Related papers: Hamiltonian Quantum Cellular Automata in 1D
We propose how to compute the complexity of operators generated by Hamiltonians in quantum field theory (QFT) and quantum mechanics (QM). The Hamiltonians in QFT/QM and quantum circuit have a few essential differences, for which we…
We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of Continuous-Variable Quantum Computing…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic…
The observation of genuine quantum effects in systems governed by non-Hermitian Hamiltonians has been an outstanding challenge in the field. Here we simulate the evolution under such Hamiltonians in the quantum regime on a superconducting…
We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian from a single pair of initial and final states related by time evolution with the Hamiltonian. We then propose a practical version of the protocol…
Analog quantum simulation offers a hardware-specific approach to studying quantum dynamics, but mapping a model Hamiltonian onto the available device parameters requires matching the hardware dynamics. We introduce a paradigm for quantum…
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
We prove that the theorems of TDDFT can be applied to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used…
The rapid development of reliable Quantum Processing Units (QPU) opens up novel computational opportunities for machine learning. Here, we introduce a procedure for measuring the similarity between graph-structured data, based on the…
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged…
Optimal control techniques provide a means to tailor the control pulses required to generate customized quantum gates, which helps to improve the resilience of quantum simulations to gate errors and device noise. However, the significant…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…
We consider a hybrid quantum system consisting of a qubit system continuously evolving according to its fixed own Hamiltonian and a quantum computer. The qubit system couples to a quantum computer through a fixed interaction Hamiltonian,…
Quantum simulators with hundreds of qubits and engineerable Hamiltonians have the potential to explore quantum many-body models that are intractable for classical computers. However, learning the simulated Hamiltonian, a prerequisite for…
We prove that adiabatic computation is equivalent to standard quantum computation even when the adiabatic quantum system is restricted to be a set of particles on a one-dimensional chain. We give a construction that uses a 2-local…