Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an input to the device that may find numerous applications in quantum information technologies. In the present paper, we address a scheme of a classification of input states, which is nondestructive and deterministic for certain inputs, while probabilistic, in general case. This can be achieved by incorporating phase estimation algorithm into the hybrid quantum-classical computation scheme, where quantum block is trained classically. We perform proof-of-principle implementation of this idea using superconducting quantum processor of IBM Quantum Experience. Another aspect we are interested in is a mitigation of errors occurring due to the quantum device imperfections. We apply a series of heuristic tricks at the stage of classical postprocessing in order to improve raw experimental data and to recognize patterns in them. These ideas may find applications in other realization of hybrid quantum-classical computations with noisy quantum machines
Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an input to the device that may find numerous applications in quantum information technologies. In the present paper, we address a scheme of a classification of input states, which is nondestructive and deterministic for certain inputs, while probabilistic, in general case. This can be achieved by incorporating phase estimation algorithm into the hybrid quantum-classical computation scheme, where quantum block is trained classically. We perform proof-of-principle implementation of this idea using superconducting quantum processor of IBM Quantum Experience. Another aspect we are interested in is a mitigation of errors occurring due to the quantum device imperfections. We apply a series of heuristic tricks at the stage of classical postprocessing in order to improve raw experimental data and to recognize patterns in them. These ideas may find applications in other realization of hybrid quantum-classical computations with noisy quantum machines
A wealth of quantum algorithms developed during the past decades brought about the concept of quantum supremacy. The state-of-the-art noisy intermediate-scale quantum (NISQ) devices, although imperfect, enable certain computational tasks that are demonstrably beyond the capabilities of modern classical supercomputers. However, present quantum computations are restricted to probing the quantum processor power, whereas implementation of specific full-scale quantum algorithms remains a challenge. Here we realize hybrid quantum algorithm for solving a linear system of equations with exponential speedup that utilizes quantum phase estimation, one of the exemplary core protocols for quantum computing. Our experiment carried out on superconducting IBMQ devices reveals the main shortcomings of the present quantum processors, which must be surpassed in order to boost quantum data processing via phase estimation. The developed algorithm demonstrates quantum supremacy and holds high promise to meet practically relevant challenges.
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the calculation of the eigenvalues of unitary matrices. The QPE algorithm has been combined with Kitaev's algorithm and the inverse quantum Fourier transform (IQFT) which are utilized as a fundamental component of such quantum algorithms. In this paper, we explore the computational challenges of implementing QPE algorithms on noisy intermediate-scale quantum (NISQ) machines using the IBM Q Experience (e.g., the IBMQX4, 5-qubit quantum computing hardware platform). Our experimental results indicate that the accuracy of finding the phase using these QPE algorithms is severely constrained by the NISQ computer's physical characteristics such as coherence time and error rates. To mitigate these physical limitations, we propose implementing a modified solution by reducing the number of controlled rotation gates and phase shift operations, thereby increasing the accuracy of the finding phase in near-term quantum computers.
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are restricted to exploring specific simplified protocols, whereas the implementation of full-scale quantum algorithms aimed at solving concrete large scale problems arising in data analysis and numerical modelling remains a challenge. Here we introduce and implement a hybrid quantum algorithm for solving linear systems of equations with exponential speedup, utilizing quantum phase estimation, one of the exemplary core protocols for quantum computing. We introduce theoretically classes of linear systems that are suitable for current generation quantum machines and solve experimentally a 217-dimensional problem on superconducting IBMQ devices, a record for linear system solution on quantum computers. The considered large-scale algorithm shows superiority over conventional solutions, demonstrates advantages of quantum data processing via phase estimation and holds high promise for meeting practically relevant challenges.
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.
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum algorithms is quite difficult, and many of these genuine quantum algorithms, like Shor's prime factoring or phase estimation, require extremely long circuit depth for any practical application, which necessitates error correction. In contrast, we show that machine learning can be used as a systematic method to construct algorithms, that is, to non-algorithmically “program” quantum computers. Quantum machine learning enables us to perform computations without breaking down an algorithm into its gate “building blocks”, eliminating that difficult step and potentially increasing efficiency by simplifying and reducing unnecessary complexity. In addition, our non-algorithmic machine learning approach is robust to both noise and to decoherence, which is ideal for running on inherently noisy NISQ devices which are limited in the number of qubits available for error correction. We demonstrate this using a fundamentally nonclassical calculation: experimentally estimating the entanglement of an unknown quantum state. Results from this have been successfully ported to the IBM hardware and trained using a hybrid reinforcement learning method.
The Quantum Phase Difference Estimation (QPDE) algorithm, as an extension of the Quantum Phase Estimation (QPE), is a quantum algorithm designed to compute the differences of two eigenvalues of a unitary operator by exploiting the quantum superposition of two eigenstates. Unlike QPE, QPDE is free of controlled-unitary operations, and is suitable for calculations on noisy intermediate-scale quantum (NISQ) devices. We present the implementation and verification of a novel early fault-tolerant QPDE algorithm for determining energy gaps across diverse spin system configurations using NISQ devices. The algorithm is applied to the systems described by two and three-spin Heisenberg Hamiltonians with different geometric arrangements and coupling strengths, including symmetric, asymmetric, spin-frustrated, and non-frustrated configurations. By leveraging the match gate-like structure of the time evolution operator of Heisenberg Hamiltonian, we achieve constant-depth quantum circuits suitable for NISQ hardware implementation. Our results on IBM quantum processors show remarkable accuracy ranging from 85\% to 93\%, demonstrating excellent agreement with classical calculations even in the presence of hardware noise. The methodology incorporates sophisticated quantum noise suppression techniques, including Pauli Twirling and Dynamical Decoupling, and employs an adaptive framework. Our findings demonstrate the practical viability of the QPDE algorithm for quantum many-body simulations on current NISQ hardware, establishing a robust framework for future applications.