arXiv subjects

Man-Hong Yung

Publications and source records attributed to Man-Hong Yung.

141 records · Page 8Linked to original sources

arXiv2012

Simulating chemistry efficiently on fault-tolerant quantum computers

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposed chemical simulation algorithms computationally fast on fault-tolerant quantum computers in the circuit model. Fault tolerance constrains the choice of available gates, so that arbitrary gates required for a simulation algorithm must be constructed from sequences of fundamental operations. We examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm [C.M. Dawson and M.A. Nielsen, \emph{Quantum Inf. Comput.}, \textbf{6}:81, 2006]. For a given approximation error $ε$, arbitrary single-qubit gates can be produced fault-tolerantly and using a limited set of gates in time which is $O(\log ε)$ or $O(\log \log ε)$; with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for Lithium hydride.

quant-ph↗

arXiv2012

Introduction to Quantum Algorithms for Physics and Chemistry

In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems, thermal-state preparation, simulation of time dynamics, adiabatic quantum simulation, and density functional theory.

quant-ph↗

arXiv2012

Exciton transport in thin-film cyanine dye J-aggregates

We present a theoretical model for the study of exciton dynamics in J-aggregated monolayers of fluorescent dyes. The excitonic evolution is described by a Monte-Carlo wave function approach which allows for a unified description of the quantum (ballistic) and classical (diffusive) propagation of an exciton on a lattice in different parameter regimes. The transition between the ballistic and diffusive regime is controlled by static and dynamic disorder. As an example, the model is applied to three cyanine dye J-aggregates: TC, TDBC, and U3. Each of the molecule-specific structure and excitation parameters are estimated using time-dependent density functional theory. The exciton diffusion coefficients are calculated and analyzed for different degrees of film disorder and are correlated to the physical properties and the structural arrangement of molecules in the aggregates. Further, exciton transport is anisotropic and dependent on the initial exciton energy. The upper-bound estimation of the exciton diffusion length in the TDBC thin-film J-aggregate is of the order of hundreds of nanometers, which is in good qualitative agreement with the diffusion length estimated from experiments.

physics.chem-ph↗

arXiv2011

Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet

Many interesting problems in physics, chemistry, and computer science are equivalent to problems of interacting spins. However, most of these problems require computational resources that are out of reach by classical computers. A promising solution to overcome this challenge is to exploit the laws of quantum mechanics to perform simulation. Several "analog" quantum simulations of interacting spin systems have been realized experimentally. However, relying on adiabatic techniques, these simulations are limited to preparing ground states only. Here we report the first experimental results on a "digital" quantum simulation on thermal states; we simulated a three-spin frustrated magnet, a building block of spin ice, with an NMR quantum information processor, and we are able to explore the phase diagram of the system at any simulated temperature and external field. These results serve as a guide for identifying the challenges for performing quantum simulation on physical systems at finite temperatures, and pave the way towards large scale experimental simulations of open quantum systems in condensed matter physics and chemistry.

quant-ph↗

arXiv2011

Spin Star as Switch for Quantum Networks

Quantum state transfer is an important task in quantum information processing. It is known that one can engineer the couplings of a one-dimensional spin chain to achieve the goal of perfect state transfer. To leverage the value of these spin chains, a spin star is potentially useful for connecting different parts of a quantum network. In this work, we extend the spin-chain engineering problem to the problems with a topology of a star network. We show that a permanently coupled spin star can function as a network switch for transferring quantum states selectively from one node to another by varying the local potentials only. Together with one-dimensional chains, this result allows applications of quantum state transfer be applied to more general quantum networks.

quant-ph↗

arXiv2011

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than classical computers.

quant-ph↗

arXiv2010

A Quantum-Quantum Metropolis Algorithm

Recently, the idea of classical Metropolis sampling through Markov chains has been generalized for quantum Hamiltonians. However, the underlying Markov chain of this algorithm is still classical in nature. Due to Szegedy's method, the Markov chains of classical Hamiltonians can achieve a quadratic quantum speedup in the eigenvalue gap of the corresponding transition matrix. A natural question to ask is whether Szegedy's quantum speedup is merely a consequence of employing classical Hamiltonians, where the eigenstates simply coincide with the computational basis, making cloning of the classical information possible. We solve this problem by introducing a quantum version of the method of Markov-chain quantization combined with the quantum simulated annealing (QSA) procedure, and describe explicitly a novel quantum Metropolis algorithm, which exhibits a quadratic quantum speedup in the eigenvalue gap of the corresponding Metropolis Markov chain for any quantum Hamiltonian. This result provides a complete generalization of the classical Metropolis method to the quantum domain.

