It is difficult to simulate quantum systems on classical computers, while quantum computers have been proved to be able to efficiently perform such kinds of simulations. We report an NMR implementation simulating the hydrogen molecule (H2) in a minimal basis to obtain its ground-state energy. Using an iterative NMR interferometer to measure the phase shift, we achieve a 45-bit estimation of the energy value. The efficiency of the adiabatic state preparation is also experimentally tested with various configurations of the same molecule.

The fundamental principle of artificial intelligence is the ability of machines to learn from previous experience and do future work accordingly. In the age of big data, classical learning machines often require huge computational resources in many practical cases. Quantum machine learning algorithms, on the other hand, could be exponentially faster than their classical counterparts by utilizing quantum parallelism. Here, we demonstrate a quantum machine learning algorithm to implement handwriting recognition on a four-qubit NMR test bench. The quantum machine learns standard character fonts and then recognizes handwritten characters from a set with two candidates. Because of the wide spread importance of artificial intelligence and its tremendous consumption of computational resources, quantum speedup would be extremely attractive against the challenges of big data.

We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shor's algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical simulations indicate that the running time grows only quadratically with the number of qubits. While Shor's algorithm and its experimental implementation are based on the circuit (or network) model of quantum computing, different models have been proposed later. Here, we consider the adiabatic quantum computing model proposed by Farhi et al [8], The basis of this model is the quantum adiabatic theorem: A quantum system remains in its instantaneous eigenstate if the system Hamiltonian varies slowly enough and if there is a gap between this eigenvalue and the rest of the Hamiltonian's spectrum [9,10]. It has been proved to be equivalent to the conventional circuit model [11]. Several adiabatic quantum algorithms have been discussed, such as 3SAT and search of unstructured databases [8,12,13]. Compared to the network model, the adiabatic scheme appears to offer lower sentivitiy to some perturbations and thus improved robustness against errors due to dephasing, environmental noise and some unitary control errors [14,15].In this paper, we propose a factorization algorithm that uses the adiabatic approach to quantum information processing. We also implement this algorithm experimentally, using nuclear spin qubits to factorize the number 21.There is a large class of numerical problems that can be brought into the form of an optimization problem. Many of them form hard problems. The quantum adiabatic computation supplies a possible method for solving these problems. It requires an initial Hamiltonian H 0 whose ground state ψ g (0) is well known, and a problem Hamiltonian H P , whose ground state encodes the solution of the optimization problem. Implementing this method requires one to first prepare the system into the ground state of H 0 at t = 0. Subsequently, the Hamiltonian is changed, slowly enough for fulfilling the adiabatic condition, until it is turned into the problem Hamiltonian H P after a time T . In the simplest case, the change of the Hamiltonian is realized by an interpolation schemewhere the function s(t) : 0 → 1 parametrizes the interpolation. The solution of the optimization problem is then determined by measuring the final ground state ψ g (T ) of H P . We now apply this approach to find nontrivial prime factors of an ℓ-digit integer N = p × q where p and q are prime numbers. Without loss of generality, we assume that N is odd (in case of even N , we could repeatedly divide N