arXiv subjects

Nicolas PD Sawaya

Publications and source records attributed to Nicolas PD Sawaya.

9 recordsLinked to original sources

arXiv2026

Universality of Quantum Gates in Particle and Symmetry Constrained Subspaces

Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates are universal for state preparation in these subspaces. The key mechanism is Pauli $Z$ dressing: commutators of overlapping gates produce Pauli $Z$ operators on shared qubits, acting as spectator projectors that decompose multi-plane rotations into single-plane generators spanning the full $\mathfrak{so}(w)$ algebra, where $w$ is the dimension of the constrained subspace, thereby guaranteeing universality for real state preparation. Adding independent complex phases extends this to $\mathfrak{su}(w)$, enabling arbitrary complex state preparation. We provide a computationally efficient Jacobian criterion for verifying that a circuit can explore any direction on the target manifold from almost any parameter configuration. Our findings are applicable to many problem areas, including Fermi-Hubbard models, Bose-Hubbard models, and molecular electronic structure. We apply our framework to two physical settings: we prove the completeness of the binary encoded multi-level particles ansatz on the conserved-particle-number subspace, and we construct symmetry-preserving circuits for the fuzzy sphere regularisation of the 3D Ising conformal field theory (CFT). For the latter, we variationally prepare the ground and excited states to extract CFT scaling dimensions.

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arXiv2026

Overlapped groupings for quantum energy estimation: Maximal variance reduction and deterministic algorithms for reducing variance

Grouping-based measurement strategies are widely used to reduce measurement complexity in near-term quantum algorithms. While these schemes have typically produced disjoint groups, recently this has been relaxed in what is known as overlapped grouping or coefficient splitting where operators may appear in more than one compatible group. In recent work, it has been numerically shown that this strategy can reduce the variance of energy estimates on small benchmark problems, motivating both the application and further analysis of the method. Here we prove that overlapped grouping for energy estimation can lead to a maximal variance reduction that is linear in the number of Hamiltonian terms. We introduce a new algorithm which we call repacking to transform existing groups into overlapped groups, and we show this repacking procedure iteratively reduces variance under mild assumptions. We also perform numerical simulations with Hamiltonians up to $44$ qubits and $575 \cdot 10^{3}$ terms, assessing overlapped grouping at scale on problems of practical importance. Our numerics show that the variance reduction relative to state-of-the-art (disjoint) grouping increases linearly with the problem size, suggesting that overlapped grouping methods can be a powerful strategy for quantum energy estimation at the scale of Megaquop computers and beyond.

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arXiv2026

The cost of quantum algorithms for biochemistry: A case study in metaphosphate hydrolysis

We evaluate the quantum resource requirements for ATP/metaphosphate hydrolysis, one of the most important reactions in all of biology with implications for metabolism, cellular signaling, and cancer therapeutics. In particular, we consider three algorithms for solving the ground state energy estimation problem: the variational quantum eigensolver, quantum Krylov, and quantum phase estimation. By utilizing exact classical simulation, numerical estimation, and analytical bounds, we provide a current and future outlook for using quantum computers to solve impactful biochemical and biological problems. Our results show that variational methods, while being the most heuristic, still require substantially fewer overall resources on quantum hardware, and could feasibly address such problems on current or near-future devices. We include our complete dataset of biomolecular Hamiltonians and code as benchmarks to improve upon with future techniques.

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arXiv2024

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max-$k$-SAT, Max-$k$-Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies.

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arXiv2024

Surrogate optimization of variational quantum circuits

Variational quantum eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has not yet been realized, with few claims of quantum advantage and high resource estimates, especially due to the need for optimization in the presence of noise. Finding algorithms and methods to improve convergence is important to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal, we look to use modern approaches developed in circuit simulations and stochastic classical optimization, which can be combined to form a surrogate optimization approach to quantum circuits. Using an approximate (classical CPU/GPU) state vector simulator as a surrogate model, we efficiently calculate an approximate Hessian, passed as an input for a quantum processing unit or exact circuit simulator. This method will lend itself well to parallelization across quantum processing units. We demonstrate the capabilities of such an approach with and without sampling noise and a proof-of-principle demonstration on a quantum processing unit utilizing 40 qubits.

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arXiv2023

Data is often loadable in short depth: Quantum circuits from tensor networks for finance, images, fluids, and proteins

Though there has been substantial progress in developing quantum algorithms to study classical datasets, the cost of simply \textit{loading} classical data is an obstacle to quantum advantage. When the amplitude encoding is used, loading an arbitrary classical vector requires up to exponential circuit depths with respect to the number of qubits. Here, we address this ``input problem'' with two contributions. First, we introduce a circuit compilation method based on tensor network (TN) theory. Our method -- AMLET (Automatic Multi-layer Loader Exploiting TNs) -- proceeds via careful construction of a specific TN topology and can be tailored to arbitrary circuit depths. Second, we perform numerical experiments on real-world classical data from four distinct areas: finance, images, fluid mechanics, and proteins. To the best of our knowledge, this is the broadest numerical analysis to date of loading classical data into a quantum computer. The required circuit depths are often several orders of magnitude lower than the exponentially-scaling general loading algorithm would require. Besides introducing a more efficient loading algorithm, this work demonstrates that many classical datasets are loadable in depths that are much shorter than previously expected, which has positive implications for speeding up classical workloads on quantum computers.

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arXiv2023

Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra

Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems of equations. Here we present three related algorithms for calculating transition probabilities. First, we extend a previously published short-depth algorithm, allowing for the two input states to be non-orthogonal. Building on this first procedure, we then derive a higher-depth algorithm based on Trotterization and Richardson extrapolation that requires fewer circuit evaluations. Third, we introduce a tunable algorithm that allows for trading off circuit depth and measurement complexity, yielding an algorithm that can be tailored to specific hardware characteristics. Finally, we implement proof-of-principle numerics for models in physics and chemistry and for a subroutine in variational quantum linear solving (VQLS). The primary benefits of our approaches are that (a) arbitrary non-orthogonal states may now be used with small increases in quantum resources, (b) we (like another recently proposed method) entirely avoid subroutines such as the Hadamard test that may require three-qubit gates to be decomposed, and (c) in some cases fewer quantum circuit evaluations are required as compared to the previous state-of-the-art in NISQ algorithms for transition probabilities.

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arXiv2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

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arXiv2022

mat2qubit: A lightweight pythonic package for qubit encodings of vibrational, bosonic, graph coloring, routing, scheduling, and general matrix problems

Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different algorithmic choices. Here we describe mat2qubit, a Python package for encoding several classes of classical and quantum problems into qubit representations. It is intended for use especially on Hamiltonians and functions defined over variables (e.g. particles) with cardinality larger than 2. More specifically, mat2qubit may be used to compile bosonic, phononic/vibrational, and spin-$s$ problems, as well as classical problems such as graph coloring, routing, scheduling, and classical linear algebra more generally. In order to facilitate numerical analyses and ease of programmability, a built-in computer algebra system (CAS) allows for fully symbolic preparation and manipulation of problems (with symbolic operators, symbolic coefficients, and symbolic particle labels) before the final compilation into qubits is performed. We expect this code to be useful in the preparation and analysis of various classes of physics, chemistry, materials, and optimization problems for execution on digital quantum computers.

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