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Register a new userQuantum Poker A game for quantum computers suitable for benchmarking error mitigation techniques on NISQ devices
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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.
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We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.
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.
Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental emph{response matrix} that describes the error associated with measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially in the number of qubits $n$. In this work, we modify standard matrix inversion techniques using two perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high order bitflip events is strongly suppressed. Given a characteristic error rate $q$, our first method recovers the probability of the all-zeros bitstring $p_0$ by sampling only a small subspace of the response matrix before inverting readout error resulting in a relative speedup of $text{poly}left(2^{n} / big(begin{smallmatrix} n w end{smallmatrix}big)right)$, which we motivate using a simplified error model for which the approximation incurs only $O(q^w)$ error for some integer $w$. We then provide a generalized technique to efficiently recover full output distributions with $O(q^w)$ error in the perturbative limit. These approximate techniques for readout error correction may greatly accelerate near term quantum computing applications.
Current quantum devices suffer from the rapid accumulation of error that prevents the storage of quantum information over extended periods. The unintentional coupling of qubits to their environment and each other adds significant noise to computation, and improved methods to combat decoherence are required to boost the performance of quantum algorithms on real machines. While many existing techniques for mitigating error rely on adding extra gates to the circuit or calibrating new gates, our technique leverages the gates already present in a quantum program and does not extend circuit runtime duration. In this paper, we exploit scheduling time for single-qubit gates that occur in idle windows, scheduling the gates such that their timing can counteract some errors. Spin-echo corrections act as inspiration for this technique, which can mitigate dephasing, or phase accumulation, that appears as a result of qubit inactivity. Theoretical models, however, fail to capture all sources of noise in near-term quantum devices, making practical solutions necessary that better minimize the impact of unpredictable errors in quantum machines. This paper presents TimeStitch: a novel framework that pinpoints the optimum execution schedules for single-qubit gates within quantum circuits. TimeStitch, implemented as a compilation pass, leverages the reversible nature of quantum computation to improve the success of quantum circuits on real quantum machines. Unlike past approaches that apply reversibility properties to improve quantum circuit execution, TimeStitch boosts fidelity without violating critical path frontiers in either the slack tuning procedures or the final rescheduled circuit. On average, TimeStitch is able to achieve 24% improvement in success rates, with a maximum of 75%, while observing depth criteria.
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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