Funded by: NCN Sonata project no. 2022/47/D/ST2/03393
Principal investigator: dr Piotr Czarnik
Realization: 2023-2026
Quantum computing promises quantum advantage for difficult computational problems. In particular, recent years brought rapid progress in development of gate-based quantum computers resulting in the first quantum advantage experiments. At the same time the computational power of current quantum computers is limited by decoherence and imperfect implementation of quantum gates which are called noise. It is commonly expected that in future errors introduced by the noise will be detected and corrected on fly by quantum error correction (QEC). Nevertheless, a successful implementation of QEC at a scale guaranteeing quantum advantage requires quantum resources which are not expected to be available in near future. That necessitates alternative techniques to reduce effects of the noise. One of the goals of this proposal is development and application of such techniques which are called error mitigation (EM). They mitigate effects of the noise by classical post-processing of quantum computation outcomes partially compromised by the noise and require much smaller quantum resources than QEC.
While many EM methods have been proposed and successfully demonstrated for particular applications robust and reliable EM remains challenging. One of the primary limitations on accuracy of EM is propagation of the measurement uncertainty through the EM classical post-processing called also a shot noise uncertainty. While EM decreases bias of expected values of observables due to the noise, at the same time it usually increases their shot noise uncertainty. Therefore, a larger number of measurements is required to maximize accuracy of error mitigated observables. First of the goals of this proposal is to optimize EM methods in order to minimize a number of measurements required to obtain a low shot noise uncertainty. I will do that using a framework of learning-based EM which utilizes classically simulable circuits similar to a circuit of interest in order to learn effects of the noise.
Another limitation on performance of current EM methods is time variability of the real-world noise as vast majority of error mitigation methods assume that the noise is time-invariant. It has been demonstrated that time variability of the quantum computers is significant enough to substantially alter performance of EM limiting accuracy of the current EM methods. To overcome this limitation, I will develop learning-based EM methods for the time-dependent noise.
The second goal of this proposal is an application of learning-based EM methods to extend range of state-of-the-art near-term methods for simulation of dynamical properties of quantum many-body systems. To maximize quality and efficiency of EM for those methods I will develop application-specific improvements of EM methods exploiting symmetries of the simulated systems and special properties of quantum simulation algorithms.
While the gate-based quantum computers are the most promising path to universal quantum computing, recent years brought also fast development of analog quantum simulators tailored to specific applications. Such simulators enable simulation of quantum many-body systems which are an order of magnitude larger than classically simulable ones. They are also affected by the noise similarly to the gate-based quantum computers and their potential can be enhanced by EM methods. The third goal of this proposal is development of learning-based EM methods for the analog simulators.
Very recently the first hardware implementations of primitives of QEC have been demonstrated. These developments signal that within next few years first quantum computers using quantum error corrected logical qubits may emerge. At the same time a logical qubit consists of multiple noisy qubits. Consequently, the first quantum computers with QEC will have much less logical qubits than a number required for a quantum advantage. Taking into account the limited number of logical qubits available it might be beneficial to combine the logical qubits with the noisy qubits in order to boost the computer computational power. Such a hybrid architecture would interpolate in between a noisy near-term quantum computer and a quantum error corrected device. The presence of the noisy qubits would increase a system size which can be simulated with the device. The final goal of this proposal is to design implementations of such an architecture and to evaluate to what extent they improve on the noisy devices.