quant-ph↗

arXiv2010

Simulation of Classical Thermal States on a Quantum Computer: A Transfer Matrix Approach

We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one at a time. We identify a class of classical models for which our method is efficient and avoids potential exponential overheads encountered by Grover-like or quantum Metropolis schemes. Our algorithm also gives an exponential advantage for 2D Ising models with magnetic field on a square lattice, compared with the previously known Zalka's algorithm.

quant-ph↗

arXiv2010

Simulating chemistry using quantum computers

The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.

quant-ph↗

arXiv2008

Thermal Noise on Adiabatic Quantum Computation

The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the minimal energy gap. However, at finite temperatures, it might need to be fast enough to avoid thermal excitations. The question is, how fast does it need to be? The structure of evolution Hamiltonians for AQC is generally too complicated for answering this question. Here we model an adiabatic quantum computer as a (parametrically driven) harmonic oscillator. The advantages of this model are (1) it offers high flexibility for quantitative analysis on the thermal effect, (2) the results qualitatively agree with previous numerical calculation, and (3) it could be experimentally verified with quantum electronic circuits.

quant-ph↗

arXiv2007

Independent Noise Approximation for Spin-Boson Decoherence

Quantum error correction is a solution to preserve the fidelity of quantum information encoded in physical systems subject to noise. However, unfavorable correlated errors could be induced even for non-interacting qubits through the environment (bath), when they are "packed" together. The question is, to what extent can we treat the noise induced by the bath as independent? In the context of the spin-boson model, we show that, under some reasonable constraints, the independent noise approximation could be valid. On the other hand, in the strongly correlated limit, we show how the method of decoherence free subspace can be made applicable. Combining these two methods makes fault-tolerant quantum computation promising in fighting against correlated errors.

quant-ph↗

arXiv2006

Quantum Speed Limit for Perfect State Transfer in One Dimension

The basic idea of spin chain engineering for perfect quantum state transfer (QST) is to find a set of coupling constants in the Hamiltonian, such that a particular state initially encoded on one site will evolve freely to the opposite site without any dynamical controls. The minimal possible evolution time represents a speed limit for QST. We prove that the optimal solution is the one simulating the precession of a spin in a static magnetic field. We also argue that, at least for solid-state systems where interactions are local, it is more realistic to characterize the computation power by the couplings than the initial energy.

quant-ph↗

arXiv2006

A Processor Core Model for Quantum Computing

We describe an architecture based on a processing 'core' where multiple qubits interact perpetually, and a separate 'store' where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the core, and free evolution of the core. This enables computation using physical systems where the entangling interactions are 'always on'. Alternatively, for switchable systems our model constitutes a prescription for optimizing many-qubit gates. We discuss implementations of the quantum Fourier transform, Hamiltonian simulation, and quantum error correction.

quant-ph↗

arXiv2005

Perfect State Transfer, Effective Gates and Entanglement Generation in Engineered Bosonic and Fermionic Networks

We show how to achieve perfect quantum state transfer and construct effective two-qubit gates between distant sites in engineered bosonic and fermionic networks. The Hamiltonian for the system can be determined by choosing an eigenvalue spectrum satisfying a certain condition, which is shown to be both sufficient and necessary in mirror-symmetrical networks. The natures of the effective two-qubit gates depend on the exchange symmetry for fermions and bosons. For fermionic networks, the gates are entangling (and thus universal for quantum computation). For bosonic networks, though the gates are not entangling, they allow two-way simultaneous communications. Protocols of entanglement generation in both bosonic and fermionic engineered networks are discussed.

quant-ph↗

arXiv2003

An exact effective two-qubit gate in a chain of three spins

We show that an effective two-qubit gate can be obtained from the free evolution of three spins in a chain with nearest neighbor XY coupling, without local manipulations. This gate acts on the two remote spins and leaves the mediating spin unchanged. It can be used to perfectly transfer an arbitrary quantum state from the first spin to the last spin or to simultaneously communicate one classical bit in each direction. One ebit can be generated in half of the time for state transfer. For longer spin chains, we present methods to create or transfer entanglement between the two end spins in half of the time required for quantum state transfer, given tunable coupling strength and local magnetic field. We also examine imperfect state transfer through a homogeneous XY chain.

quant-ph↗