Related papers: Understanding Quantum Imaginary Time Evolution and…
We formulate a novel ground state quantum computation approach that requires no unitary evolution of qubits in time: the qubits are fixed in stationary states of the Hamiltonian. This formulation supplies a completely time-independent…
Simulating differential equations on classical computers becomes an intractable problem if the grid size is extremely large. Quantum computers are believed to achieve a possibly exponential speedup in the matrix operation. In this paper, we…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
Imaginary-time evolution has been shown to be a promising framework for tackling combinatorial optimization problems on quantum hardware. In this work, we propose a classical quantum-inspired strategy for solving combinatorial optimization…
Quantum algorithms on the noisy intermediate-scale quantum (NISQ) devices are expected to simulate quantum systems that are classically intractable to demonstrate quantum advantages. However, the non-negligible gate error on the NISQ…
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state…
Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization. The quantum…
Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational…
Numerous methodologies have been proposed to implement imaginary time evolution (ITE) on quantum computers. Among these, variational ITE (VITE) methods for noisy intermediate-scale quantum (NISQ) computers have attracted much attention,…
Due to the limitations of present-day quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources. When simulating quantum many-body systems on a quantum computer, straightforward…
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE -- as well as any other heuristic algorithm for finding ground states…
Imaginary-time evolution (ITE) is one of the most widely used numerical techniques for obtaining ground states of many-body Hamiltonians. In this work, we compare ITE with gradient descent (GD) within the framework of Gaussian wavefunction…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
Counting ground state degeneracy of a $k$-local Hamiltonian is important in many fields of physics. Its complexity belongs to the problem of sharp bounded-error quantum polynomial time (#BQP) class and few methods are known for its…
Maxwells equations are fundamental to our understanding of electromagnetic fields, but their solution can be computationally demanding, even for high-performance computing clusters. Quantum computers offer a promising alternative for…
Excited states of many-body quantum systems play a key role in a wide range of physical and chemical phenomena. Unlike ground states, for which many efficient variational techniques exist, there are few ways to systematically construct…
We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
We describe a protocol for preparing the ground state of a Hamiltonian $H$ on a quantum computer. This is done by designing a quantum algorithm that implements the imaginary time evolution operator: $e^{-\tau H}$. The method relies on the…