arXiv subjects

Gabriel Waite

Publications and source records attributed to Gabriel Waite.

8 recordsLinked to original sources

arXiv2026

Efficient Algorithms for Weakly-Interacting Quantum Spin Systems

We establish efficient algorithms for weakly-interacting quantum spin systems at arbitrary temperature. In particular, we obtain a fully polynomial-time approximation scheme for the partition function and an efficient approximate sampling scheme for the thermal distribution over a classical spin space. Our approach is based on the cluster expansion method and a standard reduction from approximate sampling to approximate counting.

quant-ph↗

arXiv2025

Approximate Counting in Local Lemma Regimes

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is based on the cluster expansion method. We obtain fully polynomial-time approximation schemes for both the probability of intersection and the dimension of intersection for commuting projectors. For general projectors, we provide two algorithms: a fully polynomial-time approximation scheme under a global inclusion-exclusion stability condition, and an efficient affine approximation under a spectral gap assumption. As corollaries of our results, we obtain efficient algorithms for approximating the number of satisfying assignments of conjunctive normal form formulae and the dimension of satisfying subspaces of quantum satisfiability formulae.

cs.DS↗

arXiv2025

Efficient Fidelity Estimation with Few Local Pauli Measurements

As quantum devices scale, quantifying how close an experimental state aligns with a target becomes both vital and challenging. Fidelity is the standard metric, but existing estimators either require full tomography or apply only to restricted state/measurement families. Huang, Preskill, and Soleimanifar (Nature Physics, 2025) introduced an efficient certification protocol for Haar-random states using only a polynomial number of non-adaptive, single-copy, local Pauli measurements. Here, we adopt the same data collection routine but recast it as a fidelity estimation protocol with rigorous performance guarantees and broaden its applicability. We analyze the bias in this estimator, linking its performance to the mixing time $\tau$ of a Markov chain induced by the target state, and resolve the three open questions posed by Huang, Preskill, and Soleimanifar (Nature Physics, 2025). Our analysis extends beyond Haar-random states to state $t$-designs, states prepared by low-depth random circuits, physically relevant states and families of mixed states. We introduce a $k$-generalized local escape property that identifies when the fidelity estimation protocol is both efficient and accurate, and design a practical empirical test to verify its applicability for arbitrary states. This work enables scalable benchmarking, error characterization, and tomography assistance, supports adaptive quantum algorithms in high dimensions, and clarifies fundamental limits of learning from local measurements.

quant-ph↗

arXiv2025

Physically-Motivated Guiding States for Local Hamiltonians

We study the computational complexity of the Guided Local Hamiltonian problem: given a local Hamiltonian $H$ together with a classical description of a guiding state that has non-negligible overlap with the ground state of $H$, estimate the ground-state energy within inverse-polynomial precision. This setting captures real-world scenarios in quantum chemistry and many-body physics, where trial states derived from classical heuristics can be used to guide quantum algorithms. We identify families of physically-motivated guiding states for which the computational hardness of ground-state energy estimation persists in the guided setting. Extending prior results for semi-classical subset states, we prove BQP-hardness for classes including fixed-weight states, matrix product states, Gaussian states, and Fendley states. Our hardness results are obtained via refined Feynman-Kitaev circuit-to-Hamiltonian constructions that explicitly expose the structural role of the guiding state in the reduction. Complementing these results, we give a constructive proof of BQP containment when the guiding state admits a polynomial-size classical description, establishing BQP-completeness for the canonical formulation of the problem. Our results show that quantum advantage persists for the newly introduced state classes, and classical methods also remain viable when said guiding states admit appropriate descriptions. Together, our results identify a Goldilocks zone of guiding states that are efficiently preparable, succinctly described, and sample-query accessible, within which quantum advantage for ground-state estimation can be meaningfully assessed. We additionally formalise the Guided Fermi-Hubbard Hamiltonian problem and prove BQP-completeness on 2D square and triangular lattices, both with and without magnetic fields, when provided with an appropriate fermionic guiding state.

quant-ph↗

arXiv2025

On the Complexity of the Succinct State Local Hamiltonian Problem

We study the computational complexity of the Local Hamiltonian problem under the promise that its ground state is succinctly represented. We show that the Succinct State 2-Local Hamiltonian problem, for qubit Hamiltonians, is (promise) MA-complete. The approach combines a systematic characterisation of succinct quantum states, defined through arithmetic over specific number fields, with a refined reduction that lowers the locality of Feynman-Kitaev circuit-Hamiltonians from 6 to 2, without increasing particle dimension. This reveals a complexity phase transition, parameterised by locality, and extends the scope of previously known MA-complete problem instances. Our results further clarify how succinctness behaves under circuit-based constructions, and progresses toward a better understanding of the boundary between efficiently describable and efficiently verifiable quantum systems.

quant-ph↗

arXiv2025

The Guided Local Hamiltonian Problem for Stoquastic Hamiltonians

We show that the Guided Local Hamiltonian problem for stoquastic Hamiltonians is (promise) BPP-hard. The Guided Local Hamiltonian problem extends the Local Hamiltonian problem by incorporating an additional input known as a guiding state, which is promised to overlap with the ground state. For a range of local Hamiltonian families, prior work shows this problem is (promise) BQP-hard, though for stoquastic Hamiltonians, the complexity was previously unknown. We obtain our results by first reducing from quantum-inspired BPP circuits to 6-local stoquastic Hamiltonians. We prove particular classes of quantum states, known as semi-classical encoded subset states, can guide the estimation of the ground-state energy. Our analysis shows that this BPP-hardness does not depend on locality, i.e., the result holds for 2-local stoquastic Hamiltonians. Additional arguments extend this BPP-hardness to Hamiltonians restricted to a square lattice. We further show that for stoquastic Hamiltonians with a fixed local constraint on a subset of the system qubits, the Guided Local Hamiltonian problem is BQP-hard. In addition to these hardness results, we present a deterministic classical approximation algorithm for the problem under the conditions of constant promise gap, constant overlap, and constant spectral gap, when the guiding state is preparable in constant depth by a geometrically local circuit.

quant-ph↗

arXiv2025

The Complexity of Local Stoquastic Hamiltonians on 2D Lattices

We show the 2-Local Stoquastic Hamiltonian problem on a 2D square qubit lattice is StoqMA-complete. We achieve this by extending the spatially sparse circuit construction of Oliveira and Terhal, as well as the perturbative gadgets of Bravyi, DiVincenzo, Oliveira, and Terhal. Our main contributions demonstrate StoqMA circuits can be made spatially sparse and that geometrical, stoquastic-preserving, perturbative gadgets can be constructed, without an increase to particle dimension.

quant-ph↗

arXiv2024

Local-photon model of the momentum of light

Recently we introduced a local photon approach for modelling the quantised electromagnetic field in position space. Using this approach, we define the momentum of light in this paper as in quantum mechanics as the generator for spatial translation. Afterwards, we analyse the momentum dynamics of photonic wave packets which transition from air into a denser dielectric medium. Our analysis shines new light onto the Abraham-Minkowski controversy which highlights the intricacies involved in the characterisation of the momentum of the electromagnetic field. Although our results align with Minkowski's theory and with the definition of the canonical momentum of light in quantum electrodynamics, there are also some crucial differences.

quant-ph↗