Bulletin of the American Physical Society
APS March Meeting 2021
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session A33: Noise Reduction and Error Mitigation in Quantum Computing IFocus Live

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Sponsoring Units: DQI Chair: Peter Johnson, Zapata Computing Inc 
Monday, March 15, 2021 8:00AM  8:12AM 
A33.00001: Algorithmic Error Mitigation Scheme for Current Quantum Processors Philippe Suchsland, Francesco Tacchino, Mark Fischer, Titus Neupert, Panagiotis Barkoutsos, Ivano Tavernelli We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos diagonalization method. This procedure can simultaneously reduce the impact of different sources of noise and potentially increase the quality of quantum circuit ansatzes employed in the solution of variational problems. Based on a solid mathematical framework, the proposed approach ensures consistency with the underlying physical principles, thus leading to reliable results and controllable fluctuations. Our protocol only requires an increase in the number of observables to be measured on the target circuit and, in contrast with other error mitigation schemes, it does not involve direct access to the hardware or the calibration of dedicated control pulses. Through numerical simulations and experiments on IBM Quantum superconducting hardware we demonstrate that this algorithm can be applied to a general class of quantum chemistry and physics models, crucially allowing for the reconstruction of nontrivial ground state properties and enhancing the accuracy of energy estimations beyond stateoftheart results. 
Monday, March 15, 2021 8:12AM  8:24AM Live 
A33.00002: Mitigating realistic noise in practical noisy intermediatescale quantum devices Suguru Endo, jinzhao sun, Takahiro Tsunoda, Vlatko Vedral, Simon Charles Benjamin, Xiao Yuan Quantum error mitigation (QEM) is vital for noisy intermediatescale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gatebased circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gatedependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we show it can be effectively suppressed by a novel stochastic QEM method. Since our method only assumes accurate single qubit controls, it is applicable to all digital quantum computers and various analog simulators. Meanwhile, errors in the mitigation procedure can be suppressed by leveraging the Richardson extrapolation method. As we numerically test our method with various Hamiltonians under energy relaxation and dephasing noise and digital quantum circuits with additional twoqubit crosstalk, we show an improvement of simulation accuracy by two orders. 
Monday, March 15, 2021 8:24AM  8:36AM Live 
A33.00003: Improved quasiprobabilistic quantum error mitigation Christophe Piveteau, David Sutter, Stefan Woerner Quantum error mitigation techniques promise to suppress noise on current smallscale hardware, without the need for faulttolerant quantum error correction. One method in this family of mitigation techniques is the quasiprobability method that simulates a noisefree quantum computer with a noisy one, with the caveat of only producing the correct expected values of measurement observables. The cost of a quasiprobability simulation manifests as a sampling overhead which scales exponentially in the number of errormitigated gates in the circuit. In this work, we present two novel approaches to reduce the exponential basis of that overhead. First, we introduce a robust quasiprobability method that allows for a tradeoff between the approximation error and the sampling overhead via semidefinite programming. Second, we derive a new algorithm based on mathematical optimization that aims to choose the quasiprobability decomposition in a noiseaware manner. Both techniques lead to a significantly lower overhead compared to existing approaches. 
Monday, March 15, 2021 8:36AM  8:48AM Live 
A33.00004: Scalable Quantum Computing on a Noisy Superconducting Quantum Processor via Randomized Compiling Akel Hashim, Ravi K. Naik, Alexis Morvan, JeanLoup Ville, Brad Mitchell, John Mark Kreikebaum, Marc Davis, Ethan Smith, Costin Iancu, Kevin O'Brien, Ian Hincks, Joel Wallman, Joseph V Emerson, David Ivan Santiago, Irfan Siddiqi Coherent errors in quantum hardware severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable, largescale quantum computations. Randomized compiling achieves this goal by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of aggregate performance via cycle benchmarking estimates. In this work, we demonstrate significant performance gains under randomized compiling for both the fourqubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. We also validate solution accuracy using experimentallymeasured error rates. Our results demonstrate that randomized compiling can be utilized to maximallyleverage and predict the capabilities of modernday noisy quantum processors, paving the way forward for scalable quantum computing. 
