Digital zero noise extrapolation for quantum error mitigation

Giurgica-Tiron, Tudor; Hindy, Yousef; LaRose, Ryan; Mari, Andrea; Zeng, William J.

doi:10.1109/qce49297.2020.00045

Cited by 156 publications

(132 citation statements)

References 20 publications

Supporting

Mentioning

119

Contrasting

Order By: Relevance

“…As shown in Appendix I, the fraction of errors detectable by G tot is estimated to be f Gtot ∼ 8 15 and that by G ↑/↓ is estimated to be f G ↑/↓ ∼ 2 5 . Using these and following Eq.…”

Section: Different Symmetry Expansion Schemesmentioning

confidence: 99%

“…This brings us to quantum error mitigation, which unlike quantum error correction, mostly relies on performing additional measurements instead of employing additional qubits to mitigate the damages caused by errors [3][4][5][6]. Quantum error mitigation has been successfully implemented in various experimental settings [7][8][9][10][11]. Symmetry verification is one such error-mitigation technique that projects the noisy output quantum state back into the symmetry subspace defined by the physical problem we try to solve [12,13].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Error Mitigation using Symmetry Expansion

Cai

2021

Quantum

View full text Add to dashboard Cite

Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to their limited scale. Therefore instead of relying on engineered code symmetry, symmetry verification was developed which uses the inherent symmetry within the physical problem we try to solve. In this article, we develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes beyond symmetry verification, enabling us to achieve different balances between the estimation bias and the sampling cost of the scheme. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification through cancellation between the biases due to the detectable and undetectable noise components. A practical way to search for such a small-bias scheme is introduced. By numerically simulating the Fermi-Hubbard model for energy estimation, the small-bias symmetry expansion we found can achieve an estimation bias 6 to 9 times below what is achievable by symmetry verification when the average number of circuit errors is between 1 to 2. The corresponding sampling cost for random shot noise reduction is just 2 to 6 times higher than symmetry verification. Beyond symmetries inherent to the physical problem, our formalism is also applicable to engineered symmetries. For example, the recent scheme for exponential error suppression using multiple noisy copies of the quantum device is just a special case of symmetry expansion using the permutation symmetry among the copies.

show abstract

Section: Different Symmetry Expansion Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Error Mitigation using Symmetry Expansion

Cai

2021

Quantum

View full text Add to dashboard Cite

show abstract

“…First experiments show promising results for systems of small and increasing size [74,123,124]. Various strategies of error mitigation were proposed that can further improve the performance of algorithms when run on physical devices [125][126][127][128][129][130][131][132]. Finally, considering linear algebra problems, several VQAs were also proposed to solve LSEs [133][134][135][136][137][138], and ongoing efforts are directed towards improving their workflow.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear differential equations with differentiable quantum circuits

2021

View full text Add to dashboard Cite

We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to represent function derivatives in an analytical form as differentiable quantum circuits (DQCs), thus avoiding inaccurate finite difference procedures for calculating gradients. We describe a hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions. As a particular example setting, we show how this approach can implement a spectral method for solving differential equations in a high-dimensional feature space. From a technical perspective, we design a Chebyshev quantum feature map that offers a powerful basis set of fitting polynomials and possesses rich expressivity. We simulate the algorithm to solve an instance of Navier-Stokes equations and compute density, temperature, and velocity profiles for the fluid flow in a convergent-divergent nozzle.

show abstract

“…ZNE involves collecting data at various levels of noise, achieved by stretching gate times or inserting identities, and using this noisy data to extrapolate an observable's expectation value to the zero-noise limit [6,17,23,37,45]. It has been successfully employed to correct ground-state energies for problem sizes up to 4-qubits [16,26,28].…”

Section: Introductionmentioning

confidence: 99%

Error mitigation with Clifford quantum-circuit data

Czarnik

Arrasmith

Coles

et al. 2021

Quantum

168

View full text Add to dashboard Cite

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

show abstract

Digital zero noise extrapolation for quantum error mitigation

Cited by 156 publications

References 20 publications

Quantum Error Mitigation using Symmetry Expansion

Quantum Error Mitigation using Symmetry Expansion

Solving nonlinear differential equations with differentiable quantum circuits

Error mitigation with Clifford quantum-circuit data

Contact Info

Product

Resources

About