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Quantum computing holds substantial potential for applications in biology and medicine, spanning from the simulation of biomolecules to machine learning methods for subtyping cancers on the basis of clinical features. This potential is encapsulated by the concept of a quantum advantage, which is contingent on a reduction in the consumption of a computational resource, such as time, space or data. Here, we distill the concept of a quantum advantage into a simple framework to aid researchers in biology and medicine pursuing the development of quantum applications. We then apply this framework to a wide variety of computational problems relevant to these domains in an effort to (i) assess the potential of practical advantages in specific application areas and (ii) identify gaps that may be addressed with novel quantum approaches. In doing so, we provide an extensive survey of the intersection of biology and medicine with the current landscape of quantum algorithms and their potential advantages. While we endeavour to identify specific computational problems that may admit practical advantages throughout this work, the rapid pace of change in the fields of quantum computing, classical algorithms and biological research implies that this intersection will remain highly dynamic for the foreseeable future.

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.

Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN) contraction is an algorithmic method that can efficiently simulate some quantum circuits, often greatly reducing the computational cost over methods that simulate the full Hilbert space. In this study we implement a tensor network contraction program for simulating quantum circuits using multi-core compute nodes. We show simulation results for the Max-Cut problem on 3- through 7-regular graphs using the quantum approximate optimization algorithm (QAOA), successfully simulating up to 100 qubits. We test two different methods for generating the ordering of tensor index contractions: one is based on the tree decomposition of the line graph, while the other generates ordering using a straight-forward stochastic scheme. Through studying instances of QAOA circuits, we show the expected result that as the treewidth of the quantum circuit's line graph decreases, TN contraction becomes significantly more efficient than simulating the whole Hilbert space. The results in this work suggest that tensor contraction methods are superior only when simulating Max-Cut/QAOA with graphs of regularities approximately five and below. Insight into this point of equal computational cost helps one determine which simulation method will be more efficient for a given quantum circuit. The stochastic contraction method outperforms the line graph based method only when the time to calculate a reasonable tree decomposition is prohibitively expensive. Finally, we release our software package, qTorch (Quantum TensOR Contraction Handler), intended for general quantum circuit simulation. For a nontrivial subset of these quantum circuits, 50 to 100 qubits can easily be simulated on a single compute node.

Regulating energy transfer pathways through materials is a central goal of nanotechnology, as a greater degree of control is crucial for developing sensing, spectroscopy, microscopy, and computing applications. Such control necessitates a toolbox of actuation methods that can direct energy transfer based on user input. Here we introduce a proposal for a molecular exciton gate, analogous to a traditional transistor, for regulating exciton flow in chromophoric systems. The gate may be activated with an input of light or an input flow of excitons. Our proposal relies on excitation migration via the second excited singlet (S 2 ) state of the gate molecule. It exhibits the following features, only a subset of which are present in previous exciton switching schemes: picosecond time scale actuation, amplification/gain behavior, and a lack of molecular rearrangement. We demonstrate that the device can be used to produce universal binary logic or amplification of an exciton current, providing an excitonic platform with several potential uses, including signal processing for microscopy and spectroscopy methods that implement tunable exciton flux.

Understanding the properties of electronically interacting molecular chromophores, which involve internally coupled electronic-vibrational motions, is important to the spectroscopy of many biologically relevant systems. Here we apply linear absorption, circular dichroism, and two-dimensional fluorescence spectroscopy to study the polarized collective excitations of excitonically coupled cyanine dimers (Cy3) 2 that are rigidly positioned within the opposing sugar-phosphate backbones of the double-stranded region of a double-stranded (ds)-single-stranded (ss) DNA fork construct. We show that the exciton-coupling strength of the (Cy3) 2 -DNA construct can be systematically varied with temperature below the ds-ss DNA denaturation transition. We interpret spectroscopic measurements in terms of the Holstein vibronic dimer model, from which we obtain information about the local conformation of the (Cy3) 2 dimer, as well as the degree of static disorder experienced by the Cy3 monomer and the (Cy3) 2 dimer probe locally within their respective DNA duplex environments. The properties of the (Cy3) 2 -DNA construct we determine suggest that it may be employed as a useful model system to test fundamental concepts of protein-DNA interactions and the role of electronic-vibrational coherence in electronic energy migration within exciton-coupled bio-molecular arrays.

Natural light-harvesting systems spatially organize densely packed chromophore aggregates using rigid protein scaffolds to achieve highly efficient, directed energy transfer. Here, we report a synthetic strategy using rigid DNA scaffolds to similarly program the spatial organization of densely packed, discrete clusters of cyanine dye aggregates with tunable absorption spectra and strongly coupled exciton dynamics present in natural light-harvesting systems. We first characterize the range of dye-aggregate sizes that can be templated spatially by A-tracts of B-form DNA while retaining coherent energy transfer. We then use structure-based modelling and quantum dynamics to guide the rational design of higher-order synthetic circuits consisting of multiple discrete dye aggregates within a DX-tile. These programmed circuits exhibit excitonic transport properties with prominent circular dichroism, superradiance, and fast delocalized exciton transfer, consistent with our quantum dynamics predictions. This bottom-up strategy offers a versatile approach to the rational design of strongly coupled excitonic circuits using spatially organized dye aggregates for use in coherent nanoscale energy transport, artificial light-harvesting, and nanophotonics.