arXiv subjects

Viraj Dsouza

Publications and source records attributed to Viraj Dsouza.

4 recordsLinked to original sources

arXiv2026

Measurement and reload costs in direct quantum simulation of nonlinear waves

Quantum processors encode an N-point field in log_2(N) qubits, which renders nonlinear wave equations an important application for quantum simulation. Nonlinear evolution, however, requires the field values themselves, and these are not directly accessible without quantum measurement. Existing algorithms circumvent this measurement through linear embeddings and state copies, thereby obscuring its cost within the truncation order, the auxiliary dimensions, and the state preparation. In order to expose this cost, a hybrid split-step solver is proposed in which the field is measured, updated classically, and reloaded at every step, with all shots and gates accounted for in a single cost-and-error model. Since the entire field is available at every step, a property unavailable to linear approximations in strongly nonlinear regimes, the design of the solver reduces to a budgeting problem over the timestep, the polynomial degree, and the shot count. The coherent kernels of the solver are validated on superconducting hardware. An identical structure and bottleneck govern the viscous Burgers' equation in one and two dimensions. Because every step reads the full field, the quantum cost per step, measured as circuit depth multiplied by measurement shots, exceeds the classical cost with increasing grid size. The framework consequently identifies a coherent, measurement-free nonlinear update as the quantitative target that any end-to-end advantage must meet.

quant-ph↗

arXiv2026

Variational Quantum Linear Solver via Block Encoding for the Poisson Equation

We present a variational quantum linear solver (VQLS) for the Poisson equation built on an exact block encoding of the discrete Laplacian, and demonstrate its performance on physically motivated benchmarks. Unlike LCU-based VQLS where the number of distinct circuits required per cost-function evaluation is $\mathcal{O}(L^2)$, where $L$ is the number of terms in the LCU decomposition of the discrete Laplacian operator, this approach requires only a single circuit for cost evaluation. We further empirically demonstrate that the choice of classical optimizer materially affects where the variational optimization ceases to make progress. The solver is benchmarked on three problems: a Poisson equation with sinusoidal forcing and a steady-state heat conduction problem with a localized Gaussian source, both with Dirichlet boundaries, and the pressure-Poisson equation of a two-dimensional lid-driven cavity flow, in which the solver is invoked once per time step under Neumann boundary conditions.

quant-ph↗

arXiv2026

Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions

Discrete Laplacian operators arise ubiquitously in scientific computing and frequently appear in quantum algorithms for tasks such as linear algebra, Hamiltonian simulation, and partial differential equations. Block encoding provides the standard method for accessing matrix data within quantum circuits. Efficient implementations of such algorithms require efficient block encodings of the discretized operator. While several general-purpose techniques exist for block encoding arbitrary matrices, they usually require deep quantum circuits. Moreover, existing efficient constructions that exploit Laplacian structure are limited in scope, typically assuming fixed boundary conditions or uniform grid resolutions. In this work, we present a unified framework for efficiently block encoding finite-difference discretizations of the Laplacian that supports Dirichlet, periodic, and Neumann boundary conditions in arbitrary spatial dimensions. Our construction allows different boundary conditions and grid sizes to be specified independently along each coordinate axis, enabling mixed-boundary and anisotropic discretizations within a single modular circuit architecture. We provide analytical gate-complexity estimates and perform circuit-level benchmarks after transpilation to an IBM hardware gate set. Across one-, two-, and three-dimensional examples, the resulting circuits exhibit substantially lower gate counts and higher success probabilities when compared to certain existing approaches.

quant-ph↗

arXiv2026

Quantum Simulation of Coupled Harmonic Oscillators: From Theory to Implementation

We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge the gap between theory and implementation by developing and comparing three concrete realizations of the algorithm. First, we implement a sparse initial state preparation combined with product-formula (Suzuki-Trotter) Hamiltonian simulation. Second, we implement a fully quantum, oracle-based framework in which classical data are accessed via oracles, the Hamiltonian is block-encoded, and time evolution is performed using QSVT-based Hamiltonian simulation. Third, we propose an efficient alternative that combines the sparse state-preparation routine of the first approach with the oracle and block-encoding-based simulation pipeline of the second. We provide these implementations on Classiq, a high-level quantum design platform and provide appropriate resource benchmarks. Our simulation results show that the complex initial state preparation proposed by Babbush et al. can be circumvented at least in the linear-chain case. Finally, we illustrate two physical applications-extracting normal modes and simulating coarse-grained energy propagation-demonstrating how the algorithm connects to measurable observables. Our results clarify the resource requirements of the algorithm and provide concrete pathways toward practical quantum advantage.

quant-ph↗