Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices (original) (raw)
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Incoherent quantum algorithm dynamics of an open system with near-term devices
Quantum Information Processing, 2020
Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for the density matrix obeying the von Neumann equation using an efficient Lagrangian-based approach. And then, we consider the dynamics of the ensemble-averaged of disordered quantum systems which is described by Hamiltonian ensemble with a hybrid quantum-classical algorithm. In a recent work [Phys. Rev. Lett. 120, 030403], the authors concluded that the dynamics of an open system could be simulated by a Hamiltonian ensemble because of nature of the disorder average. We investigate our algorithm to simulating incoherent dynamics (decoherence) of open system using an efficient variational quantum circuit in the form of master equations. Despite the non-unitary evolution of open systems, our method is applicable to a wide range of problems for incoherent dynamics with the unitary quantum operation.
The theory of variational hybrid quantum-classical algorithms
New Journal of Physics, 2016
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as "the quantum variational eigensolver" was developed [1] with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through relaxation of exponential splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.
Hybrid Quantum Classical Simulations
arXiv (Cornell University), 2022
We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require incremental communication between a classical central processing unit and a quantum processing unit to solve a problem. We find that the QAOA scales much better to larger problems than random guessing, but requires significant computational resources. In contrast, a coarsely discretised version of quantum annealing called approximate quantum annealing (AQA) can reach the same promising scaling behaviour using much less computational resources. For the VQE, we find reasonable results in approximating the ground state energy of the Heisenberg model when suitable choices of initial states and parameters are used. Our design and implementation of a general quasi-dynamical evolution further improves these results.
Simulating Open Quantum Systems Using Hamiltonian Simulations
2024
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order.
arXiv (Cornell University), 2022
We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediatescale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining 1
Near-optimal circuit design for variational quantum optimization
arXiv (Cornell University), 2022
Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent Ising model suitable for the quantum device. Implementing each term of the Ising model separately often results in high redundancy, significantly increasing the resources required. We overcome this issue by replacing the term-wise implementation of the Ising model with its equivalent simulation through a quantized version of a classical pseudocode function. This results in a new variant of the Quantum Approximate Optimization Algorithm (QAOA), which we name the Functional QAOA (FUNC-QAOA). By exploiting this idea for optimization tasks like the Travelling Salesman Problem and Max-K-Cut, we obtain circuits which are near-optimal with respect to all relevant cost measures (e.g., number of qubits, gates, circuit depth). While we demonstrate the power of FUNC-QAOA only for a particular set of paradigmatic problems, our approach is conveniently applicable for generic optimization problems.
ArXiv, 2023
Hybrid quantum-classical algorithms hold the potential to outperform classical computing methods for simulating quantum many-body systems. Adaptive Variational Quantum Eigensolvers (VQE) in particular have demonstrated an ability to generate highly accurate ansatz wave-functions using compact quantum circuits. However, the practical implementation of these methods on current quantum processing units (QPUs) faces a significant challenge: the need to measure a polynomially scaling number of observables during the operator selection step so as to optimise a high-dimensional, noisy cost function. In this study, we introduce new techniques to overcome these difficulties and execute hybrid adaptive algorithms on a 25-qubit error-mitigated quantum hardware coupled to a high performance GPU-accelerated quantum simulator. As a physics application, we compute the ground state of a 25-body Ising model using a greedy gradient-free adaptive VQE that requires only five circuit measurements for each iteration, regardless of the number of qubits and the size of the operator pool. As a chemistry application, we combine this greedy, gradient-free approach with the Overlap-ADAPT-VQE algorithm to approximate the ground state of a molecular system. The successful implementation of these hybrid QPU/simulator computations enhances the applicability of adaptive VQEs on QPUs and instills further optimism regarding the near-term advantages of quantum computing.
Noise-resilient variational hybrid quantum-classical optimization
Physical Review A
Variational hybrid quantum-classical optimization represents one the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of a Hamiltonian or solving some machine-learning tasks. In these devices noise is unavoidable and impossible to error-correct, yet its role in the optimization process is not much understood, especially from the theoretical viewpoint. Here we consider a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes. We show that the accuracy of the result obtained for a fixed number of iterations is bounded by a quantity related to the Quantum Fisher Information of the variational state. Using this bound, we find the unexpected result that, in some regimes, noise can be beneficial, allowing a faster solution to the optimization problem.