ترغب بنشر مسار تعليمي؟ اضغط هنا

Efficient Algorithms for Universal Quantum Simulation

97   0   0.0 ( 0 )
 نشر من قبل Barry Sanders
 تاريخ النشر 2013
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Barry C. Sanders




اسأل ChatGPT حول البحث

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 approximate 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.



قيم البحث

اقرأ أيضاً

158 - Shi-Jie Wei , Tao Xin , 2017
The study of quantum channels is the fundamental field and promises wide range of applications, because any physical process can be represented as a quantum channel transforming an initial state into a final state. Inspired by the method performing n on-unitary operator by the linear combination of unitary operations, we proposed a quantum algorithm for the simulation of universal single-qubit channel, described by a convex combination of quasiextreme channels corresponding to four Kraus operators, and is scalable to arbitrary higher dimension. We demonstrate the whole algorithm experimentally using the universal IBM cloud quantum computer and study properties of different qubit quantum channels. We illustrate the quantum capacity of the general qubit quantum channels, which quantifies the amount of quantum information that can be protected. The behaviour of quantum capacity in different channels reveal which types of noise processes can support information transmission, and which types are too destructive to protect information. There is a general agreement between the theoretical predictions and the experiments, which strongly supported our method. By realizing arbitrary qubit channel, this work provides a universal way to explore various properties of quantum channel and novel prospect of quantum communication.
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.
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 bas es 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.
Many quantum machine learning (QML) algorithms that claim speed-up over their classical counterparts only generate quantum states as solutions instead of their final classical description. The additional step to decode quantum states into classical v ectors normally will destroy the quantum advantage in most scenarios because all existing tomographic methods require runtime that is polynomial with respect to the state dimension. In this Letter, we present an efficient readout protocol that yields the classical vector form of the generated state, so it will achieve the end-to-end advantage for those quantum algorithms. Our protocol suits the case that the output state lies in the row space of the input matrix, of rank $r$, that is stored in the quantum random access memory. The quantum resources for decoding the state in $ell_2$-norm with $epsilon$ error require $text{poly}(r,1/epsilon)$ copies of the output state and $text{poly}(r, kappa^r,1/epsilon)$ queries to the input oracles, where $kappa$ is the condition number of the input matrix. With our read-out protocol, we completely characterise the end-to-end resources for quantum linear equation solvers and quantum singular value decomposition. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure, which we believe, will be of independent interest.
Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale platform w ith only a few gigabytes of main memory. However, more memory-efficient simulations are possible, requiring only polynomial or even linear space in the size of the quantum circuit being simulated. In this paper, we describe one such technique, which was recently implemented at FSU in the form of a C++ program called SEQCSim, which we releasing publicly. We also discuss the potential benefits of this simulation in quantum computing research and education, and outline some possible directions for further progress.
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