arXiv subjects

Soran Jahangiri

Publications and source records attributed to Soran Jahangiri.

16 recordsLinked to original sources

arXiv2026

Spectral Born machines: classically trainable quantum generative models for discrete data

We present \emph{spectral Born machines}, a class of quantum generative models that results from viewing and generalizing the class of IQP Born machines through the lens of group Fourier analysis. These quantum models exploit the quantum Fourier transform to create an inductive bias that make them naturally suited to learning integer-structured data, while remaining classically hard to sample from in general. Similar to IQP Born machines, spectral Born machines can be trained efficiently at scale on classical hardware via a maximum mean discrepancy loss based on graph spectral analysis, which we make available in a new \emph{tcdq} module of the PennyLane software platform. In numerical experiments, we show how the spectral bias of the model leads to significantly reduced parameter counts compared to unstructured approaches, and demonstrate the scalability of the software by training a 190-qubit model with over 1 million parameters to successfully learn a distribution of 93 nucleotide-long ribosomal RNA. Our results suggest that highly over-parameterized spectral Born machines may be immune to overfitting, even in strongly data-scarce regimes.

quant-ph↗

arXiv2026

Practical Estimation of Trotter Error for Hamiltonian Simulation

Trotter product formulas are a leading approach for Hamiltonian simulation on quantum computers, yet their practical performance has remained difficult to assess due to the challenge of accurately estimating the Trotter error. In this work, we develop new theoretical results, algorithms, and software tools that advance the state-of-the-art in Trotter error estimation by orders of magnitude in both scale and accuracy. On the theoretical side, we prove that in the asymptotic limit the error of a product formula depends on the diagonal elements of the Baker-Campbell-Hausdorff (BCH) error operator in the eigenbasis of the Hamiltonian, rather than its full spectral norm -- yielding an improved scaling for Hamiltonian simulation using product formulas. On the algorithmic side, we introduce a compact representation of the BCH expansion that reduces the number of commutators from $\mathcal{O}(n^3)$ to $\mathcal{O}(n)$ for second-order, and from $\mathcal{O}(n^5)$ to $\mathcal{O}(n^2)$ for fourth-order formulas on $n$ fragments, complemented by an importance sampling scheme to further reduce the computational cost. We provide implementations of these techniques in software and demonstrate their power on two applications: (i) X-ray absorption spectroscopy of an electronic Hamiltonian (Li$_4$Mn$_2$O) at up to 56 qubits using tensor networks; and (ii) vibronic dynamics of naphthalene at over 100 qubits using ML-MCTDH, where we find that naive analytical bounds overestimate the required number of Trotter steps by nearly five orders of magnitude. Our framework enables, for the first time, the accurate estimation of Trotter error at practically relevant system sizes, providing a foundation for fair algorithmic comparisons and rational design of product formulas.

quant-ph↗

arXiv2026

Quantum algorithm for simulating resonant inelastic X-ray scattering in battery materials

Resonant inelastic X-ray scattering (RIXS) is the workhorse experimental technique for probing the structural degradation of higher-capacity cathode materials. However, the interpretation of experimental spectra is challenging due to the lack of accurate simulations. In this work, we propose a quantum algorithm for simulating the RIXS spectrum of molecular clusters hypothesized to form in Li-excess cathodes. The algorithm uses quantum phase estimation to sample the spectrum from a state encoding the scattering transition amplitudes of the cluster valence excitations. We prepare this state in the quantum computer using a block-encoding of the dipole operator and quantum signal processing to implement the Green's function propagator over intermediate core-excited states. To showcase the algorithm, we use a model cluster proposed in recent experimental works consisting of an oxygen dimer bonded to a manganese atom. Using the PennyLane software platform, we report resource estimation for simulating RIXS spectra for chemically motivated active spaces of increasing sizes. For a classically challenging active space with 20 orbitals, the algorithm requires $2.0 \times 10^{10}$ Toffoli gates and $414$ logical qubits.

quant-ph↗

arXiv2025

Quantum Algorithms for Photoreactivity in Cancer-Targeted Photosensitizers

Photodynamic therapy (PDT) is a targeted cancer treatment that uses light-activated photosensitizers to generate reactive oxygen species that selectively destroy tumor cells, generally causing less collateral damage than conventional treatments. However, its clinical success hinges on the availability of photosensitizers with strong optical sensitivity and high efficiency in generating reactive oxygen species. While classical computational methods have provided useful insights into photosensitizer design, they struggle to scale and often lack the accuracy needed for these simulations. In this work, we show how fault-tolerant quantum algorithms can be used to identify promising photosensitizer candidates for PDT. To predict photosensitizer performance, we assess two computational properties. First, we quantify light sensitivity by calculating the cumulative absorption in the therapeutic window with a threshold projection algorithm. Second, we determine the efficiency of reactive oxygen generation by estimating intersystem crossing (ISC) rates using the evolution-proxy approach, complemented by a vibronic dynamic treatment where appropriate. We apply these algorithms to a clinically relevant and actively pursued class of photosensitizers, BODIPY derivatives, including heavy-atom and transition-metal-substituted systems that are challenging for classical methods. Our resource estimates, obtained with PennyLane, suggest that systems with active spaces ranging from 11 to 45 spatial orbitals can be simulated using $180$-$350$ logical qubits and Toffoli gate depths between $10^7$ and $10^9$, placing our algorithms within reach of realistic fault-tolerant quantum devices. This paves the way to an efficient quantum-based workflow for designing photosensitizers that can accelerate the discovery of new PDT agents.

quant-ph↗

arXiv2024

A differentiable quantum phase estimation algorithm

The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem by developing a strategy to integrate the quantum phase estimation algorithm within a fully differentiable framework. This is accomplished by devising a smooth estimator able to tackle arbitrary initial states. We provide analytical expressions to characterize the statistics and algorithmic cost of this estimator. Furthermore, we provide numerical evidence that the estimation accuracy is retained when an arbitrary state is considered and that it exceeds the one of standard majority rule. We explicitly use this procedure to estimate chemically relevant quantities, demonstrating our approach through ground-state and triplet excited state geometry optimization with simulations involving up to 19 qubits. This work paves the way for new quantum algorithms that combine interference methods and quantum differentiable programming.

quant-ph↗

arXiv2023

Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer

There is a pressing need to develop new rechargeable battery technologies that can offer higher energy storage, faster charging, and lower costs. Despite the success of existing methods for the simulation of battery materials, they can sometimes fall short of delivering accurate and reliable results. Quantum computing has been discussed as an avenue to overcome these issues, but only limited work has been done to outline how they may impact battery simulations. In this work, we provide a detailed answer to the following question: how can a quantum computer be used to simulate key properties of a lithium-ion battery? Based on recently-introduced first-quantization techniques, we lay out an end-to-end quantum algorithm for calculating equilibrium cell voltages, ionic mobility, and thermal stability. These can be obtained from ground-state energies of materials, which is the core calculation executed by the quantum computer using qubitization-based quantum phase estimation. The algorithm includes explicit methods for preparing approximate ground states of periodic materials in first quantization. We bring these insights together to perform the first estimation of the resources required to implement a quantum algorithm for simulating a realistic cathode material, dilithium iron silicate.

