Related papers: A Dequantized Algorithm for the Guided Local Hamil…
The local Hamiltonian problem is famously complete for the class QMA, the quantum analogue of NP. The complexity of its semi-classical version, in which the terms of the Hamiltonian are required to commute (the CLH problem), has attracted…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
The local Hamiltonian (LH) problem is the canonical $\mathsf{QMA}$-complete problem introduced by Kitaev. In this paper, we show its hardness in a very strong sense: we show that the 3-local Hamiltonian problem on $n$ qubits cannot be…
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…
We construct classical algorithms computing an approximation of the ground state energy of an arbitrary $k$-local Hamiltonian acting on $n$ qubits. We first consider the setting where a good ``guiding state'' is available, which is the main…
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,…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
Recent successes in producing rigorous approximation algorithms for local Hamiltonian problems such as Quantum Max Cut have exploited connections to unconstrained classical discrete optimization problems. We initiate the study of…
Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
We investigate the computational complexity of the Local Hamiltonian (LH) problem and the approximation of the Quantum Partition Function (QPF), two central problems in quantum many-body physics and quantum complexity theory. Both problems…
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…
In this work, we give two results that put new limits on distributed quantum advantage in the context of the LOCAL model of distributed computing. First, we show that there is no distributed quantum advantage for any linear program. Put…
The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and…
Hamiltonian Learning (HL) is essential for validating quantum systems in quantum computing. Not all Hamiltonians can be uniquely recovered from a steady state. HL success depends on the Hamiltonian model and steady state. Here, we analyze…
A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all local terms simultaneously. In general, even deciding whether a Hamiltonian is frustration-free is a hard task, as it is closely related…
Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective…
We present a Hamiltonian quantum computation scheme universal for quantum computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of time-independent, constant-norm, 2-local…