Quantum-enhanced Markov chain Monte Carlo.

Quantum computers promise to solve certain computational problems much faster than classical computers. However, current quantum processors are limited by their modest size and appreciable error rates. Recent efforts to demonstrate quantum speedups have therefore focused on problems that are both classically hard and naturally suited to current quantum hardware, such as sampling from complicated-although not explicitly useful-probability distributions1-3. Here we introduce and experimentally demonstrate a quantum algorithm that is similarly well suited to current hardware, but which samples from complicated distributions arising in several applications. The algorithm performs Markov chain Monte Carlo (MCMC), a prominent iterative technique4, to sample from the Boltzmann distribution of classical Ising models. Unlike most near-term quantum algorithms, ours provably converges to the correct distribution, despite being hard to simulate classically. But like most MCMC algorithms, its convergence rate is difficult to establish theoretically, so we instead analysed it through both experiments and simulations. In experiments, our quantum algorithm converged in fewer iterations than common classical MCMC alternatives, suggesting unusual robustness to noise. In simulations, we observed a polynomial speedup between cubic and quartic over such alternatives. This empirical speedup, should it persist to larger scales, could ease computational bottlenecks posed by this sampling problem in machine learning5, statistical physics6 and optimization7. This algorithm therefore opens a new path for quantum computers to solve useful-not merely difficult-sampling problems.

First-Order Trotter Error from a Second-Order Perspective.

Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near term are the simplest, which use the Trotter formula and its higher-order variants to approximate the dynamics of interest. The approximation error of these algorithms is often poorly understood, even in the most basic and topical cases where the target Hamiltonian decomposes into two realizable terms: H=H_{1}+H_{2}. Recent studies have reported anomalously low approximation error with unexpected scaling in such cases, which they attribute to quantum interference between the errors from different steps of the algorithm. Here, we provide a simpler picture of these effects by relating the Trotter formula to its second-order variant for such H=H_{1}+H_{2} cases. Our method generalizes state-of-the-art error bounds without the technical caveats of prior studies, and elucidates how each part of the total error arises from the underlying quantum circuit. We compare our bound to the true error numerically, and find a close match over many orders of magnitude in the simulation parameters. Our findings further reduce the required circuit depth for the least experimentally demanding quantum simulation algorithms, and illustrate a useful method for bounding simulation error more broadly.

Bias in Error-Corrected Quantum Sensing.

The sensitivity afforded by quantum sensors is limited by decoherence. Quantum error correction (QEC) can enhance sensitivity by suppressing decoherence, but it has a side effect: it biases a sensor's output in realistic settings. If unaccounted for, this bias can systematically reduce a sensor's performance in experiment, and also give misleading values for the minimum detectable signal in theory. We analyze this effect in the experimentally motivated setting of continuous-time QEC, showing both how one can remedy it, and how incorrect results can arise when one does not.

Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator.

Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.

Ancilla-Free Quantum Error Correction Codes for Quantum Metrology.

Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a specialized error-correcting code, as most existing codes correct away both the dominant errors and the signal. To date, however, few such specialized codes are known, among which most require noiseless, controllable ancillas. We show here that such ancillas are not needed when the signal Hamiltonian and the error operators commute, a common limiting type of decoherence in quantum sensors. We give a semidefinite program for finding optimal ancilla-free sensing codes in general, as well as closed-form codes for two common sensing scenarios: qubits undergoing dephasing, and a lossy bosonic mode. Finally, we analyze the sensitivity enhancement offered by the qubit code under arbitrary spatial noise correlations, beyond the ideal limit of orthogonal signal and noise operators.

Experimental validation of optimum input polarization states for Mueller matrix determination with a dual photoelastic modulator polarimeter.

Dual photoelastic modulator polarimeters can measure light polarization, which is often described as a Stokes vector. By evaluating changes in polarization when light interacts with a sample, the sample Mueller matrix also can be derived, completely describing its interaction with polarized light. The choice of which and how many input Stokes vectors to use for sample investigation is under the experimenter's control. Previous work has predicted that sets of input Stokes vectors forming the vertices of platonic solids on the Poincaré sphere allow for the most robust Mueller matrix determination. Further, when errors specific to the dual photoelastic modulator polarimeter are considered, simulations revealed that one specific shape and orientation of Stokes vectors (cube on the Poincaré sphere with vertices away from principal sphere axes) allows for the most robust Mueller matrix determination. Here we experimentally validate the optimum input Stokes vectors for dual photoelastic modulator Mueller polarimetry, toward developing a robust polarimetric platform of increasing relevance to biophotonics.