arXiv subjects

Joel Bierman

Publications and source records attributed to Joel Bierman.

10 recordsLinked to original sources

arXiv2026

Scalable Qumode-Qubit State Transfer and Fast-forward Quantum Fourier Transform using Oscillators

Transferring the information stored in the expansion coefficients of a multi-qubit state to the coefficients of a continuous-variable state is an important protocol for communicating quantum information. It was shown in previous work how to transfer an $n$-qubit state to a single qumode in $\mathcal{O}(2^n)$ time. We show that by transferring this state to $m$ qumodes, the runtime can be improved to $\mathcal{O}(2^{n/m})$. Furthermore, we demonstrate how multi-qumode state transfer can be used as a subroutine for approximately realizing the $n$-qubits quantum Fourier transform on $m$-qumode with runtime scaling $\mathcal{O}(m2^{n/m}/ε+m^2)$, accelerating qubit quantum Fourier transform using qumodes. This work presents a scalable approach to convert discrete and continuous quantum information between an arbitrary number of qubits and qumodes. It represents a crucial step forward in mixed analog-digital quantum signal processing for computing, sensing, and communication.

quant-ph↗

arXiv2026

Bootstrap Embedding for Interacting Electrons in Phonon Coherent-state Mean Field

We develop a fermi-bose bootstrap embedding (fb-BE) framework for the ground state of interacting elec- trons coupled to phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron-phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for frag- ment size and total system size are demonstrated for one-dimensional Hubbard-Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to infinite system size. Benchmarking against density matrix renormalization group for small 8-site system at half- and quarter-filling shows orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

cond-mat.str-el↗

arXiv2026

Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations

Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this Perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented including construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this Perspective serves as a gentle introduction of state-of-the-art quantum algorithms to the computational science community, and inspires future development on scalable quantum computational science methodologies that bridge theory and practice.

quant-ph↗

arXiv2025

Hybrid continuous-discrete-variable quantum computing: a guide to utility

Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this paper, we discuss some of the advantages of this modality, and lay out a number of potential applications that can make use of it; these include applications from physics, chemistry, and computer science. We also briefly overview some of the algorithmic and software considerations for this new paradigm.

quant-ph↗

arXiv2025

State-Specific Orbital Optimization for Enhanced Excited-States Calculation on Quantum Computers

We propose a state-specific orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for the use on near-term quantum computers, which can be combined with any overlap-based excited-state quantum eigensolver. We derived the gradient of the overlap term between different states generated by different orbitals with respect to the orbital rotation matrix and use the gradient-based optimization methods to optimize the orbitals. This scheme allows for more flexibility in the choice of orbitals. We implement the state-specific orbital optimization scheme with the variational quantum deflation (VQD) algorithm, and show that it achieves higher accuracy than the state-averaged orbital optimization scheme on various molecules including H4 and LiH.

quant-ph↗

arXiv2025

Genesis: A Compiler Framework for Hamiltonian Simulation on Hybrid CV-DV Quantum Computers

This paper introduces Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems. Genesis is a two-level compilation system. At the first level, it decomposes an input Hamiltonian into basis gates using the native instruction set of the target hybrid CV-DV quantum computer. At the second level, it tackles the mapping and routing of qumodes/qubits to implement long-range interactions for the gates decomposed from the first level. Rather than a typical implementation that relies on SWAP primitives similar to qubit-based (or DV-only) systems, we propose an integrated design of connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for hybrid CV-DV systems. We also introduce an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CV-DV gate set. Genesis has successfully compiled several important Hamiltonians, including the Bose-Hubbard model, $\mathbb{Z}_2-$Higgs model, Hubbard-Holstein model, Heisenberg model and Electron-vibration coupling Hamiltonians, which are critical in domains like quantum field theory, condensed matter physics, and quantum chemistry. Our implementation is available at Genesis-CVDV-Compiler(https://github.com/ruadapt/Genesis-CVDV-Compiler).

quant-ph↗

arXiv2025

Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets

This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of $O(n)$ with about $n$ ancilla qubits, enhancing the computational capabilities for analyzing fermionic systems. The non-unitarity of the transformation allows us to transform a wave function from one basis to another, which can span different spaces. By this trick, we can calculate the overlap of two wavefunctions that live in different (but non-distinct Hilbert subspaces) with different basis representations. This provides the opportunity to use state specific ansatzes to calculate different energy eigenstates under orbital-optimized settings and may improve the accuracy when computing the energies of multiple eigenstates simultaneously in VQE or other framework. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry.

quant-ph↗

arXiv2024

Qubit Count Reduction by Orthogonally-Constrained Orbital Optimization for Variational Quantum Excited States Solvers

We propose a state-averaged orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for use on near-term quantum computers. Instead of parameterizing the orbital rotation operator in the conventional fashion as an exponential of an anti-hermitian matrix, we parameterize the orbital rotation as a general partial unitary matrix. Whereas conventional orbital optimization methods minimize the state-averaged energy using successive Newton steps of the second-order Taylor expansion of the energy, the method presented here optimizes the state-averaged energy using an orthogonally-constrained gradient projection method which does not require any expansion approximations. Through extensive benchmarking of the method on various small molecular systems, we find that the method is capable of producing more accurate results than fixed basis FCI while simultaneously using fewer qubits. In particular, we show that for $\mathrm{H_2}$, the method is capable of matching the accuracy of FCI in the cc-pVTZ basis (56 qubits) while only using 14 qubits.

physics.chem-ph↗

arXiv2023

Improving the Accuracy of Variational Quantum Eigensolvers With Fewer Qubits Using Orbital Optimization

Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited to small molecules using minimal basis sets for this reason. In this work we propose incorporating an orbital optimization scheme into quantum eigensolvers wherein a parameterized partial unitary transformation is applied to the basis functions set in order to reduce the number of qubits required for a given problem. The optimal transformation is found by minimizing the ground state energy with respect to this partial unitary matrix. Through numerical simulations of small molecules up to 16 spin orbitals, we demonstrate that this method has the ability to greatly extend the capabilities of near-term quantum computers with regard to the electronic structure problem. We find that VQE paired with orbital optimization consistently achieves lower ground state energies than traditional VQE when using the same number of qubits and even frequently achieves lower ground state energies than VQE methods using more qubits.

physics.chem-ph↗

arXiv2022

Quantum Orbital Minimization Method for Excited States Calculation on Quantum Computer

We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parameterized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts classical optimizer to minimize the objective function with respect to parameters in ansatz circuits. The objective function has orthogonality implicitly embedded, which allows qOMM to apply a different ansatz circuit to each reference state. We carry out numerical simulations that seek to find excited states of the $\text{H}_{2}$, $\text{LiH}$, and a toy model consisting of 4 hydrogen atoms arranged in a square lattice in the STO-3G basis and UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.

physics.chem-ph↗