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There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.
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We consider the implementation of two-qubit gates when the physical systems used to realize the qubits are weakly anharmonic and therefore possess additional quantum states in the accessible energy range. We analyze the effect of the additional quantum states on the maximum achievable speed for quantum gates in the qubit state space. By calculating the minimum gate time using optimal control theory, we find that higher energy levels can help make two-qubit gates significantly faster than the reference value based on simple qubits. This speedup is a result of the higher coupling strength between higher energy levels. We then analyze the situation where the pulse optimization algorithm avoids pulses that excite the higher levels. We find that in this case the presence of the additional states can lead to a significant reduction in the maximum achievable gate speed. We also compare the optimal control gate times with those obtained using the cross-resonance/selective-darkening gate protocol. We find that the latter, with some parameter optimization, can be used to achieve a relatively fast implementation of the CNOT gate. These results can help the search for optimized gate implementations in realistic quantum computing architectures, such as those based on superconducting qubits. They also provide guidelines for desirable conditions on anharmonicity that would allow optimal utilization of the higher levels to achieve fast quantum gates.
Most ions lack the fast, cycling transitions that are necessary for direct laser cooling. In most cases, they can still be cooled sympathetically through their Coulomb interaction with a second, coolable ion species confined in the same potential. If the charge-to-mass ratios of the two ion types are too mismatched, the cooling of certain motional degrees of freedom becomes difficult. This limits both the achievable fidelity of quantum gates and the spectroscopic accuracy. Here we introduce a novel algorithmic cooling protocol for transferring phonons from poorly- to efficiently-cooled modes. We demonstrate it experimentally by simultaneously bringing two motional modes of a Be$^{+}$-Ar$^{13+}$ mixed Coulomb crystal close to their zero-point energies, despite the weak coupling between the ions. We reach the lowest temperature reported for a highly charged ion, with a residual temperature of only $Tlesssim200~mathrm{mu K}$ in each of the two modes, corresponding to a residual mean motional phonon number of $langle n rangle lesssim 0.4$. Combined with the lowest observed electric field noise in a radiofrequency ion trap, these values enable an optical clock based on a highly charged ion with fractional systematic uncertainty below the $10^{-18}$ level. Our scheme is also applicable to (anti-)protons, molecular ions, macroscopic charged particles, and other highly charged ion species, enabling reliable preparation of their motional quantum ground states in traps.
Quantum annealing is an optimization technique which potentially leverages quantum tunneling to enhance computational performance. Existing quantum annealers use superconducting flux qubits with short coherence times, limited primarily by the use of large persistent currents $I_mathrm{p}$. Here, we examine an alternative approach, using qubits with smaller $I_mathrm{p}$ and longer coherence times. We demonstrate tunable coupling, a basic building block for quantum annealing, between two flux qubits with small ($sim 50~mathrm{nA}$) persistent currents. Furthermore, we characterize qubit coherence as a function of coupler setting and investigate the effect of flux noise in the coupler loop on qubit coherence. Our results provide insight into the available design space for next-generation quantum annealers with improved coherence.
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We theoretically investigate a possibility to establish multi-qubit quantum correlations in one-dimensional chains of qubits. We combine a reservoir engineering strategy with coherent dynamics to generate multi-qubit entangled states. We find that an interplay between the coherent and incoherent dynamics result in the generation of stable (time-independent) many-body entangled steady states. Our results will be relevant in the context of the dissipative generation of quantum states, with applications in short-distance quantum computation and for exploring the emergence of collective phenomena in many-body open quantum systems.
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