quant-ph↗

arXiv2023

Differentiable quantum computational chemistry with PennyLane

This work describes the theoretical foundation for all quantum chemistry functionality in PennyLane, a quantum computing software library specializing in quantum differentiable programming. We provide an overview of fundamental concepts in quantum chemistry, including the basic principles of the Hartree-Fock method. A flagship feature in PennyLane is the differentiable Hartree-Fock solver, allowing users to compute exact gradients of molecular Hamiltonians with respect to nuclear coordinates and basis set parameters. PennyLane provides specialized operations for quantum chemistry, including excitation gates as Givens rotations and templates for quantum chemistry circuits. Moreover, built-in simulators exploit sparse matrix techniques for representing molecular Hamiltonians that lead to fast simulation for quantum chemistry applications. In combination with PennyLane's existing methods for constructing, optimizing, and executing circuits, these methods allow users to implement a wide range of quantum algorithms for quantum chemistry. We discuss how PennyLane can be used to implement variational algorithms for calculating ground-state energies, excited-state energies, and energy derivatives, all of which can be differentiated with respect to both circuit and Hamiltonian parameters. We provide an example workflow describing how to jointly optimize circuit parameters, nuclear coordinates, and basis set parameters for quantum chemistry algorithms. We discuss a functionality for reducing the number of qubits by using symmetries and explain how PennyLane can be used to estimate quantum resources needed to implement several quantum algorithms. By combining insights from quantum computing, computational chemistry, and machine learning, PennyLane is the first library for differentiable quantum computational chemistry.

quant-ph↗

arXiv2022

Quantum simulation of molecules in solution

Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in gas-phase. Molecules in liquid solution are however most relevant for Chemistry. Continuum solvation models represent a good compromise between computational affordability and accuracy in describing solvation effects within a quantum chemical description of solute molecules. Here we report on the extension of the Variational Quantum Eigensolver to solvated systems, using the Polarizable Continuum Model. We show that accounting for solvation effects does not impact the algorithmic efficiency. Numerical results of noiseless simulations for molecular systems with up to twelve spin-orbitals (qubits) are presented. Furthermore, calculations performed on a simulated quantum hardware (IBM Q Mumbai), thus including noise, yield computed solvation free energies in fair agreement with the classical calculations without the inclusion of any error mitigation protocol.

quant-ph↗

arXiv2022

PennyLane: Automatic differentiation of hybrid quantum-classical computations

PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

quant-ph↗

arXiv2022

Tailgating quantum circuits for high-order energy derivatives

To understand the chemical properties of molecules, it is often important to study derivatives of energies with respect to nuclear coordinates or external fields. Quantum algorithms for computing energy derivatives have been proposed, but only limited work has been done to address the specific challenges that arise in this context, where calculations are more complicated and involve more stringent requirements on accuracy compared to single-point energy calculations. In this work, we introduce a technique to improve the performance of variational quantum circuits calculating energy derivatives. The method, which we refer to as tailgating, is an adaptive procedure that selects gates based on their gradient with respect to the expectation value of Hamiltonian derivatives. These gates are then added at the end of a quantum circuit originally designed to calculate ground- or excited-state energies. A distinguishing feature of this approach is that the appended gates do not need to be optimized: their parameters can be set to zero and varied only for the purpose of computing energy derivatives, via calculating derivatives with respect to circuit parameters. We support the validity of this method by establishing sufficient conditions for a circuit to compute accurate energy gradients. This is achieved through a connection between energy derivatives and eigenstates of Taylor approximations of the Hamiltonian. We illustrate the advantages of the tailgating approach by performing simulations calculating the vibrational modes of beryllium hydride and water: quantities that depend on second-order energy derivatives.

quant-ph↗

arXiv2022

Universal quantum circuits for quantum chemistry

Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that controlled single-excitation gates in the form of Givens rotations are universal for particle-conserving unitaries. Single-excitation gates describe an arbitrary $U(2)$ rotation on the two-qubit subspace spanned by the states $|01\rangle, |10\rangle$, while leaving other states unchanged -- a transformation that is analogous to a single-qubit rotation on a dual-rail qubit. The proof is constructive, so our result also provides an explicit method for compiling arbitrary particle-conserving unitaries. Additionally, we describe a method for using controlled single-excitation gates to prepare an arbitrary state of a fixed number of particles. We derive analytical gradient formulas for Givens rotations as well as decompositions into single-qubit and CNOT gates. Our results offer a unifying framework for quantum computational chemistry where every algorithm is a unique recipe built from the same universal ingredients: Givens rotations.

