Polar molecules are an emerging platform for quantum technologies based on their long-range electric dipole-dipole interactions, which open new possibilities for quantum information processing and the quantum simulation of strongly correlated systems. Here, we use magnetic and microwave fields to design a fast entangling gate with >0.999 fidelity and which is robust with respect to fluctuations in the trapping and control fields and to small thermal excitations. These results establish the feasibility to build a scalable quantum processor with a broad range of molecular species in optical-lattice and optical-tweezers setups.

Cooling the qubit into a pure initial state is crucial for realizing fault-tolerant quantum information processing. Here we envisage a star-topology arrangement of reset and computation qubits for this purpose. The reset qubits cool or purify the computation qubit by transferring its entropy to a heat-bath with the help of a heat-bath algorithmic cooling procedure. By combining standard NMR methods with powerful quantum control techniques, we cool central qubits of two large startopology systems, with 13 and 37 spins respectively. We obtain polarization enhancements by a factor of over 24, and an associated reduction in the spin temperature from 298 K down to 12 K. Exploiting the enhanced polarization of computation qubit, we prepare combination-coherences of orders up to 15. By benchmarking the decay of these coherences we investigate the underlying noise process. Further, we also cool a pair of computation qubits and subsequently prepare them in an effective pure-state.

A robust control over quantum dynamics is of paramount importance for quantum technologies. Many of the existing control techniques are based on smooth Hamiltonian modulations involving repeated calculations of basic unitaries resulting in time complexities scaling rapidly with the length of the control sequence. On the other hand, the bang-bang controls need one-time calculation of basic unitaries and hence scale much more efficiently. By employing a global optimization routine such as the genetic algorithm, it is possible to synthesize not only highly intricate unitaries, but also certain nonunitary operations. Here we demonstrate the unitary control through the first implementation of the optimal fixed-point quantum search algorithm in a three-qubit NMR system. More over, by combining the bang-bang pulses with the twirling process, we also demonstrate a nonunitary transformation of the thermal equilibrium state into an effective pure state in a five-qubit NMR system.

Since 2005 there has been a huge growth in the use of engineered control pulses to perform desired quantum operations in systems such as NMR quantum information processors. These approaches, which build on the original gradient ascent pulse engineering (GRAPE) algorithm, remain computationally intensive because of the need to calculate matrix exponentials for each time step in the control pulse. Here we discuss how the propagators for each time step can be approximated using the Trotter-Suzuki formula, and a further speed up achieved by avoiding unnecessary operations. The resulting procedure can give a substantial speed gain with negligible cost in propagator error, providing a more practical approach to pulse engineering. PACS numbers:Quantum information processors encode information in two-level quantum systems (qubits) and manipulate this through a series of elementary unitary transformations (quantum logic gates) [1,2]. Quantum control seeks to implement some target unitary propagator U in a quantum system with background Hamiltonian H 0 by applying some time-dependent Hamiltonian H 1 (t). The resulting operator can be written aswhere T is the Dyson time-ordering operator. To make progress beyond this formal solution it is usually necessary to replace this continuously varying Hamiltonian by a piecewise constant form, so thatand to write the time-varying portion of the Hamiltonian as a weighted sum of a set of p distinct control fieldsAny particular control pulse can then be described by the corresponding set of amplitudes, a k j , and the time step δt, here taken as fixed. The quality of a control pulse can be measured by its fidelity with the desired operation Uwhere the Hilbert-Schmidt inner product is defined by U |V = tr(U † V ), possibly normalised by the dimension of the operators [2]. The optimal control problem is then to find the set of amplitudes which maximises this fidelity, usually in the presence of practical constraints on the magnitudes of the amplitudes and the total length * Electronic address: jonathan.jones@physics.ox.ac.uk of the sequence. This is computationally challenging as the dimension of the underlying Hilbert space rises exponentially with the number of qubits to be controlled, although this difficulty can in some cases be reduced by using subsystems to simplify the calculations [3]. One recent approach [4] is to use subsystem methods to find approximate control pulses and then optimise these directly using the quantum system itself. Whatever approach is adopted, it is important to perform any computations as efficiently as possible.

The task of testing whether quantum theory applies to all physical systems and all scales requires considering situations where a quantum probe interacts with another system that need not obey quantum theory in full. Important examples include the cases where a quantum mass probes the gravitational field, for which a unique quantum theory of gravity does not yet exist, or a quantum field, such as light, interacts with a macroscopic system, such as a biological molecule, which may or may not obey unitary quantum theory. In this context a class of experiments has recently been proposed, where the non-classicality of a physical system that need not obey quantum theory (the gravitational field) can be tested indirectly by detecting whether or not the system is capable of entangling two quantum probes. Here we illustrate some of the subtleties of the argument, to do with the role of locality of interactions and of non-classicality, and perform proof-of-principle experiments illustrating the logic of the proposals, using a Nuclear Magnetic Resonance quantum computational platform with four qubits. OPEN ACCESS RECEIVED