Research On Benchmarking And Implementation Techniques Of Quantum Advantages

Quantum computing utilizes quantum mechanics for computation tasks and can be far more superior over its classical counterpart for some important computational problems.Quantum advantage,which is also called quantum supremacy2,represents that the quantum computers can beat any classical computers for some specific computational tasks.The realization of quantum advantages indicates that quantum computing has been developed from theory into demonstration,which is an important milestone towards building a universal quantum computer.Benchmarking the baseline for quantum advantage candidate tasks,which requires to evaluate the performance limit of classical computers on corresponding tasks,is a significantly crucial scientific problem within the research of quantum computing.In the meantime,the physical implementation of corresponding quantum system is the core of the demonstration of quantum advantages.Addressing this,this thesis focuses on three candidate tasks under different quantum computing models and goes into the classical benchmarking and implementation techniques.1.Under the quantum circuit model,the random quantum circuit sampling problem can show quantum advantages with circuits under fixed format,which is often used in the demonstration of quantum advantages on super-conducting quantum computing platforms.Focusing on random quantum circuit sampling problem,the work of this thesis is listed as follows.(1)We design and implement the general purpose quantum circuit simulator based on projected-entangled pair states and evaluate the benchmarking baseline of quantum advantages for the random quantum circuit sampling problem.Unlike the conventional quantum circuit simulators,the classical complexity of this simulator is related to the entanglement generation of the underlying quantum circuit rather than the number of qubits or gate operations.We apply this simulator to the simulation of random quantum circuit on Tianhe-2 supercomputer.The results and corresponding analysis reflect that simulating a circuit containing 8 × l(l ? 8)qubits and40 layers of commuting two-qubit quantum gates,or a circuit containing 10 × l(l ? 10)qubits and 32 layers of commuting two-qubit quantum gates is within the reach of current supercomputer platforms,which could serve as a benchmarking baseline for demonstrating quantum advantages.(2)We propose the method for quantum state tomography based on the variational quantum circuits,which is structurally similar to the random quantum circuits and can generate highly-entangled states.The information of the target state is extracted and then stored into the parameters of the variational quantum circuit.We demonstrate this method through numerical simulations.The results reflect that this method effectively decreases the number of quantum measurement as well as the copies of the target state from an exponential number to a polynomial number,and can obtain the information of the target state with high fidelity.2.Under the many-body quantum walk model,Boson sampling is promising to show quantum advantages,which is suitable for photonic quantum computing platform.Focusing on boson sampling problem,the contributions and innovations are summarized as follows.(1)We propose the Sample caching Markov chain Monte Carlo approach.This sampling method tackles the autocorrelation issue of the conventional Markov chain Monte Carlo method,as well as the sample loss caused by the autocorrelation issue.We apply this method to the boson sampling simulation,and the results indicate that this approach successfully generates approximately independent samples,and obtains a speedup of 100 times over the previously fastest general sampling method.(2)We evaluate the benchmarking baseline of advantages for boson sampling problem.We execute the massively parallel simulation of boson sampling on Tianhe-2 supercomputer,and compare the performance of the quantum boson sampling devices and classical simulators.The results indicate that the full system of Tianhe-2 supercomputer could generate a 50-photon sample in every ?100 minutes,which can be regarded as the benchmarking baseline of demonstrating quantum advantages by boson sampling.Moreover,the theoretical analysis suggests that currently,improving the transmission rate of photons could be a more effective way to approach quantum advantages compared with merely increasing the number of photons.3.Under the quantum randomness processing model,the quantum Bernoulli factory can show quantum advantages in the range of solvable problems,which can be demonstrated with readily-available quantum resources.Focusing on quantum Bernoulli factory problem,the contributions of this work are shown as follows.(1)We analyze the set of constructible functions in the quantum Bernoulli factory,and propose the algorithms for constructing arbitrary constructible states.We analyze the set of constructible states with arbitrary qubits,and study the impacts of the capabilities of different quantum processors on the quantum advantages.The analysis reflects that with the enhancement of the quantum processor,the efficiency of the process is enhanced and the resource consumption decreases.(2)We demonstrate the quantum Bernoulli factory on a photonic platform.We design the circuit and photonic logic of the basic operations within the quantum Bernoulli factory,and demonstrate these operations via an entangled 2-photon source and a reconfigurable photonic logic.Further,we demonstrate a classically hard example,and the results reflect that the quantum process can be two order of magnitudes faster and resource-saving than the classical process.