a new algorithm, SQD-AA, which improves the efficiency of calculating the ground and excited states of molecules using quantum computers. This method addresses a fundamental problem in sample-based quantum diagonalization by making it more likely to observe crucial quantum states, reducing the total query complexity by a factor of over 100 for certain distributions. Evaluations on real molecules indicate SQD-AA requires fewer T-gates and shallower circuits than alternative methods like iterative quantum phase estimation, potentially enabling feasible calculations on early fault-tolerant quantum computers. The authors are currently working to improve the scalability of SQD-AA for even larger molecules and broader applications within quantum chemistry.