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Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained…
The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE…
Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then…
As the advances in quantum hardware bring us into the noisy intermediate-scale quantum (NISQ) era, one possible task we can perform without quantum error correction using NISQ machines is the variational quantum eigensolver (VQE) due to its…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as "the quantum variational eigensolver" was developed…
A new method is proposed for determining the ground state wave function of a quantum many-body system on a quantum computer, without requiring an initial trial wave function that has good overlap with the true ground state. The technique of…
Quantum algorithms are prominent in the pursuit of achieving quantum advantage in various computational tasks. However, addressing challenges, such as limited qubit coherence and high error rate in near-term devices, requires extensive…
Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…
We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. Using a massively parallel universal quantum computer…
The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum/classical variational approaches. This methodology can be applied to a variety of optimization problems,…
By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…
Advances in quantum simulator technology is increasingly required because research on quantum algorithms is becoming more sophisticated and complex. State vector simulation utilizes CPU and memory resources in computing nodes exponentially…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization…
Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these…
A general time-dependent quantum system can be driven fast from its initial ground state to its final ground state without generating transitions by adding a steering term to the Hamiltonian. We show how this technique can be modified to…
We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate.…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…