Related papers: Halving the Cost of Controlled Time-Evolution
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial…
Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltonian simulation subroutine, which may introduce extra…
Simulation of quantum many-body systems is a promising application of quantum computers. However, implementing the time-evolution operator as a quantum circuit efficiently on near-term devices with limited resources is challenging. Standard…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase…
Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains…
Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary…
The quantum stochastic drift protocol, also known as qDRIFT, has become a popular algorithm for implementing time-evolution of quantum systems using randomised compiling. In this work we develop qFLO, a higher order randomised algorithm for…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
Trotterization in quantum mechanics is an important theoretical concept in handling the exponential of noncommutative operators. In this communication, we give a mathematical formulation of the Trotter Product Formula, and apply it to basic…
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
A bound on the error introduced by truncating a quantum addition is given. This bound shows that only a few controlled rotation gates will be necessary to get a reliable computation.
Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid…
Vibronic interactions between nuclear motion and electronic states are critical for the accurate modeling of photochemistry. However, accurate simulations of fully quantum non-adiabatic dynamics are often prohibitively expensive for…
Accurate simulations of vibrational molecular spectra are expensive on conventional computers. Compared to the electronic structure problem, the vibrational structure problem with quantum computers is less investigated. In this work we…