Session Z36: Noise Reduction and Error Mitigation in Quantum Computing IV

Error Filtration for Quantum Computation

Efficient suppression of errors without error correction is crucial for applications with NISQ devices. Error mitigation allows us to suppress errors in measuring expectation values without the need for any error correction code, but its applications are limited because it does not provide us with high-fidelity quantum operations acting on arbitrary quantum states. To address this challenge, we propose to use error filtration (EF) for gate-based quantum computation, as a practical error suppression scheme without resorting to full quantum error correction. We further analyze the application of EF to quantum random access memory, where EF offers a hardware-efficient error suppression scheme.   

Noise reduction in quantum simulations of scalar QED via qudit encodings

This work examines the robustness against noise for real-time simulations of quantum field theories using emulations of noisy qubit and qudit quantum computers with similar native gate sets. We will compare the robustness of the qubit and qudit encodings to demonstrate the improvements qudit based hardware could provide for small scale simulations in the NISQ era.   

Neural Error Mitigation of Near-Term Quantum Simulations

While variational methods for NISQ devices, such as VQE, are promising approaches to finding ground states of quantum systems relevant in physics, chemistry, and materials science, they are constrained by the effects of noise and device limitations, which motivates application of error mitigation techniques. We introduce neural error mitigation (NEM), a novel method that uses quantum many-body machine learning techniques to improve estimates of ground states and their observables obtained using VQE on noisy quantum devices. We apply NEM to finding molecular and lattice gauge theory ground states, and show that it improves numerical and experimental VQE results to yield low energy errors and infidelities, and accurate estimations of more complex observables, without requiring additional quantum resources. NEM is agnostic to the type of quantum hardware and the particular noise channel, and is therefore a promising versatile strategy for extending the reach of near-term quantum computers to solve complex quantum simulation problems.   

Error-mitigation techniques for quantum simulations of spin defects on quantum computers

Recently, we formulated a quantum defect embedding theory [1,2] for hybrid classical-quantum calculations of the electronic structure of spin defects, where one defines an effective Hamiltonian describing the electronic states of the defects within the environment of a periodic solid. Here we focus on finding the ground and excited states of the effective Hamiltonian representing a nitrogen-vacancy center in diamond and a divacancy in silicon carbide, on a quantum computer. We use two techniques, a variational quantum eigensolver (VQE) [3] and a quantum subspace expansion [4]. We show that by combining partial constraints on electron occupation to overcome the unphysical state problem [5] of VQE and zero noise extrapolation [6], we can obtain reasonably accurate results on near-term-noisy architectures not only for ground state properties of the spin-defects, but also for their excited state properties.

[1] Ma, He, et al. npj Computational Materials 6.1 (2020): 1-8.

[2] Ma, He, et al. JCTC 17.4 (2021): 2116-2125.

[3] Peruzzo, Alberto, et al. Nature communications 5.1 (2014): 1-7.

[4] McClean, Jarrod R., et al. Physical Review A 95.4 (2017): 042308.

[5] Sawaya, Nicolas PD, et al. JCTC 12.7 (2016): 3097-3108.

[6] Li, Ying, and Simon C. Benjamin. Physical Review X 7.2 (2017): 021050.   

Withdrawn

Despite the unprecedented technological advances in the development of quantum computing platforms seen in recent years, fault-tolerance remains too demanding. Thus, developing alternative strategies to improve the performance of the noisy devices currently available is of timely importance. To tackle this problem we provide two error mitigation protocols (named ``Quasi-Probabilistic Protocol'' and ``Cycle Extrapolation'') that can significantly upgrade the performance of the cycles of gates applied in experimental setups. By combining popular mitigation strategies such as error cancellation and noise amplification with the efficient noise reconstruction methods developed by the Quantum Benchmark team at Keysight Technologies, our protocols can mitigate a wide range of noise processes that afflict today's devices, including non-local and gate-dependent processes. We demonstrate our protocols on a superconducting processor at Berkeley Lab. Our experiments show significant improvements for structured circuits, such as circuits preparing W states or implementing the quantum phase estimation algorithm, as well as for random circuits. Overall, our work demonstrates a practical and reliable toolkit to characterise and mitigate the noise afflicting today's devices.   

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Variational Quantum Algorithms (VQAs) are widely viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs by exponentially flattening the cost landscape. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of noisy VQAs. In this work, we first unify many of the most widely studied EM protocols in the literature under one framework. Moreover, under this framework, we show that exponential cost concentration cannot be resolved without spending exponential resources. Second, we show analytically and numerically that, surprisingly, some EM protocols can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.   

Error mitigation in variational quantum eigensolvers using probabilistic machine learning

Quantum-classical hybrid schemes based on variational quantum eigensolvers (VQEs) may transform our ability of simulating materials and molecules already within the next few years. However, one of the main obstacles that we still have to overcome in order to achieve practical near-term  quantum advantage is to improve our ability of mitigating the "noise effects," characteristic of the current generation of quantum processing units (QPUs). To this end, here we design a method based on probabilistic machine learning, which allows us to mitigate the noise by imbuing within the computation prior (system-independent) information about the variational landscape. We perform benchmark calculations of a 4-qubit impurity model, showing that our method improves considerably the accuracy of the VQE outputs. Finally, we show that applying our method results also in more reliable quantum-embedding simulations of the Hubbard model with a VQE impurity solver.   

Reference-state Error Mitigation: A Chemistry Inspired Strategy for Improving Molecular Energy Evaluations on NISQ Devices

Current and near-term quantum computational hardware suffers from various forms of noise that limit their potential advantage [1]. This presentation outlines a strategy for mitigating the effects of systematic hardware-errors on quantum chemical calculations performed using the Variational Quantum Eigensolver algorithm. The Reference-State Error Mitigation (REM) strategy can be straightforwardly implemented on current devices, requiring at most one additional measurement of the molecular Hamiltonian, followed by minimal post-processing. Some of the most precise energy evaluations on a real quantum device to date is demonstrated by combining REM with VQE calculations of small molecules, including H₂, HeH⁺, LiH, and BeH₂. The strategy can be applied concurrently with other error mitigation techniques, such as readout error mitigation, and offers a marked improvement for treating chemical problems on both current and future devices.

 

 

[1]  Cao,  et al.  Quantum Chemistry in the Age of Quantum Computing. Chemical Reviews, 119(19):10856–10915, 10 2019.   

Framework of Generalized Quantum Subspace Expansion Method

Undoubtedly it is crucial to control the effect of noise to achieve computational advantage using erroneous quantum computers. Since the rapidly growing quantum resources are still years or decades away from full fault tolerance, the near-term challenge would be to develop practical hardware-friendly quantum error mitigation (QEM) techniques. In this work, we propose a generalization of the quantum subspace expansion method which is capable of mitigating all stochastic, coherent, and algorithmic errors in quantum computers. We show that, without relying on any information of noise, the error in the energy spectra of a given Hamiltonian can be mitigated efficiently. The performance of our method is investigated under two highly practical setups, in which the quantum subspaces are mainly spanned by powers of a noisy state ρ^m and a set of error-boosted states, respectively.  In both situations, we provide numerical demonstrations that we can suppress error by orders of magnitude, and also that our protocol inherits the advantages of previous error-agnostic QEM techniques.   

Fundamental limits of quantum error mitigation

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantage. This motivated the development of various quantum error-mitigation protocols, each representing a method to extract useful computational output by combining measurement data from multiple samplings of the available imperfect quantum device. What are the ultimate performance limits universally imposed on such protocols? In this talk, we present a fundamental bound on the sampling overhead that applies to a general class of error-mitigation protocols, assuming only the laws of quantum mechanics. We discuss its immediate consequences, including (1) the sampling overhead to mitigate local depolarizing noise for layered circuits --- such as the ones used for variational quantum algorithms --- must scale exponentially with circuit depth, and (2) the optimality of probabilistic error cancellation method among all strategies in mitigating a certain class of noise, demonstrating that our results provide a means to identify when a given quantum error-mitigation strategy is optimal and when there is potential room for improvement.   

Bipartite Control of Coherent Noise Using Quantum Approximate Optimization Algorithm

We employ bipartite control with a Quantum Approximate Optimization Algorithm (QAOA) control ansatz to mitigate coherent quantum noise. We illustrate the approach with application to protection of quantum gates performed on i) a central spin qubit coupling to bath qubits through isotropic Heisenberg interactions and ii) a superconducting transmon qubit coupling to environmental two-level-systems (TLS) through dipole-dipole interactions. The control field is classical and only acts on the system qubit. We use policy gradient (PG) and sequential convex programming (SCP) as classical optimization methods to optimize the QAOA control protocols with a fidelity objective defined with respect to specific target quantum gates, to find the optimal protocol for implementation of the target gate with high fidelity. We demonstrate effective suppression of coherent noise, with numerical studies achieving target gate implementation having fidelities over 0.999999 in the majority of our test cases. We analyze how will the control depth, total evolution time, number of bath systems and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite QAOA control.   

Improving the resilience of quantum denoising process

Quantum autoencoders aim to automate denoising algorithms. These quantum neural networks are trained to surpass noise channels and return arbitrary entangled states of our interest with high-fidelity. So far the successful training has shown tolerance up to 30% of bit flip and depolarization. Stronger noise results in poor training and denoising failure. [1]

In this talk I describe an inexpensive change in the network topology that can be extendable to all scales and can improve the tolerance significantly.  This has a side advantage that it can provide even higher fidelity values for successful training. It indeed helps the encoder by reducing the dimension of the decision boundary between perfect and noisy states. Such a simplification of the classification task relies heavily on quantum properties of the neural units. We show that Renyi entropy associated with a small partition of the network undergoes a second order phase transition when training fails, and this can serve as a good measure to distinguish between failure and success in denoising process. 

[1] D. Bondarenko and P. Feldmann, “Quantum autoencoders to denoise quantum data”, Phys. Rev. Lett., vol. 124, no. 13, p. 130502, 2020.   

Deep Neural Networks for High-fidelity Measurement of Multiqubit Circuits.

Superconducting qubits are a leading candidate for fault-tolerant quantum computing; however, it is challenging to maintain high measurement fidelity as systems are scaled to large size. In this work, we perform numerical simulations to benchmark various Deep Neural Network (DNN) architectures on the task of multiplexed dispersive measurement of superconducting qubits. We compare the robustness of the different state assignment approaches against three sources of measurement infidelity:  added measurement noise, qubit relaxation during measurement, and state initialization errors. We find that transformer and convolutional neural network architectures increase readout fidelity relative to conventional thresholding and that these approaches are robust against labeling error in the training datasets. In addition, we calculate the theoretical limit for readout fidelity and demonstrate that the transformer approach provides assignment fidelity approaching the theoretical limit.