Related papers: Improving Hamiltonian encodings with the Gray code
We reformulate the continuous space Schr\"odinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. Binary encoding…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized…
The quantum open-system simulation is an important category of quantum simulation. By simulating the thermalisation process at the zero temperature, we can solve the ground-state problem of quantum systems. To realise the open-system…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine…
We analyze decoherence-free (DF) quantum information in the presence of an arbitrary non-nearest-neighbor bath-induced system Hamiltonian using a Markovian master equation. We show that the most appropriate encoding for N qubits is probably…
The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
Assemblies of strongly interacting fermions, whether in a condensed-matter or a quantum chemistry context, range amongst the most promising candidate systems for which quantum computing platforms could provide an advantage. Near-term…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer. We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian,…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is…