ترغب بنشر مسار تعليمي؟ اضغط هنا

Hardware Efficient Quantum Algorithms for Vibrational Structure Calculations

84   0   0.0 ( 0 )
 نشر من قبل Pauline Ollitrault
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference modal bases and Hamiltonian representations, including the ones that are routinely used in classical vibrational structure calculations. We test different parametrizations of the vibrational wave function, which can be encoded in quantum hardware, based either on heuristic circuits or on the bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel compact heuristic circuit and demonstrate that it provides the best compromise in terms of circuit depth, optimization costs, and accuracy. We evaluate the requirements, number of qubits and circuit depth, for the calculation of vibrational energies on quantum hardware and compare them with state-of-the-art classical vibrational structure algorithms for molecules with up to seven atoms.



قيم البحث

اقرأ أيضاً

324 - Ji Liu , Huiyang Zhou 2021
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grovers search alg orithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grovers search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grovers search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward translation of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.
98 - Barry C. Sanders 2013
A universal quantum simulator would enable efficient simulation of quantum dynamics by implementing quantum-simulation algorithms on a quantum computer. Specifically the quantum simulator would efficiently generate qubit-string states that closely ap proximate physical states obtained from a broad class of dynamical evolutions. I provide an overview of theoretical research into universal quantum simulators and the strategies for minimizing computational space and time costs. Applications to simulating many-body quantum simulation and solving linear equations are discussed.
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these int eracting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient variational quantum eigensolver with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.
We consider the natural generalization of the Schr{o}dinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an $n$-qubit system for time $t$ within precision $epsilon$. If the Lindbladian consists of $mathrm{poly}(n)$ operators that can each be expressed as a linear combination of $mathrm{poly}(n)$ tensor products of Pauli operators then the gate cost of our algorithm is $O(t, mathrm{polylog}(t/epsilon)mathrm{poly}(n))$. We also obtain similar bounds for the cases where the Lindbladian consists of local operators, and where the Lindbladian consists of sparse operators. This is remarkable in light of evidence that we provide indicating that the above efficiency is impossible to attain by first expressing Lindblad evolution as Schr{o}dinger evolution on a larger system and tracing out the ancillary system: the cost of such a textit{reduction} incurs an efficiency overhead of $O(t^2/epsilon)$ even before the Hamiltonian evolution simulation begins. Instead, the approach of our algorithm is to use a novel variation of the linear combinations of unitaries construction that pertains to channels.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا