arXiv subjects

S. A. Fldzhyan

Publications and source records attributed to S. A. Fldzhyan.

7 recordsLinked to original sources

arXiv2026

Perturbative photonic matrix-vector multiplication with reduced phase-shift range

Programmable photonic meshes provide a promising platform for analog matrix-vector multiplication, but their scalability is often limited by the large phase-shift ranges required in universal interferometer circuits. We introduce a perturbative programming method that operates the circuit near a fixed reference configuration and realizes the target transformation through interferometric subtraction, thereby reducing the required programmable phase excursion. We develop this approach for photonic matrix-vector multiplication architectures based on universal unitary meshes, and low-depth non-unitary constructions based on sums of unitaries. We identify favorable reference configurations through a local conditioning criterion, analyze the phase statistics obtained for random target matrices, and show that perturbative programming produces phase distribution shrinking as the matrix size increases. Identified reference point allows for the subtraction to be carried out electronically after detection, avoiding the interferometric subtraction loss. We further quantify the trade-off between reduced phase range and the intrinsic overhead introduced by the subtraction architecture, and show that for sufficiently lossy phase shifters the reduced phase range can compensate for this penalty. These results identify perturbative programming as a conditional but potentially useful route toward more scalable programmable photonic matrix processors.

physics.optics↗

arXiv2026

Improving fermionic variational quantum eigensolvers with Majorana swap networks

Simulating computationally hard fermionic systems is a promising application of quantum computing. However, mapping nonlocal fermionic operators to qubits often produces deep circuits, rendering such simulations impractical on near-term hardware. We introduce two Majorana swap network compilation strategies for variational quantum eigensolvers that reduce circuit depth and two-qubit gate count. First, we develop a cyclic compilation algorithm that localizes all two-particle interaction terms in a general fermionic Hamiltonian containing up to $\mathcal{O}(M^4)$ such terms using only $\mathcal{O}(M^3)$ auxiliary Majorana-swap transpositions, where $M$ is the number of fermionic modes. Here, the cubic scaling refers to auxiliary routing; a complete UCCGSD ansatz still contains $\mathcal{O}(M^4)$ double-excitation rotations. Second, we design a Majorana swap network for the $k$-UpCCGSD variational ansatz, which is already more compact than UCCGSD. In this setting, our network yields constant-factor reductions of approximately $50$ % in circuit depth and $20$ % in two-qubit gate count under all-to-all connectivity. For the more restricted $2\times N$ connectivity, the reductions are larger --- about $55$ % in circuit depth an $40$ % in gate count. These structural improvements are accompanied by improved robustness in numerical noise simulations on the small molecular instances tested.

quant-ph↗

arXiv2026

Native QR Factorization on Programmable Photonic Meshes

We propose a photonic native procedure for computing the QR factorization of a matrix using a programmable unitary interferometer mesh. The method configures the mesh through a sequence of local power routing steps within tunable two mode interferometric elements, while reading out the resulting upper triangular factor directly from the optical outputs. The number of physical operations grows as $ O(N\log_2N)$ with matrix size $N$, reducing the runtime relative to standard digital QR routines, which scale cubically ($O(N^3)$). Beyond single factorizations, the same architecture supports iterative spectral computations by reusing the configured interferometer in a mirrored arrangement that implements the core update step of the QR eigenvalue algorithm. We also describe related optical procedures for Hessenberg reduction and bidiagonalization, serving as compatible preprocessors for QR and SVD workflows. A comparison with the systolic array computational architecture is provided. Our approach exhibits comparable asymptotic complexity for blocked QR decomposition and is more efficient for Hessenberg reduction and bidiagonalization.

physics.optics↗

arXiv2026

Universal low-depth two-unitary design of programmable photonic circuits

The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses, hardware errors, and difficulties in programmability. We propose an enhanced architecture for programmable photonic circuits that minimizes circuit depth and offers analytical programmability, properties that have not been simultaneously achieved in previous circuit designs. Our proposal exploits a previously overlooked representation of general nonunitary matrices as sums of two unitaries. Furthermore, similar to the traditional singular value decomposition-based circuits, the circuits in our unitary-sum-based architecture inherit the advantages of the constituent unitary circuits. Overall, our proposal provides a significantly improved solution for matrix-vector multiplication compared to the established approaches.

physics.optics↗

arXiv2024

Programmable entangled qubit states on a linear-optical platform

We present an experimental platform for linear-optical quantum information processing. Our setup utilizes multiphoton generation using a high-quality single-photon source, which is demultiplexed across multiple spatial channels, a custom-designed, programmable, low-loss photonic chip, and paired with high-efficiency single-photon detectors. We demonstrate the platform's capability in producing heralded arbitrary two-qubit dual-rail encoded states, a crucial building block for large-scale photonic quantum computers. The programmable chip was fully characterized through a calibration process that allowed us to create a numerical model accounting for fabrication imperfections and measurement errors. As a result, using on-chip quantum state tomography (QST), we achieved high-fidelity quantum state preparation, with a fidelity of 98.5\% specifically for the Bell state.

quant-ph↗

arXiv2024

Low-depth, compact and error-tolerant photonic matrix-vector multiplication beyond the unitary group

Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce a novel architecture of photonic circuits capable of implementing non-unitary transfer matrices, usually required by photonic neural networks, iterative equation solvers or quantum samplers. Our architecture exploits compact low-depth beam-splitter meshes rather than bulky fully connected mixing blocks used in previous designs, making it more compatible with planar integrated photonics technology. We have shown that photonic circuits designed with our architecture have lower depth than their standard counterparts and are extremely tolerant to hardware errors.

physics.optics↗

arXiv2024

Fast reconstruction of programmable interferometers with intensity-only measurements

Programmable linear optical interferometers are promising for classical and quantum applications. Their integrated design makes it possible to create more scalable and stable devices. To use them in practice, one has to reconstruct the whole device model taking the manufacturing errors into account. The inability to address individual interferometer elements complicates the reconstruction problem. A naive approach is to train the model via some complex optimization procedure. A faster optimization-free algorithm has been recently proposed [Opt. Express 31, 16729 (2023)]. However, it requires the full transfer matrix tomography while a more practical setup measures only the fields intensities at the interferometer output. In this paper, we propose the modification of the fast algorithm, which uses additional set of interferometer configurations in order to reconstruct the model in the case of intensity-only measurements. We show that it performs slightly worse than the original fast algorithm but it is more practical and still does not require intensive numerical optimization.

quant-ph↗