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Modern computation relies crucially on modular architectures, breaking a complex algorithm into self-contained subroutines. A client can then call upon a remote server to implement parts of the computation independently via an application programming interface (API). Present APIs relay only classical information. Here we implement a quantum API that enables a client to estimate the absolute value of the trace of a server-provided unitary $U$. We demonstrate that the algorithm functions correctly irrespective of what unitary $U$ the server implements or how the server specifically realizes $U$. Our experiment involves pioneering techniques to coherently swap qubits encoded within the motional states of a trapped Yb ion, controlled on its hyperfine state. This constitutes the first demonstration of modular computation in the quantum regime, providing a step towards scalable, parallelization of quantum computation.
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The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes which can be described by continuous variables in an infinite dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian $|erangle langle e| ( a^{dagger} b + a b^{dagger})$ that swaps the quantum states of two motional modes, depending on the ions internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.
Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from being affordable for near-term technologies. To alleviate the detrimental effects of errors, quantum error mitigation techniques have been proposed, which require no additional qubit resources. Here, we benchmark the performance of a quantum error mitigation technique based on probabilistic error cancellation in a trapped-ion system. Our results clearly show that effective gate fidelities exceed physical fidelities, i.e. we surpass the break-even point of eliminating gate errors, by programming quantum circuits. The error rates are effectively reduced from $(1.10pm 0.12)times10^{-3}$ to $(1.44pm 5.28)times10^{-5}$ and from $(0.99pm 0.06)times10^{-2}$ to $(0.96pm 0.10)times10^{-3}$ for single- and two-qubit gates, respectively. Our demonstration opens up the possibility of implementing high-fidelity computations on a near-term noisy quantum device.
We present a cryogenic ion trapping system designed for large scale quantum simulation of spin models. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap over 100 $^{171}$Yb$^+$ ions in a linear configuration for hours due to a low background gas pressure from differential cryo-pumping. We characterize the cryogenic vacuum by using trapped ion crystals as a pressure gauge, measuring both inelastic and elastic collision rates with the molecular background gas. We demonstrate nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials. This reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of spin models that are intractable with classical computer modelling.
Scaling-up from prototype systems to dense arrays of ions on chip, or vast networks of ions connected by photonic channels, will require developing entirely new technologies that combine miniaturized ion trapping systems with devices to capture, transmit and detect light, while refining how ions are confined and controlled. Building a cohesive ion system from such diverse parts involves many challenges, including navigating materials incompatibilities and undesired coupling between elements. Here, we review our recent efforts to create scalable ion systems incorporating unconventional materials such as graphene and indium tin oxide, integrating devices like optical fibers and mirrors, and exploring alternative ion loading and trapping techniques.
Molecules are the most demanding quantum systems to be simulated by quantum computers because of their complexity and the emergent role of quantum nature. The recent theoretical proposal of Huh et al. (Nature Photon., 9, 615 (2015)) showed that a multi-photon network with a Gaussian input state can simulate a molecular spectroscopic process. Here, we report the first experimental demonstration of molecular vibrational spectroscopy of SO$_{2}$ with a trapped-ion system. In our realization, the molecular scattering operation is decomposed to a series of elementary quantum optical operations, which are implemented through Raman laser beams, resulting in a multimode Gaussian (Bogoliubov) transformation. The molecular spectroscopic signal is reconstructed from the collective projection measurements on phonon modes of the trapped-ion system. Our experimental demonstration would pave the way to large-scale molecular quantum simulations, which are classically intractable.
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