quant-ph↗

arXiv2021

Quantum Algorithm for Simulating Molecular Vibrational Excitations

The excitation of vibrational modes in molecules affects the outcome of chemical reactions, for example by providing molecules with sufficient energy to overcome activation barriers. In this work, we introduce a quantum algorithm for simulating molecular vibrational excitations during vibronic transitions. We discuss how a special-purpose quantum computer can be programmed with molecular data to optimize a vibronic process such that desired modes get excited during the transition. We investigate the effect of such excitations on selective bond dissociation in pyrrole and butane during photochemical and mechanochemical vibronic transitions. The results are discussed with respect to experimental observations and classical simulations. We also introduce quantum-inspired classical algorithms for simulating molecular vibrational excitations in special cases where only a limited number of modes are of interest.

quant-ph↗

arXiv2021

Variational quantum algorithm for molecular geometry optimization

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum algorithm for finding the most stable structure of a molecule by explicitly considering the parametric dependence of the electronic Hamiltonian on the nuclear coordinates. The equilibrium geometry of the molecule is obtained by minimizing a more general cost function that depends on both the quantum circuit and the Hamiltonian parameters, which are simultaneously optimized at each step. The algorithm is applied to find the equilibrium geometries of the $\mathrm{H}_2$, $\mathrm{H}_3^+$, $\mathrm{BeH}_2$ and $\mathrm{H}_2\mathrm{O}$ molecules. The quantum circuits used to prepare the electronic ground state for each molecule were designed using an adaptive algorithm where excitation gates in the form of Givens rotations are selected according to the norm of their gradient. All quantum simulations are performed using the PennyLane library for quantum differentiable programming. The optimized geometrical parameters for the simulated molecules show an excellent agreement with their counterparts computed using classical quantum chemistry methods.

quant-ph↗

arXiv2020

Quantum Algorithm for Simulating Single-Molecule Electron Transport

An accurate description of electron transport at a molecular level requires a precise treatment of quantum effects. These effects play a crucial role in determining the electron transport properties of single molecules, such as current-voltage curves, which can be challenging to simulate classically. Here we introduce a quantum algorithm to efficiently calculate the electronic current through single-molecule junctions in the weak-coupling regime. We show that a quantum computer programmed to simulate vibronic transitions between different charge states of a molecule can be used to compute sequential electron transfer rates and electric current. In the harmonic approximation, the algorithm can be implemented using Gaussian boson sampling devices, which are a near-term platform for photonic quantum computing. We apply the algorithm to simulate the current and conductance of a magnesium porphine molecule. The simulations demonstrate quantum effects that are manifested as discrete steps in the current and conductance, in agreement with experimental and theoretical data.

quant-ph↗

arXiv2019

Applications of Near-Term Photonic Quantum Computers: Software and Algorithms

Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Recent efforts have led to the discovery of GBS algorithms with applications to graph-based problems, point processes, and molecular vibronic spectra in chemistry. The development of dedicated quantum software is a key enabler in permitting users to program devices and implement algorithms. In this work, we introduce a new applications layer for the Strawberry Fields photonic quantum computing library. The applications layer provides users with the necessary tools to design and implement algorithms using GBS with only a few lines of code. This paper serves a dual role as an introduction to the software, supported with example code, and also a review of the current state of the art in GBS algorithms.

quant-ph↗

arXiv2019

Point Processes with Gaussian Boson Sampling

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of quantum computing to statistical modeling by establishing a connection between point processes and Gaussian Boson Sampling, an algorithm for special-purpose photonic quantum computers. We show that Gaussian Boson Sampling can be used to implement a class of point processes based on hard-to-compute matrix functions which, in general, are intractable to simulate classically. We also discuss situations where polynomial-time classical methods exist. This leads to a family of efficient quantum-inspired point processes, including a new fast classical algorithm for permanental point processes. We investigate the statistical properties of point processes based on Gaussian Boson Sampling and reveal their defining property: like bosons that bunch together, they generate collections of points that form clusters. Finally, we discuss several additional properties of these point processes which we illustrate with example applications.

quant-ph↗