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Journal ArticleDOI

Hardware-efficient variational quantum algorithms for time evolution

TL;DR: This work presents alternatives to the time-dependent variational principle that are hardware-efficient and do not require matrix inversion in relation to imaginary time evolution and presents algorithms of systematically increasing accuracy and hardware requirements.
Abstract: Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational algorithms need to be as hardware-efficient as possible. Here we present alternatives to the time-dependent variational principle that are hardware-efficient and do not require matrix inversion. In relation to imaginary time evolution, our approach significantly reduces the hardware requirements. With regards to real time evolution, where high precision can be important, we present algorithms of systematically increasing accuracy and hardware requirements. We numerically analyze the performance of our algorithms using quantum Hamiltonians with local interactions.
Citations
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Posted Content
TL;DR: In this article, the authors provide a thorough summary of NISQ computational paradigms and algorithms, their limitations and advantages, as well as a comprehensive overview of various benchmarking and software tools useful for programming and testing.
Abstract: A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, we provide a thorough summary of NISQ computational paradigms and algorithms. We discuss the key structure of these algorithms, their limitations, and advantages. We additionally provide a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices.

92 citations

Posted Content
TL;DR: In this paper, the authors developed several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator.
Abstract: In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator. By comparing all methods with previous techniques based on Trotter decompositions we demonstrate that the Arnoldi method is the best one, reaching extremely good accuracy with moderate resources. Finally we apply this algorithm to studying the formation of molecules in an optical lattices when crossing a Feschbach resonance with a cloud of two-species hard-core bosons.

86 citations

Journal ArticleDOI
TL;DR: A novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits realizes an iterative, global projection of the exact time evolution onto the parameterized manifold, equivalent to the McLachlan's variational principle.
Abstract: We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected - Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.

41 citations


Cites methods from "Hardware-efficient variational quan..."

  • ...To alleviate this issue, new variational methods based on partial, local optimisations of the variational parameters have been recently proposed [43, 44, 45]....

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Posted Content
TL;DR: It is demonstrated a neural predictor guided QAS can discover powerful quantum circuit ansatz, yielding state-of-the-art results for various examples from quantum simulation and quantum machine learning.
Abstract: Variational quantum algorithms (VQAs) are widely speculated to deliver quantum advantages for practical problems under the quantum-classical hybrid computational paradigm in the near term. Both theoretical and practical developments of VQAs share many similarities with those of deep learning. For instance, a key component of VQAs is the design of task-dependent parameterized quantum circuits (PQCs) as in the case of designing a good neural architecture in deep learning. Partly inspired by the recent success of AutoML and neural architecture search (NAS), quantum architecture search (QAS) is a collection of methods devised to engineer an optimal task-specific PQC. It has been proven that QAS-designed VQAs can outperform expert-crafted VQAs under various scenarios. In this work, we propose to use a neural network based predictor as the evaluation policy for QAS. We demonstrate a neural predictor guided QAS can discover powerful PQCs, yielding state-of-the-art results for various examples from quantum simulation and quantum machine learning. Notably, neural predictor guided QAS provides a better solution than that by the random-search baseline while using an order of magnitude less of circuit evaluations. Moreover, the predictor for QAS as well as the optimal ansatz found by QAS can both be transferred and generalized to address similar problems.

29 citations

Journal ArticleDOI
TL;DR: In this article , the authors present a brief introduction to challenging problems and potential opportunities in the emerging areas of quantum estimation, control and learning, including quantum state estimation, quantum parameter identification, quantum filtering, quantum open-loop control, quantum feedback control, machine learning for estimation and control of quantum systems and quantum machine learning.

28 citations

References
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Book ChapterDOI

[...]

01 Jan 2012

139,059 citations


"Hardware-efficient variational quan..." refers methods in this paper

  • ...Promising alternatives are variational hybrid quantum-classical algorithms [13, 14] and variational quantum simulation [15, 16]....

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Book
01 Nov 1996

8,608 citations


"Hardware-efficient variational quan..." refers background in this paper

  • ...Matrix inversion is numerically unstable when the condition number of the matrix is large and small errors in the matrix can become large errors in the matrix inverse [57]....

    [...]

Journal ArticleDOI
TL;DR: The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future.
Abstract: Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansatze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry--calculating the ground-state molecular energy for He-H(+). The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future.

3,114 citations

Journal ArticleDOI
23 Aug 1996-Science
TL;DR: Feynman's 1982 conjecture, that quantum computers can be programmed to simulate any local quantum system, is shown to be correct.
Abstract: Feynman's 1982 conjecture, that quantum computers can be programmed to simulate any local quantum system, is shown to be correct.

2,678 citations


"Hardware-efficient variational quan..." refers background in this paper

  • ...Although significant progress has been made based on the original quantum algorithm for simulating time evolution [2], this algorithm faces obstacles on current quantum hardware which lacks quantum error correction [10–12]....

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  • ...[2] Seth Lloyd, “Universal quantum simulators,” Science 273, 1073–1078 (1996)....

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Journal ArticleDOI
14 Sep 2017-Nature
TL;DR: The experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms is demonstrated, determining the ground-state energy for molecules of increasing size, up to BeH2.
Abstract: The ground-state energy of small molecules is determined efficiently using six qubits of a superconducting quantum processor. Quantum simulation is currently the most promising application of quantum computers. However, only a few quantum simulations of very small systems have been performed experimentally. Here, researchers from IBM present quantum simulations of larger systems using a variational quantum eigenvalue solver (or eigensolver), a previously suggested method for quantum optimization. They perform quantum chemical calculations of LiH and BeH2 and an energy minimization procedure on a four-qubit Heisenberg model. Their application of the variational quantum eigensolver is hardware-efficient, which means that it is optimized on the given architecture. Noise is a big problem in this implementation, but quantum error correction could eventually help this experimental set-up to yield a quantum simulation of chemically interesting systems on a quantum computer. Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers1. Finding exact solutions to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet experimental implementations have so far been restricted to molecules involving only hydrogen and helium2,3,4,5,6,7,8. Here we demonstrate the experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, determining the ground-state energy for molecules of increasing size, up to BeH2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepared trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians9 and a robust stochastic optimization routine10. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our experiments and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.

2,348 citations


"Hardware-efficient variational quan..." refers methods in this paper

  • ...In this work, we call hardware-efficient any variational quantum algorithm that (i) can use parameterized quantum circuits tailored to the physical device [42] or (ii) exploits other concepts that reduce the number of qubits or gates [43, 44] such as causal cones....

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