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Efficiently calculating the low-lying eigenvalues of Hamiltonians, written as sums of Pauli operators, is a fundamental challenge in quantum computing. While various methods have been proposed to reduce the complexity of quantum circuits…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the…
Variational quantum eigensolver (VQE) for electronic structure calculations is believed to be one major potential application of near term quantum computing. Among all proposed VQE algorithms, the unitary coupled cluster singles and doubles…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally…
The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-size quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the…
Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate that…
We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea…
We present classical and quantum algorithms for approximating partition functions of classical Hamiltonians at a given temperature. Our work has two main contributions: first, we modify the classical algorithm of \v{S}tefankovi\v{c},…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
We present the meta-VQE, an algorithm capable to learn the ground state energy profile of a parametrized Hamiltonian. By training the meta-VQE with a few data points, it delivers an initial circuit parametrization that can be used to…
Variational quantum eigensolver (VQE), which attracts attention as a promising application of noisy intermediate-scale quantum devices, finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum…
Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…
An intrinsic problem of classifiers based on machine learning (ML) methods is that their learning time grows as the size and complexity of the training dataset increases. For this reason, it is important to have efficient computational…
We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum…
Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…