Related papers: A generalized framework for quantum subspace diago…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
Holonomic quantum computation exploits a quantum state's non-trivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through…
A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state). This book explores quadratizations for pseudo-Boolean optimization, perturbative gadgets used…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…
We describe quantum circuits with only $\widetilde{\cal O}(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary (e.g., molecular) orbitals. With ${\cal O}(\lambda / \epsilon)$…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
Quantum Bit String Comparators (QBSC) operate on two sequences of n-qubits, enabling the determination of their relationships, such as equality, greater than, or less than. This is analogous to the way conditional statements are used in…
Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of $N$ spin-orbitals into an $N$-qubit system, but many of the fermionic…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes…
We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $\phi^4$ theory. Unlike traditional lattice discretisation methods, HT approximates…
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach…
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the…
Quantum simulation of the interactions of fermions and bosons -- the fundamental particles of nature -- is essential for modeling complex quantum systems in material science, chemistry and high-energy physics and has been proposed as a…
We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum…
In recent years, there is a growing interest in using quantum computers for solving combinatorial optimization problems. In this work, we developed a generic, machine learning-based framework for mapping continuous-space inverse design…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…