Related papers: Hybrid Quantum-Classical Eigensolver Without Varia…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
In this work, we consider a fundamental task in quantum many-body physics - finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value…
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…
One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds…
The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to…
We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the…
We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wavefunctions. Our approach directly determines system-specific representations of qubit…
Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship…
Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
We propose a simple procedure to produce energy eigenstates of a Hamiltonian with discrete eigenvalues. We use ancilla qubits and quantum entanglement to separate an energy eigenstate from the other energy eigenstates. We exhibit a few…