Quantum Computation
Quantum Error Correction
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow straightforward gate implementation needed for data processing. To exploit the particular advantages of different topological codes for fault-tolerant quantum computation, it is necessary to be able to switch between them.
A practical solution to this problem is subsystem lattice surgery [Hendrik Poulsen Nautrup, Nicolai Friis, and Hans J. Briegel, Nat. Commun. 8, 1321 (2017)], which requires only two-body nearest-neighbor interactions in a fixed layout in addition to the indispensable error correction. This method can be used for the fault-tolerant transfer of quantum information between arbitrary topological subsystem codes in two dimensions and beyond. In particular, it can be employed to create a simple interface, a quantum bus, between noise resilient surface code memories and flexible color code processors. A first experimental demonstration of using this technique to entangled two logical qubits encoded in two topological codes has been carried out in [Alexander Erhard, Hendrik Poulsen Nautrup, et al., Nature 589, 220-224 (2021)]. |
Black-Box Subroutines -- Coherent controlization in trapped-ion qubits
Trapped ions are one of the most promising candidates to implement quantum computational tasks. Seminal theoretical proposals such as [Cirac, Zoller, Phys. Rev. Lett. 74, 4091 (1995)], and [Mølmer, Sørensen, Phys. Rev. Lett. 82, 1835 (1999)], paired with the precise control of modern ion-trap setups [see, e.g., Schmidt-Kaler et al., Nature 422, 408 (2003); Barreiro et al., Nature 470, 486 (2011)] allow universal quantum computation with several qubits, represented by the internal energy levels of the ions. In other words, discrete universal sets of quantum gates can be realized, and any arbitrary quantum gate may be approximated by sequentially applying a combination of the universal gates.
However, an apparent issue arises when an unknown operation -a black box- is introduced into this picture. It was shown in [Araújo, Feix, Costa, Brukner, New J. Phys. 16 093026 (2014), arXiv:1309.7976] and [Thompson, Gu, Modi, Vedral, New J. Phys. 20, 013004 (2018), arXiv:1310.2927] that inserting a single unknown subroutine U into a quantum circuit that is independent of U, cannot realize ctrl-U, i.e., a single operation U may not generally be conditioned on the value of a control qubit. Nonetheless, control can be added when the "single use" of the unknown operation is interpreted in practical terms, for instance, when a single physical device is provided that acts on internal degrees of freedom of a photon [see Zhou, Ralph, Kalasuwan, Zhang, Peruzzo, Lanyon, O'Brien, Nat. Commun. 2, 413 (2011)]. |
In our paper [Friis, Dunjko, Dür, Briegel, Phys. Rev. A 89, 030303(R) (2014), e-print arXiv:1401.8128] we show how the techniques for quantum computation with trapped ions can be harnessed to allow quantum control to be added to arbitrary, unknown single-qubit unitaries U that are realized by a single laser pulse on a single trapped ion. By using the famous method of Cirac and Zoller [Phys. Rev. Lett. 74, 4091 (1995)] the state of the control qubit, realized in one ion, is swapped to the axial centre-of-mass vibrational mode of two ions, see the Figure above. The ground state |0> and excited state |1> of the vibrational mode generate two submanifolds within the ions electronic levels. Two red-detuned laser pulses, H1 and H2, are then used to "hide" one of these manifolds from the laser pulse realizing the unknown unitary U, which drives the transition between the qubit levels |g> and |e>.
Black-Box Subroutines -- Coherent controlization using superconducting qubits
In [Friis, Melnikov, Kirchmair, Briegel, Sci. Rep. 5, 18036 (2015)] we have found an in principle scalable method to implement coherent controlization in a system of superconducting transmon qubits. These systems, which are very resilient against charge noise, see [Koch et al., Phys. Rev. A 76, 042319 (2007)] have long coherence times (roughly up to 100μs) and are therefore a promising system. Coupling transmon qubits to a microwave resonator then allows to split and recombine resonator state components that correspond to different qubits states (coloured circles in the figure on the right). Using unconditional displacements D(α), waiting periods Δt and single-qubit unitaries U(θ) that are conditioned on the ground state of the resonator, we can then add control to these single-qubit unitaries, realizing the circuits shown below, or construct more complicated conditioned operations.
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