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Register a new userClassical-Quantum Noise Mitigation for NISQ Hardware
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Andrew Shaw
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In this work, the global white-noise model is proved from first principles. The adherence of NISQ hardware to the global white-noise model is used to perform noise mitigation using Classical White-noise Extrapolation (CLAWE).
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Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a game similar to the Poker variant Texas hold em with the intention to serve as an engaging pedagogical tool to learn the basics rules of quantum computing. The concepts of quantum states, quantum operations and measurement can be learned in a playful manner. The difference to the classical variant is that the community cards are replaced by a quantum register that is randomly initialized, and the cards for each player are replaced by quantum gates, randomly drawn from a set of available gates. Each player can create a quantum circuit with their cards, with the aim to maximize the number of $1$s that are measured in the computational basis. The basic concepts of superposition, entanglement and quantum gates are employed. We provide a proof-of-concept implementation using Qiskit. A comparison of the results for the created circuits using a simulator and IBM machines is conducted, showing that error rates on contemporary quantum computers are still very high. For the success of noisy intermediate scale quantum (NISQ) computers, improvements on the error rates and error mitigation techniques are necessary, even for simple circuits. We show that quantum error mitigation (QEM) techniques can be used to improve expectation values of observables on real quantum devices.
We numerically emulate noisy intermediate-scale quantum (NISQ) devices and determine the minimal hardware requirements for two-site hybrid quantum-classical dynamical mean-field theory (DMFT). We develop a circuit recompilation algorithm which significantly reduces the number of quantum gates of the DMFT algorithm and find that the quantum-classical algorithm converges if the two-qubit gate fidelities are larger than 99%. The converged results agree with the exact solution within 10%, and perfect agreement within noise-induced error margins can be obtained for two-qubit gate fidelities exceeding 99.9%. By comparison, the quantum-classical algorithm without circuit recompilation requires a two-qubit gate fidelity of at least 99.999% to achieve perfect agreement with the exact solution. We thus find quantum-classical DMFT calculations can be run on the next generation of NISQ devices if combined with the recompilation techniques developed in this work.
Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such devices is a topic of considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited for execution on NISQ devices by combining quantum computers with classical computers, and are expected to be the first useful applications for quantum computing. Meanwhile, mitigation of errors on quantum processors is also crucial to obtain reliable results. In this article, we review the basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques. Since quantum computing with NISQ devices is an actively developing field, we expect this review to be a useful basis for future studies.
Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which requires large qubit overhead, we turn to quantum error mitigation, in which we make use of extra measurements. Error extrapolation is an error mitigation technique that has been successfully implemented experimentally. Numerical simulation and heuristic arguments have indicated that exponential curves are effective for extrapolation in the large circuit limit with an expected circuit error count around unity. In this article, we extend this to multi-exponential error extrapolation and provide more rigorous proof for its effectiveness under Pauli noise. This is further validated via our numerical simulations, showing orders of magnitude improvements in the estimation accuracy over single-exponential extrapolation. Moreover, we develop methods to combine error extrapolation with two other error mitigation techniques: quasi-probability and symmetry verification, through exploiting features of these individual techniques. As shown in our simulation, our combined method can achieve low estimation bias with a sampling cost multiple times smaller than quasi-probability while without needing to be able to adjust the hardware error rate as required in canonical error extrapolation.
Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum circuit describing the algorithm into an equivalent one that obeys the connectivity restrictions. In this work we construct a circuit synthesis scheme that takes as input the qubit connectivity graph and a quantum circuit over the gate set generated by ${text{CNOT},R_{Z}}$ and outputs a circuit that respects the connectivity of the device. As a concrete application, we apply our techniques to Googles Bristlecone 72-qubit quantum chip connectivity, IBMs Tokyo 20-qubit quantum chip connectivity, and Rigettis Acorn 19-qubit quantum chip connectivity. In addition, we also compare the performance of our scheme as a function of sparseness of randomly generated quantum circuits. Note: Recently, the authors of arXiv:1904.00633 independently presented a similar optimization scheme. Our work is independent of arXiv:1904.00633, being a longer version of the seminar presented by Beatrice Nash at the Dagstuhl Seminar 18381: Quantum Programming Languages, pg. 120, September 2018, Dagstuhl, Germany, slide deck available online at https://materials.dagstuhl.de/files/18/18381/18381.BeatriceNash.Slides.pdf.
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