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Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…
We propose quantum algorithms for projective ground-state preparation and calculations of the many-body Green's functions directly in frequency domain. The algorithms are based on the linear combination of unitary (LCU) operations and…
Accurately solving the Schr\"odinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding…
We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one…
Molecular ground-state simulation is one of the most promising fields for demonstrating practical quantum advantage on near-term quantum computers. However, the Variational Quantum Eigensolver (VQE), a leading algorithm for this task, still…
Quantum computers have the potential to solve important problems which are fundamentally intractable on a classical computer. The underlying physics of quantum computing platforms supports using multi-valued logic, which promises a boost in…
We present several improvements to the recently developed ground state preparation algorithm based on the Quantum Eigenvalue Transformation for Unitary Matrices (QETU), apply this algorithm to a lattice formulation of U(1) gauge theory in…
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…
We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parameterized ansatz circuits…
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…
The preparation of Hamiltonian eigenstates is essential for many applications in quantum computing; the efficiency with which this can be done is of key interest. A canonical approach exploits the quantum phase estimation (QPE) algorithm.…
Quantum state preparation (QSP) for a general $n$-qubit state requires $O(2^n)$ CNOT gates and circuit depth, making exact amplitude encoding (EAE) impractical for near-term quantum hardware. We introduce an ancilla-free hybrid…
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational…
The development of Fault-Tolerant Quantum Computer (FTQC) gradually raises a possibility to implement the Quantum Phase Estimation (QPE) algorithm. However, QPE works only for normalized systems. This requires the minimum and maximum of…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more…
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…
We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a…