# Quantum Computing for Natural Sciences: Technology and Applications Agenda

Introduction and welcome remarks by chairs

30 minutes talk with 5 minutes Q&A

**Abstract:** One of the most promising expected applications of near-term quantum computers lies in the study of static and dynamical properties of quantum many-body systems. Many quantum computing algorithms have been proposed with this goal in mind, with a focus on Hamiltonian eigenvalue extraction, a problem central to chemistry, physics, and materials science. However, the majority of established quantum algorithms require a prohibitively large number of resources for near-term hardware. Here we discuss a number of quantum algorithms relying on real-time evolution for energy eigenvalue determination such as quantum Krylov methods and the recently introduced observable-Dynamic Mode Decomposition. Real-time evolution is native to quantum hardware, making these algorithms particularly suited for the near term. We provide strong theoretical and numerical evidence that these methods can converge rapidly even in the presence of noise and demonstrate their efficacies numerically on a range of chemically relevant Hamiltonians.

15 minutes talk with 2 minutes Q&A each

**1***Lia Yeh*(Quantinuum) – Light-matter interaction in the ZXW calculus

**Abstract: **In this paper, we develop a graphical calculus to rewrite photonic circuits involving light-matter interactions and non-linear optical effects. We introduce the infinite ZW calculus, a graphical language for linear operators on the bosonic Fock space which captures both linear and non-linear photonic circuits. This calculus is obtained by combining the QPath calculus, a diagrammatic language for linear optics, and the recently developed qudit ZXW calculus, a complete axiomatisation of linear maps between qudits. It comes with a ‘lifting’ theorem allowing to prove equalities between infinite operators by rewriting in the ZXW calculus. We give a method for representing bosonic and fermionic Hamiltonians in the infinite ZW calculus. This allows us to derive their exponentials by diagrammatic reasoning. Examples include phase shifts and beam splitters, as well as non-linear Kerr media and Jaynes-Cummings light-matter interaction.

**2***Declan Millar (*IBM Research) – Quantum algorithm for the Vlasov-Maxwell equations

**Abstract: **The Vlasov-Maxwell equations model the dynamics of collisionless classical plasmas. Unfortunately, the dimensionality of the system makes large-scale simulations intractable on current classical computers. This classical limitation necessitates reduced dimensionality or approximate, reduced physics models. The development of quantum algorithms for this system could alleviate this computational bottleneck. We present our ongoing work developing a quantum algorithm for the Vlasov-Maxwell equations. These represent a significant class of nonlinear partial differential equations (PDEs). Currently, we present no new results. We will initially focus on a quantum algorithm for the more limited Vlasov-Poisson equations. We further simplify the system by restricting the equations to one space and velocity dimension. Our algorithm will use Carleman embedding with demonstrated termination boundary conditions. The resultant algorithm could also form a basis for research into quantum algorithms for the Vlasov-Fokker-Planck equation allowing accurate calculations of kinetic heat transport towards a multi-scale plasma physics simulation package. We aim to understand the end-to-end complexity of the quantum simulation algorithm, including quantum-state initialization, dynamics, and measurement. We will begin with a test case—Landau damping in one phase space dimension with a Maxwellian initial distribution function. We will compare the performance of our algorithm with the quantum literature and state-of-the-art classical Vlasov codes using numerical validation on quantum hardware. We are writing a software package to do this based on the Qiskit SDK. We aim to use a 127-qubit system.

**3***Stefano Barison*(École Polytechnique Fédérale de Lausanne) – Embedding quantum circuits in classical variational methods

**Abstract: **We introduce a novel combined quantum-classical variational ansatz to extend the near-term device capabilities to approximate ground states of interacting quantum systems. The proposed method integrates variational quantum circuits implemented on quantum hardware with artificial neural networks on classical hardware. In a spirit similar to quantum embedding methods, the quantum hardware is used to treat only the most correlated degrees of freedom of the system, whereas the classical part models the rest. At variance with similarly existing methods, our approach is fully variational, thus providing a well-defined route to improve the results and scale to larger systems. Furthermore, it is global in the sense that it allows for the simultaneous optimization of both classical and quantum parameters. We demonstrate the effectiveness of the combined protocol on spin chains and small molecular systems and provide insights into its accuracy and computational cost.

Lunch break

30 minutes talk with 5 minutes Q&A

**Abstract: TBC**

15 minutes talk with 2 minutes Q&A each

**4***Nils Herrmann*(Quantum Brilliance) – Early**quantum chemistry benchmarks of an on-site room-temperature quantum computer**

**Abstract: **Since its inception, the simulation of quantum systems has often been considered as one of the most promising applications of quantum computing. More recently, the development of hybrid quantum applications such as the variational quantum eigensolver (VQE) has sparked hopes to utilize these applications on NISQ era quantum devices. Unfortunately, the required quantum resources for VQEs can easily overwhelm currently available devices. In this talk, an alternative technique – quantum wave function sampling – based on a generative machine learning model is introduced. Here, the probabilistic nature of quantum computing is utilized to learn an optimal representation of the electronic wave function within the measured probability distribution. In contrast to VQEs, wave function sampling is quantum resource friendly, requiring the measurement of only a single quantum circuit. We propose quantum wave function sampling as a cost-effective, easily scalable application benchmark to be adopted by the NISQ community. By combining the approach with a qubit-efficient many-particle basis encoding, we deployed test calculations on the first on-site, fully-integrated room-temperature quantum computer at the Pawsey Supercomputing Centre. In this proof of concept, ground state energies of the H2, LiH, and Li2 molecule were obtained with chemical accuarcy using just two qubits.

