[Paper Review] Extending the computational reach of a noisy superconducting quantum processor

Abhinav Kandala, Kristan Temme+4 more|arXiv (Cornell University)|May 11, 2018

Quantum Computing Algorithms and ArchitectureComputer Science28 references118 citations

TL;DR

The paper experimentally implements zero-noise extrapolation error mitigation on a 5-qubit superconducting processor to enhance the accuracy of short-depth quantum circuits for variational eigensolvers in quantum chemistry and quantum magnetism.

ABSTRACT

Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of computation based off expectation values of quantum observables can be enhanced through an extrapolation of results from a collection of varying noisy experiments. Here, we demonstrate this error mitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors on canonical single- and two-qubit experiments and then extend its application to the variational optimization of Hamiltonians for quantum chemistry and magnetism. We effectively demonstrate that the suppression of incoherent errors helps unearth otherwise inaccessible accuracies to the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will be critical to significantly enhance the capabilities of near-term quantum computing hardware.

Motivation & Objective

• Motivate improvement of quantum computations on near-term hardware by mitigating incoherent errors without adding hardware resources.
• Show that zero-noise extrapolation can enhance expectation-value accuracy for single- and two-qubit experiments on superconducting qubits.
• Extend error mitigation to hardware-efficient variational quantum eigensolvers for spin models and small molecules.
• Quantify how incoherent error suppression enables deeper circuits to yield more accurate variational solutions.

Proposed method

• Express any quantum circuit as evolution under a time-dependent drive K(t) with Pauli operators Pα.
• Use Richardson’s deferred approach to the limit to construct mitigated estimates E*K(λ) by combining measurements at stretched noise levels c_iλ.
• Implement scaled drive protocols K^I(t) with time-translation-invariant noise to emulate amplified noise strengths without hardware changes.
• Stretch gate lengths, rise/fall times, and buffers by factors c_i and calibrate to realize ÊK^n(λ) via linear constraints on {c_i}.
• Apply zero-noise extrapolation to random single- and two-qubit Clifford circuits and to hardware-efficient VQE Ansätze for Heisenberg, H2, and LiH problems.

Experimental results

Research questions

• RQ1 Can zero-noise extrapolation extend the useful computational reach of near-term noisy superconducting quantum processors for variational algorithms?
• RQ2 How does error mitigation impact the convergence and accuracy of hardware-efficient VQE for quantum magnets and small molecular systems?
• RQ3 What are the practical considerations (coherence fluctuations, sampling, gate non-linearities) that affect the implementation of zero-noise extrapolation on superconducting qubits?

Key findings

• Zero-noise extrapolation suppresses higher-order error terms in both single-qubit and two-qubit experiments, improving estimates toward zero-noise limits.
• Mitigation enables deeper hardware-efficient trial circuits to yield more accurate energies in Heisenberg spin models than would be possible without mitigation.
• Mitigated energies and Pauli-term expectations in H2 and LiH align more closely with exact results than unmitigated ones, using comparable coherence properties.
• Sampling variance and coherence-time fluctuations are critical factors; bootstrapping is used to estimate mitigation error, and faster initialization would further improve results.
• The approach is problem-agnostic and complements gate characterization and quantum optimization efforts without requiring error-correcting hardware.