33 research outputs found

    Qudit-Basis Universal Quantum Computation using χ(2)\chi^{(2)} Interactions

    Full text link
    We prove that universal quantum computation can be realized---using only linear optics and χ(2)\chi^{(2)} (three-wave mixing) interactions---in any (n+1)(n+1)-dimensional qudit basis of the nn-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ(2)\chi^{(2)} Hamiltonians and photon-number operators generate the full u(3)\mathfrak{u}(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-ZZ gate can be implemented with only linear optics and χ(2)\chi^{(2)} interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection/subtraction, a technique enabled by χ(2)\chi^{(2)} interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.Comment: 9 pages, 3 figure

    Beyond Heisenberg Limit Quantum Metrology through Quantum Signal Processing

    Full text link
    Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a quantum-metrology method based on the quantum-signal-processing framework to overcome these realistic noise-induced limitations in practical quantum metrology. Our algorithm separates the gate parameter φ\varphi~(single-qubit Z phase) that is susceptible to time-dependent error from the target gate parameter θ\theta~(swap-angle between |10> and |01> states) that is largely free of time-dependent error. Our method achieves an accuracy of 10410^{-4} radians in standard deviation for learning θ\theta in superconducting-qubit experiments, outperforming existing alternative schemes by two orders of magnitude. We also demonstrate the increased robustness in learning time-dependent gate parameters through fast Fourier transformation and sequential phase difference. We show both theoretically and numerically that there is an interesting transition of the optimal metrology variance scaling as a function of circuit depth dd from the pre-asymptotic regime d1/θd \ll 1/\theta to Heisenberg limit dd \to \infty. Remarkably, in the pre-asymptotic regime our method's estimation variance on time-sensitive parameter φ\varphi scales faster than the asymptotic Heisenberg limit as a function of depth, Var(φ^)1/d4\text{Var}(\hat{\varphi})\approx 1/d^4. Our work is the first quantum-signal-processing algorithm that demonstrates practical application in laboratory quantum computers

    Finite-key analysis for time-energy high-dimensional quantum key distribution

    Get PDF
    Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.United States. Office of Naval Research (Grant N00014- 13-1-0774)United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0052)Natural Sciences and Engineering Research Council of Canada (Postdoctoral Fellowship

    Unity-Efficiency Parametric Down-Conversion via Amplitude Amplification

    Get PDF
    We propose an optical scheme, employing optical parametric down-converters interlaced with nonlinear sign gates (NSGs), that completely converts an n-photon Fock-state pump to n signal-idler photon pairs when the down-converters’ crystal lengths are chosen appropriately. The proof of this assertion relies on amplitude amplification, analogous to that employed in Grover search, applied to the full quantum dynamics of single-mode parametric down-conversion. When we require that all Grover iterations use the same crystal, and account for potential experimental limitations on crystal-length precision, our optimized conversion efficiencies reach unity for 1 ≤ n ≤ 5, after which they decrease monotonically for n values up to 50, which is the upper limit of our numerical dynamics evaluations. Nevertheless, our conversion efficiencies remain higher than those for a conventional (no NSGs) down-converter

    Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network

    Full text link
    Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our decoder outperforms state-of-the-art algorithmic decoders on real-world data from Google's Sycamore quantum processor for distance 3 and 5 surface codes. On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk, leakage, and analog readout signals, and sustains its accuracy far beyond the 25 cycles it was trained on. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers