Error mitigation has been one of the recently sought after methods to reduce the effects of noise when computation is performed on a noisy near-term quantum computer. Interest in simulating stochastic processes with quantum models gained popularity after being proven to require less memory than their classical counterparts. With previous work on quantum models focusing primarily on further compressing memory, this work branches out into the experimental scene; we aim to bridge the gap between theoretical quantum models and practical use with the inclusion of error mitigation methods. It is observed that error mitigation is successful in improving the resultant expectation values. While our results indicate that error mitigation work, we show that its methodology is ultimately constrained by hardware limitations in these quantum computers.
Error mitigation has been one of the recently sought after methods to reduce the effects of noise when computation is performed on a noisy near-term quantum computer. Interest in simulating stochastic processes with quantum models gained popularity after being proven to require less memory than their classical counterparts. With previous work on quantum models focusing primarily on further compressing memory, this work branches out into the experimental scene; we aim to bridge the gap between theoretical quantum models and practical use with the inclusion of error mitigation methods. It is observed that error mitigation is successful in improving the resultant expectation values. While our results indicate that error mitigation work, we show that its methodology is ultimately constrained by hardware limitations in these quantum computers.
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
The realization of fault-tolerant quantum computers remains a challenging endeavor, forcing state-of-the-art quantum hardware to rely heavily on noise mitigation techniques. Standard quantum error mitigation is typically based on post-processing strategies. In contrast, the present work explores a pre-processing approach, in which the effects of noise are mitigated before performing a measurement on the output state. The main idea is to find an observable Y such that its expectation value on a noisy quantum state E(ρ) matches the expectation value of a target observable X on the noiseless quantum state ρ. Our method requires the execution of a noisy quantum circuit, followed by the measurement of the surrogate observable Y. The main enablers of our method in practical scenarios are Tensor Networks. The proposed method improves over Tensor Error Mitigation (TEM) in terms of average error, circuit depth, and complexity, attaining a measurement overhead that approaches the theoretical lower bound. The improvement in terms of classical computation complexity is in the order of ∼106 times when compared to the post-processing computational cost of TEM in practical scenarios. Such gain comes from eliminating the need to perform the set of informationally complete positive operator-valued measurements (IC-POVM) required by TEM, as well as any other tomographic strategy.
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault-tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively 'undone' for larger system sizes. Our framework rigorously captures large classes of error-mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to those of current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. Noise also impacts other near-term applications by constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively `undone' for larger system sizes. Our framework rigorously captures large classes of error mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to the current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. They also impact other near-term applications, constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.
Abstract Ever since the discussions about a possible quantum computer arised, quantum simulations have been at the forefront of possible utilities, with the task of quantum simulations being one that promises quantum advantage. Recently, advancements have made it feasible to simulate complex molecules using Variational Quantum Eigensolvers or study the dynamics of many‐body spin Hamiltonians. These simulations have the potential to yield valuable outcomes through the application of error mitigation techniques. Simulating smaller models carries a great amount of importance as well and currently, in the Noisy Intermediate Scale Quantum era, is more feasible since it is less prone to errors. The objective of this work is to examine the theoretical background and the circuit implementation of a quantum tunneling simulation, with an emphasis on hardware considerations. This study presents the theoretical background required for such implementation and highlights the main stages of its development. By building on classic approaches of quantum tunneling simulations, this study aims at improving the result of such simulations by employing error mitigation techniques, Zero Noise Extrapolation, and Readout Error Mitigation and uses them in conjunction with multiprogramming of the quantum chip, a technique used for solving the hardware under‐utilization problem that arises in such contexts.
Analog quantum simulation has been proposed as an efficient approach for
probing classically intractable many-body physics. In contrast to digital,
gate-based quantum simulation, the analog approach involves configuring the
quantum hardware to directly mimic the physics of the target system. This
reduces the level of control required and can offer a degree of inherent
robustness, but it comes at the cost that known error-handling techniques may
be inapplicable. Accumulation of error is thus a major challenge facing
medium-scale and large-scale analog quantum simulation with current and
near-term noisy quantum (NISQ) devices. Here we propose a hybrid error
mitigation scheme that can suppress general local Markovian noise in analog
quantum simulators. We employ stochastic error mitigation for physical noise
and use Richardson extrapolation to compensate for model estimation error. We
numerically test the error mitigation scheme for an Ising-type Hamiltonian with
energy relaxation and dephasing noise, and show an improvement of simulation
accuracy by two orders. We assess the resource cost of our error mitigation
scheme and conclude that analog quantum simulation at scale is feasible with
NISQ hardware.