arXiv subjects

Robin Ollive

Publications and source records attributed to Robin Ollive.

5 recordsLinked to original sources

arXiv2026

Projector Quantum Variational Ansatz

Quantum computing offers several algorithms to compute the ground state of a problem Hamiltonian. The most desirable algorithms belong to the Fault Tolerant QuantumComputing (FTQC) regime, such as quantum algorithms with repetitive structure like Quantum Phase Estimation (QPE) and Quantum Signal Processing (QSP). However, in the Noisy In-termediate Scale Quantum (NISQ) regime, the most realistic approaches involve Variational Quantum Eigensolver (VQE) algorithms and their variants. VQE is an algorithm that searches for a parametrized unitary matrix called an ansatz whose purposeis to transform an easily prepared initial state into the groundstate of a given Hamiltonian. Adaptive Derivative-AssembledPseudo-Trotter (ADAPT)-VQE is a variant of VQE that im-proves this approach by constructing the ansatz iteratively so that the associated quantum circuit is as shallow as possible. A major difference between FTQC (i.e. not variational) algorithms and VQE is that FTQC algorithms do not construct a state transitiondirectly. Instead, they construct a projector that identifies the ground state using ancillary qubits that flag the good solution. The desired state is then obtained via amplitude amplification orpost-selection. In this work, we propose a VQE ansatz whose structure is more similar to that of an FTQC algorithm. Depending on its parametrization, this ansatz can be equivalent to either an Intermediate Scale Quantum (ISQ)-QSP or to an ADAPT-VQE quantum circuit structure. Our experimental results show that this first proposal of Projector Variational Ansatz (PVA) converges with a shallower ansatz than the usual ADAPT-VQE.

quant-ph↗

arXiv2026

Hamiltonian Simulation and Linear Combination of Unitary Decomposition of Structured Matrices

To process a problem with a Quantum Processing Unit (QPU), it must be transformed into a sequence of quantum operators, or gates. These operators are either packed into a query (i.e. quantum algorithm primitive) that encodes the problem, or used to construct the cost function for Variationnal Quantum Algorithm (VQA). Typical queries are the problem Hamiltonian Simulation (HS) and the problem Block-Encoding (BEing). To construct the circuits associated with the quantum description, the problem must be mapped as a Linear Combination of Hamiltonian (LCH) or a Linear Combination of nitaries (LCU) matrices. All the summed Hamiltonian matrices or unitary matrices must have a known decomposition in basic gates. The complexity of this query should be incorporated into the quantum algorithm's query complexity, thereby limiting the processing possibilities of QPU for many problems. In this work, we propose Hamiltonian matrices used to map the problem of interest, and that behave like a single qubit when expressed in the appropriate basis. It leads to a framework, the Special Tripotent Hamiltonian (STH) Framework, able to implement most of the typical problems considered for quantum computing. These methods address many problems implemented on QPUs, ranging from second-quantization chemistry operators to graphs associated with Partial Differential Equations (PDE), sparse matrices, and higher-order optimization problems. This work underlines interesting properties associated with the STH basic gate decomposition. These include the ability to switch between LCH and LCU, map non-Hermitian problems, and construct the quantum circuit queries required for quantum computing. We also provide a list of STH that are used for the matrix decomposition of many structured matrices. These structured matrices are associated with graph adjacency matrices that can be combined to implement structured matrices.

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arXiv2026

Numerical Error Extraction by Quantum Measurement Algorithm

Important quantum algorithm routines allow the implementation of specific quantum operations (a.k.a. gates) by combining basic quantum circuits with an iterative structure. In this structure, the number of repetitions of the basic circuit pattern is associated to convergence parameters. This iterative structure behaves similarly to function approximation by series expansion: the higher the truncation order, the better the target gate (i.e. operation) approximation. The asymptotic convergence of the gate error with respect to the number of basic pattern repetitions is known. It is referred to as the query complexity. The underlying convergence law is bounded, but not in an explicit fashion. Upper bounds are generally too pessimistic to be useful in practice. The actual convergence law contains constants that depend on the joint properties of the matrix encoded by the query and the initial state vector, which are difficult to compute classically. This paper proposes a strategy to study this convergence law and extract the associated constants from the gate (operation) approximation at different accuracy (convergence parameter) constructed directly on a Quantum Processing Unit (QPU). This protocol is called Numerical Error Extraction by Quantum Measurement Algorithm (NEEQMA). NEEQMA concepts are tested on specific instances of Quantum Signal Processing (QSP) and Hamiltonian Simulation by Trotterization. Knowing theexact convergence constants allows for selecting the smallest convergence parameters that enable reaching the required gate approximation accuracy, hence satisfying the quantum algorithm's requirements.

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arXiv2025

Quantum Arithmetic-based on Quantum Signal Processing

As in classical reversible computing, Quantum Arithmetic is typically seen as a set of tools that process binary data encoded into a quantum register to set the value of another quantum register. This article presents another approach to explain the Quantum Arithmetic in quantum computing. Here, Quantum Arithmetic is addressed with a matrix processing point of view. Quantum Arithmetic is a convenient way to construct the Query that implements the mathematical problem of interest. This approach is not only an interpretation with the matrix approach to encode the problem of interest; it also allows us to derive a new original technique to construct Quantum Arithmetic with the framework of embedded Quantum Signal Processing (QSP). This work uses the link between the eigenstate amplitude and the operator phase to transform the QSP processed amplitude into binary value extracted by Quantum Phase Estimation(QPE). The explanations allowing the QSP based Quantum Arithmetic construction let appear natively sub-routines and functions used by well-known algorithms such as Ancilla Quantum Encoding (AQE)'s Harrow-Hassidim-Lloyd algorithm (HHL) and Quantum Amplitude Estimation (QAE). Methods to implement this circuit are presented in the paper.

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arXiv2024

Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Chemistry and Finite Difference Method

This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit generation technique. It leads to a gate decomposition and a scaling different from the usual strategy based on a Linear Combination of Unitaries (LCU) reformulation of the problem. It can significantly reduce the quantum circuit number of rotational gates, multi-qubit gates, and the circuit depth. This method leads to one exact Hamiltonian simulation for each summed term and Trotter step. Each of these Hamiltonian simulation unitary matrices also allows the construction of the non-exponential terms with a maximum of six unitary matrices to be Block-encoding (BE). The formalism is easy to apply to the widely studied Highorder Unconstrained Binary Optimization (HUBO), fermionic transition Hamiltonian, and basic finite difference method instances. For the HUBO, our implementation exponentially reduces the number of gates for high-order cost functions with respect to the HUBO order. The individual electronic transitions are implemented without error for the second-quantization Fermionic Hamiltonian. Finite difference proposed matrix decompositions are straightforward, very versatile, and scale as the state-of-the-art proposals.

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