Monday, March 15, 2021 8:48AM  9:00AM Live 
A33.00005: Error mitigation via verified phase estimation Thomas O'Brien, Stefano Polla, Nicholas Rubin, William Huggins, Sam McArdle, Sergio Boixo, Jarrod McClean, Ryan Babbush The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. This paper presents a new error mitigation technique based on quantum phase estimation that can also reduce errors in expectation value estimation (e.g., for variational algorithms). The general idea is to apply phase estimation while effectively postselecting for the system register to be in the starting state, which allows us to catch and discard errors which knock us away from there. We show that this "verified phase estimation" (VPE) technique can be adapted to function without the use of control qubits in order to simplify the control circuitry for nearterm implementations. We apply this technique to simulations of intermediate scale quantum circuits wand show multiple orders of magnitude improvement over unmitigated estimation at nearterm error rates. Our results suggest that VPE can mitigate against single errors that occur  the error in the estimated expectation values often scale as O(p^2), where p is the probability of an error occurring at any point in the circuit. This property, combined with robustness to sampling noise, shows VPE a practical technique for mitigating errors in nearterm quantum experiments. 
Monday, March 15, 2021 9:00AM  9:12AM Live 
A33.00006: Leveraging Randomized Compiling for the QITE Algorithm JeanLoup Ville, Alexis Morvan, Akel Hashim, Ravi K. Naik, Brad Mitchell, John Mark Kreikebaum, Kevin O'Brien, Marc Davis, Ethan Smith, Ed Younis, Costin Iancu, Ian Hincks, Joel Wallman, Joseph V Emerson, David Ivan Santiago, Irfan Siddiqi Recent progress on quantum hardware has enabled the successful implementation of quantum algorithms to simulate small molecules or textbook condensed matter models on a limited number of qubits. The results of quantum algorithms executed on such NISQ hardware are, however, limited by the remaining noise, mainly on the multiqubit gates. Randomized compiling has recently been shown to mitigate the coherent part of the noise to, easier to handle, stochastic noise. In this work, we implement a new noisemitigation technique, taking advantage of the noise tailoring property of randomized compiling, and then compensating for the stochastic noise. We apply this method to the quantum imaginary time evolution (QITE) algorithm which has attracted a lot of attention recently and is very sensitive to the measurement of expectation values, making it a good benchmark for our scheme. Our method is simple to implement and does not require any additional hardware. 
Monday, March 15, 2021 9:12AM  9:24AM Live 
A33.00007: Simulating the FermiHubbard model on Google's superconducting quantum processor Zhang Jiang, Vadim Smelyanskiy Strongly correlated quantum systems give rise to many exotic physical phenomena, including hightemperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the onedimensional FermiHubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of errormitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 twoqubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices. 
Monday, March 15, 2021 9:24AM  10:00AM Live 
A33.00008: Error mitigating NISQ chemistry computations Invited Speaker: Nicholas Rubin

Monday, March 15, 2021 10:00AM  10:12AM Live 
A33.00009: Quantumassisted NMR Inference on Noisy Rydberg Atom Devices Sambuddha Chattopadhyay, Dries Sels, Eugene Demler Inferring molecular parameters from NMR spectra, an important task in the biomedical sciences, is a computationally challenging task. Hybrid quantumclassical approaches on nearterm devices could make NMR inference tractable. A recent proposal couples quantum computation of the NMR spectra of hypothetical molecules with machine learning to optimize molecular parameters of small molecules [1]. With an eye towards implementing this hybrid approach, we study Hamiltonian simulation on NISQ Rydberg atom devices. Specifically, we construct an experimentally realistic error model for Rydberg atoms and use it to optimize protocols which balance hardware error with Trotterization error to achieve highfidelity Hamiltonian simulation for spectral computation. On the learning side, we study the proliferation of spurious local minima in the NMR inference landscape of an exactly solvable model. Our approach provides an analytical lens into the barren plateaus problem for NMR inference. 
