33 research outputs found

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

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    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

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    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

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    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

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    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

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    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
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