**5***William Clements*(ORCA Computing) – Hybrid quantum/classical GANs for molecular conformation generation

**Abstract: **In chemistry, the conformer generation problem consists of identifying the different conformations (i.e., three-dimensional shapes) that a molecule can adopt. A molecule’s conformation determines many of its physical and chemical properties, however determining stable conformations of a molecule is a challenging and computationally intensive task. We present a hybrid quantum/classical generative adversarial network (GAN) algorithm for solving this problem, in which an ORCA Computing photonic quantum processor provides inputs to a classical generator consisting of a graph neural network. This algorithm is trained to generate the set of angles between the atoms in a molecule that is most likely to correspond to a stable conformation. We benchmark this algorithm on a dataset consisting of alkane molecules of different sizes, and find that our approach yields sets of angles that are up to 20% more accurate than those yielded by comparable classical GANs. These results indicate that hybrid quantum/classical algorithms are a promising route for achieving near-term improvements in the performance of machine learning algorithms for chemistry.

**6***Alessandro Summer*(Trinity College Dublin) – Calculating the many-body density of states on a digital quantum computer

(online presentation)

**Abstract: **Quantum statistical mechanics allows us to extract thermodynamic information from a microscopic description of a many-body system. A key step is the calculation of the density of states, from which the partition function and all finite-temperature equilibrium thermodynamic quantities can be calculated. In this work, we devise and implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer which is inspired by the kernel polynomial method. Classically, the kernel polynomial method allows to sample spectral functions via a Chebyshev polynomial expansion. Our algorithm computes moments of the expansion on quantum hardware using a combination of random state preparation for stochastic trace evaluation and a controlled unitary operator. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18 qubits. This not only represents a state-of-the-art calculation of thermal properties of a many-body system on quantum hardware, but also exploits the controlled unitary evolution of a many-qubit register on an unprecedented scale.

Afternoon break.

30 minutes talk with 5 minutes Q&A

**Abstract: **Quantum computers promise to impact industrial applications, for which quantum chemical calculations are required, by virtue of their high accuracy. This talk will explore the challenges and opportunities of applying quantum computers to drug design. I will discuss where they could transform industrial research and elaborate on what is needed to reach this goal. I will show the use cases our team has identified and present the results of our research to bring practical quantum computing usage closer.

15 minutes talk with 2 minutes Q&A each

**7***Koichi Miyamoto (*Osaka University) – Quantum algorithms to search patterns in data: from gravitational waves to DNA.

**Abstract:** Finding specific patterns that have important information from data is a common task in various fields of natural science. However, if the size of the data and/or the number of the searched patterns are large, this task is so time-consuming on a classical computer that the speedup by quantum computing may be considered. In this paper, we consider the two pattern search problems in the completely different fields, astronomy and biology: the signal detection by matched filtering in a gravitational wave experiment and finding sequence motifs in biological sequences such as DNA by position weight matrix matching. Interestingly, both of these tasks can be described as calculating sums and searching large ones, and thus sped up by quantum algorithms in a unified framework, namely a combination of quantum Monte Carlo integration and quantum amplitude amplification. We believe that there are many other problems that fall into this type and it is worth to search further applications of the above framework.

**8***Kelly Ann Pawlak*(Atom Computing) – Subspace Correction for Constrained Optimization

**Abstract: **We outline a new class of hybrid algorithms, which we describe as subspace correction, that utilize projective measurement and feedback to maintain a constrained subspace during the course of quantum circuit execution. Subspace correction, like error correction, relies on two components: syndrome detection and recovery. Here, the syndrome is the violation of a constraint on the chosen subspace, and it can be detected with a generalized quantum operation. Many recovery strategies can be constructed for a given syndrome, with an emergent trade-space between wall-clock time and recovery quality. When subspace correction is paired with an appropriate optimal-state preparation unitary and a well-chosen recovery strategy, one can reduce the shot overhead for optimization required by algorithms such as QAOA by orders of magnitude. To actualize the generality of this approach, we explicitly construct operations to prepare syndromes and basic recoveries for a number of common constraint terms in QUBO-based problems. This class of algorithm, unlike previous hybrid NISQ algorithms, requires long coherence times as the hybrid computation and recovery takes place within the coherent execution of the quantum algorithm. It also generally requires more qubits, depending on the desired degree of ancilla simul- taneity during execution. Moreover, the multi-qubit operations needed for detection and recovery can decompose into high-depth 1Q/2Q sequences unless the hardware supports native multi-quibt entangling gates, in which case most operations are constant or low-poly in depth. As such, the tar- get platforms for subspace correction are necessarily next generation hardware such as neutral atom quantum computers. Subspace correction is applicable beyond optimization and can be incorporated into quantum simulation and quantum machine learning algorithms.

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