Dynamic decoupling (DD) can suppress decoherence caused by environmental noise, while in hybrid system it also hinders coherent manipulation between qubits. We realized the universal high-fidelity quantum gate set and the preparation of Bell states using dynamical decoupling gates (DD gates) in a silicon-based phosphorus-doped (Si:P) system, effectively resolving the contradiction between decoherence protection and manipulation of qubits. The simulation results show that the fidelity of the universal quantum gate set are all above 99%, and the fidelity of Bell state preparation is over 96%. This work realized the compatibility between coherent protection and high-fidelity manipulation of quantum states, provided a reliable theoretical support for high-fidelity quantum computing.
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum computing (AQC) is discussed. A performance comparison between two deterministic DD schemes is given, where preference towards one particular method is found due to sequence structure and procedure from which higher accuracy sequences are generated.
Environmental noise that couples longitudinally to a quantum system dephases that system and can limit its coherence lifetime. Performance using quantum superposition in clocks, information processors, communication networks, and sensors depends on careful state and external field selection to lower sensitivity to longitudinal noise. In many cases time varying external control fields--such as the Hahn echo sequence originally developed for nuclear magnetic resonance applications--can passively correct for longitudinal errors. There also exist continuous versions of passive correction called continuous dynamical decoupling (CDD), or spin-locking depending on context. However, treating quantum systems under CDD as qubits has not been well explored. Here, we develop universal single-qubit gates that are ``fast'' relative to perturbative Rabi gates and applicable to any CDD qubit architecture. We demonstrate single-qubit gates with fidelity
F=0.9947(1) on a frequency tunable CDD transmon superconducting circuit operated where it is strongly sensitive to longitudinal noise, thus establishing this technique as a potentially useful tool for operating qubits in applications requiring high fidelity under non-ideal conditions.
We investigate the possibility of achieving high-fidelity universal two-qubit gates by supplementing optimal tuning of individual qubits with dynamical decoupling (DD) of local
1/f noise. We consider simultaneous local pulse sequences applied during the gate operation and compare the efficiencies of periodic, Carr-Purcell, and Uhrig DD with hard $\ensuremath{\pi}$ pulses along two directions (${\ensuremath{\pi}}_{z/y}$ pulses). We present analytical perturbative results (Magnus expansion) in the quasistatic noise approximation combined with numerical simulations for realistic
1/f noise spectra. The gate efficiency is studied as a function of the gate duration, of the number
n of pulses, and of the high-frequency roll-off. We find that the gate error is nonmonotonic in
n, decreasing as ${n}^{\ensuremath{-}\ensuremath{\alpha}}$ in the asymptotic limit, $\ensuremath{\alpha}\ensuremath{\ge}2$, depending on the DD sequence. In this limit ${\ensuremath{\pi}}_{z}$-Urhig is the most efficient scheme for quasistatic
1/f noise, but it is highly sensitive to the soft UV cutoff. For small number of pulses, ${\ensuremath{\pi}}_{z}$ control yields anti-Zeno behavior, whereas ${\ensuremath{\pi}}_{y}$ pulses minimize the error for a finite
n. For the current noise figures in superconducting qubits, two-qubit gate errors $\ensuremath{\sim}{10}^{\ensuremath{-}6}$, meeting the requirements for fault-tolerant quantum computation, can be achieved. The Carr-Purcell-Meiboom-Gill sequence is the most efficient procedure, stable for
1/f noise with UV cutoff up to gigahertz.
A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of charge noise to well within an error bound of ${10}^{\ensuremath{-}3}$.
A scaled quantum computer with donor spins in silicon would benefit from a viable semiconductor framework and a strong inherent decoupling of the qubits from the noisy environment. Coupling neighboring spins via the natural exchange interaction according to current designs requires gate control structures with extremely small length scales. We present a silicon architecture where bismuth donors with long coherence times are coupled to electrons that can shuttle between adjacent quantum dots, thus relaxing the pitch requirements and allowing space between donors for classical control devices. An adiabatic SWAP operation within each donor/dot pair solves the scalability issues intrinsic to exchange-based two-qubit gates, as it does not rely on subnanometer precision in donor placement and is robust against noise in the control fields. We use this SWAP together with well established global microwave Rabi pulses and parallel electron shuttling to construct a surface code that needs minimal, feasible local control.