Monday, March 15, 2021 10:12AM  10:24AM Live 
A33.00010: Effectiveness of errormitigation techniques for VQE under realistic noise sources José Solís, Armando Aguilar, Russell Batista, Roberto Gonzalez, Mauricio Gutierrez It is estimated that NISQ technology will become a reality in the near future, and with its arrival, some light will be shed over the standing conjecture that the threshold of useful quantum supremacy lies somewhere between 50 and 100 qubits. This intermediate scale is however insufficient to attain faulttolerance. Hybrid quantumclassical algorithms, like the Variational Quantum Eigensolver (VQE) and errormitigation techniques might become a necessity to produce meaningful calculations. We perform full densitymatrix simulations of the VQE algorithm to estimate the electronic ground state energies of small molecules and study the effectiveness of various error mitigation techniques to reduce the deleterious impact of different realistic noise sources. We focus on noise sources relevant to trappedion and spin qubits. We determine the resources needed to perform proofofconcept VQEbased quantum chemical calculations on nearterm quantum computers. 
Monday, March 15, 2021 10:24AM  10:36AM Live 
A33.00011: Error Mitigation Via Emulated Measurement of Stabilizers Amy Greene, Morten Kjaergaard, Gabriel O Samach, Mollie Schwartz, Andreas Bengtsson, Chris McNally, Michael O'Keeffe, David K Kim, Milad Marvian, Alexander Melville, Bethany Niedzielski, Antti Vepsalainen, Roni Winik, Jonilyn Yoder, Danna Rosenberg, Seth Lloyd, Terry Philip Orlando, Iman Marvian, Simon Gustavsson, William Oliver While closedloop control is the ideal for quantum error correction, openloop techniques are more accessible given current technologies. Dynamical decoupling is the goto error mitigation technique, but many of the noise mechanisms encountered in experimental implementations, such as microwave crosstalk or coherent gate errors, are not amenable to simple dynamical decoupling schemes. An alternative technique for these errors is to emulate measurement of stabilizer operators via the stochastic application of gates from the set of stabilizers. We demonstrate the errormitigating effects of this emulated quantum measurement protocol on a small superconducting qubit processor. 
Monday, March 15, 2021 10:36AM  10:48AM On Demand 
A33.00012: Measurement Error Mitigation for Variational Quantum Algorithms George S Barron, Christopher J Wood Variational Quantum Algorithms (VQAs) are a promising application for nearterm quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal with noise that can be applied to these algorithms. Recent work introduced a technique for mitigating expectation values against correlated measurement errors that can be applied to measurements of 10s of qubits. We apply these techniques to VQAs and demonstrate its effectiveness in improving estimates to the cost function. Moreover, we use the data resulting from this technique to experimentally characterize measurement errors in terms of the device connectivity on devices of up to 20 qubits. These results should be useful for better understanding the nearterm potential of VQAs as well as understanding the correlations in measurement errors on large, nearterm devices. 
Monday, March 15, 2021 10:48AM  11:00AM On Demand 
A33.00013: Noise reconstruction in quantum hardware via convex optimization Li Li, Harry James Slatyer, Harrison Ball, Michael Hush, Michael Biercuk, Alistair R Milne, Cornelius Hempel, Claire L Edmunds Interactions between a quantum system and noisy control hardware, or its environment, critically limits the performance and capabilities of noisy intermediatescale quantum (NISQ) devices, as well as future quantum computing technologies. Accurately characterizing the noise profile of these systems is of central importance in developing techniques to improve hardware performance. This includes detailed microscopic characterization of timedependent noise processes. We introduce a novel machinelearning technique allowing the efficient, flexible, and quantitatively accurate reconstruction of a noise process’s frequencyresolved power spectral density. By reformatting PSD reconstruction based on a measurement record as a convex optimization problem, our algorithm does not need to assume any specific shape of the noise spectral and can easily incorporate physicallymotivated constraints for reconstruction without the loss of numerical efficiency. Moreover, this technique permits reconstruction using an arbitrary set of measurements, relaxing constraints previously imposed to limit the introduction of numerical artefacts. We present details of the approach as well as experimental demonstrations of trappedion motionalmode noise characterization via spinmotional entanglement. 
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