Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization.

Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.

Estimation of Electrostatic Interaction Energies on a Trapped-Ion Quantum Computer.

We present the first hardware implementation of electrostatic interaction energies by using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of NO to N2O catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would require in the straightforward supermolecular approach.

Accurate non-covalent interaction energies on noisy intermediate-scale quantum computers via second-order symmetry-adapted perturbation theory.

The calculation of non-covalent interaction energies on noisy intermediate-scale quantum (NISQ) computers appears to be challenging with straightforward application of existing quantum algorithms. For example, the use of the standard supermolecular method with the variational quantum eigensolver (VQE) would require extremely precise resolution of the total energies of the fragments to provide for accurate subtraction to the interaction energy. Here we present a symmetry-adapted perturbation theory (SAPT) method that may provide interaction energies with high quantum resource efficiency. Of particular note, we present a quantum extended random-phase approximation (ERPA) treatment of the SAPT second-order induction and dispersion terms, including exchange counterparts. Together with previous work on first-order terms (Chem. Sci., 2022, 13, 3094), this provides a recipe for complete SAPT(VQE) interaction energies up to second order, which is a well established truncation. The SAPT interaction energy terms are computed as first-level observables with no subtraction of monomer energies invoked, and the only quantum observations needed are the VQE one- and two-particle density matrices. We find empirically that SAPT(VQE) can provide accurate interaction energies even with coarsely optimized, low circuit depth wavefunctions from a quantum computer, simulated through ideal statevectors. The errors of the total interaction energy are orders of magnitude lower than the corresponding VQE total energy errors of the monomer wavefunctions. In addition, we present heme-nitrosyl model complexes as a system class for near term quantum computing simulations. They are strongly correlated, biologically relevant and difficult to simulate with classical quantum chemical methods. This is illustrated with density functional theory (DFT) as the predicted interaction energies exhibit a strong sensitivity with respect to the choice of functional. Thus, this work paves the way to obtain accurate interaction energies on a NISQ-era quantum computer with few quantum resources. It is the first step in alleviating one of the major challenges in quantum chemistry, where in-depth knowledge of both the method and system is required a priori to reliably generate accurate interaction energies.

Deep learning for blind structured illumination microscopy.

Blind-structured illumination microscopy (blind-SIM) enhances the optical resolution without the requirement of nonlinear effects or pre-defined illumination patterns. It is thus advantageous in experimental conditions where toxicity or biological fluctuations are an issue. In this work, we introduce a custom convolutional neural network architecture for blind-SIM: BS-CNN. We show that BS-CNN outperforms other blind-SIM deconvolution algorithms providing a resolution improvement of 2.17 together with a very high Fidelity (artifacts reduction). Furthermore, BS-CNN proves to be robust in cross-database variability: it is trained on synthetically augmented open-source data and evaluated on experiments. This approach paves the way to the employment of CNN-based deconvolution in all scenarios in which a statistical model for the illumination is available while the specific realizations are unknown or noisy.

Towards the simulation of large scale protein-ligand interactions on NISQ-era quantum computers.

We explore the use of symmetry-adapted perturbation theory (SAPT) as a simple and efficient means to compute interaction energies between large molecular systems with a hybrid method combining NISQ-era quantum and classical computers. From the one- and two-particle reduced density matrices of the monomer wavefunctions obtained by the variational quantum eigensolver (VQE), we compute SAPT contributions to the interaction energy [SAPT(VQE)]. At first order, this energy yields the electrostatic and exchange contributions for non-covalently bound systems. We empirically find from ideal statevector simulations that the SAPT(VQE) interaction energy components display orders of magnitude lower absolute errors than the corresponding VQE total energies. Therefore, even with coarsely optimized low-depth VQE wavefunctions, we still obtain sub kcal mol-1 accuracy in the SAPT interaction energies. In SAPT(VQE), the quantum requirements, such as qubit count and circuit depth, are lowered by performing computations on the separate molecular systems. Furthermore, active spaces allow for large systems containing thousands of orbitals to be reduced to a small enough orbital set to perform the quantum portions of the computations. We benchmark SAPT(VQE) (with the VQE component simulated by ideal statevector simulators) against a handful of small multi-reference dimer systems and the iron center containing human cancer-relevant protein lysine-specific demethylase 5 (KDM5A).

Scheme for Universal High-Dimensional Quantum Computation with Linear Optics.

Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise resilience. However, schemes to generate the resources required for high-dimensional quantum computing have so far been lacking in linear optics. Here, we show how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices. Combining our results with recent schemes for qudit Bell measurements, we show that universal linear optical quantum computing can be performed in arbitrary dimensions.

Localization-based two-photon wave-function information encoding.

In quantum communications, quantum states are employed for the transmission of information between remote parties. This usually requires sharing knowledge of the measurement bases through a classical public channel in the sifting phase of the protocol. Here, we demonstrate a quantum communication scheme where the information on the bases is shared "non-classically," by encoding this information in the same photons used for carrying the data. This enhanced capability is achieved by exploiting the localization of the photonic wave function, observed when the photons are prepared and measured in the same quantum basis. We experimentally implement our scheme by using a multi-mode optical fiber coupled to an adaptive optics setup. We observe a decrease in the error rate for higher dimensionality, indicating an improved resilience against noise.

Programmable four-photon graph states on a silicon chip.

Future quantum computers require a scalable architecture on a scalable technology-one that supports millions of high-performance components. Measurement-based protocols, using graph states, represent the state of the art in architectures for optical quantum computing. Silicon photonics technology offers enormous scale and proven quantum optical functionality. Here we produce and encode photonic graph states on a mass-manufactured chip, using four on-chip-generated photons. We programmably generate all types of four-photon graph state, implementing a basic measurement-based protocol, and measure high-visibility heralded interference of the chip's four photons. We develop a model of the device and bound the dominant sources of error using Bayesian inference. The combination of measurement-based quantum computation, silicon photonics technology, and on-chip multi-pair sources will be a useful one for future scalable quantum information processing with photons.

Multidimensional quantum entanglement with large-scale integrated optics.

The ability to control multidimensional quantum systems is central to the development of advanced quantum technologies. We demonstrate a multidimensional integrated quantum photonic platform able to generate, control, and analyze high-dimensional entanglement. A programmable bipartite entangled system is realized with dimensions up to 15 × 15 on a large-scale silicon photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality, and controllability of our multidimensional technology, and further exploit these abilities to demonstrate previously unexplored quantum applications, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides an experimental platform for the development of multidimensional quantum technologies.

Witnessing eigenstates for quantum simulation of Hamiltonian spectra.

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an "eigenstate witness" and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.

Scale-free correlations in starling flocks.

From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand how a globally ordered state may emerge from simple behavioral rules. Less effort has been devoted to understanding the origin of collective response, namely the way the group as a whole reacts to its environment. Yet, in the presence of strong predatory pressure on the group, collective response may yield a significant adaptive advantage. Here we suggest that collective response in animal groups may be achieved through scale-free behavioral correlations. By reconstructing the 3D position and velocity of individual birds in large flocks of starlings, we measured to what extent the velocity fluctuations of different birds are correlated to each other. We found that the range of such spatial correlation does not have a constant value, but it scales with the linear size of the flock. This result indicates that behavioral correlations are scale free: The change in the behavioral state of one animal affects and is affected by that of all other animals in the group, no matter how large the group is. Scale-free correlations provide each animal with an effective perception range much larger than the direct interindividual interaction range, thus enhancing global response to perturbations. Our results suggest that flocks behave as critical systems, poised to respond maximally to environmental perturbations.

New statistical tools for analyzing the structure of animal groups.

The statistical characterization of the spatial structure of large animal groups has been very limited so far, mainly due to a lack of empirical data, especially in three dimensions (3D). Here we focus on the case of large flocks of starlings (Sturnus vulgaris) in the field. We reconstruct the 3D positions of individual birds within flocks of up to few thousands of elements. In this respect our data constitute a unique set. We perform a statistical analysis of flocks' structure by using two quantities that are new to the field of collective animal behaviour, namely the conditional density and the pair correlation function. These tools were originally developed in the context of condensed matter theory. We explain what is the meaning of these two quantities, how to measure them in a reliable way, and why they are useful in assessing the density fluctuations and the statistical correlations across the group. We show that the border-to-centre density gradient displayed by starling flocks gives rise to an anomalous behaviour of the conditional density. We also find that the pair correlation function has a structure incompatible with a crystalline arrangement of birds. In fact, our results suggest that flocks are somewhat intermediate between the liquid and the gas phase of physical systems.