Speedup for quantum optimal control from automatic differentiation based on graphics processing units

Leung, Nelson; Abdelhafez, Mohamed; Koch, Jens; Schuster, David I.

doi:10.1103/physreva.95.042318

Cited by 143 publications

(142 citation statements)

References 84 publications

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“…Automatic differentiation is the computational engine of modern deep learning applications [43,44]. Moreover, automatic differentiation also finds applications in quantum optimal control [45] and quantum chemistry calculations such as computing forces [46] and optimizing basis parameters [47].…”

Section: A Automatic Differentiationmentioning

confidence: 99%

Differentiable Programming Tensor Networks

et al. 2019

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Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation. The concept emerges from deep learning but is not only limited to training neural networks. We present theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher order derivatives of the program accurately and efficiently using automatic differentiation. We present essential techniques to differentiate through the tensor networks contraction algorithms, including numerical stable differentiation for tensor decompositions and efficient backpropagation through fixed point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient based variational optimization of infinite projected entangled pair states for quantum antiferromagnetic Heisenberg model and obtain start-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications. * wanglei@iphy.ac.cn † txiang@iphy.ac.cn This fact has limited broad adoption of the gradient based optimization of tensor network states to more complex systems. Alternative approaches, such as computing the gradient using numerical derivative has limited accuracy and efficiency, therefore only applies to cases with few variational parameters [36,37]. While deriving the gradient manually using the chain rule is only manageable for purposely designed simple tensor network structures [38].Differentiable programming provides an elegant and efficient solution to these problems by composing the whole tensor network program in a fully differentiable manner. In this paper, we present essential automatic differentiation techniques which compute (higher order) derivatives of tensor network programs efficiently to numeric precision. This progress opens the door to gradient-based (and even Hessian-based) optimization of tensor network states in a general setting. Moreover, computing (higher order) gradients of the output of a tensor network algorithm offer a straightforward approach to compute physical quantities such as the specific heat and magnetic susceptibilities. The differentiable programming approach is agnostic to the detailed lattice geometry, Hamiltonian, and tensor network contraction schemes. Therefore, the approach is general enough to support a wide class of tensor network applications.We will focus on applications which involve two dimensional infinite tensor networks where the differentiable programming techniques offer significant benefits compared to the conventional approaches. We show that after solving m...

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Section: A Automatic Differentiationmentioning

confidence: 99%

Differentiable Programming Tensor Networks

et al. 2019

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“…GRadient Pulse Engineering (GRAPE) is a strategy for compilation that numerically finds the best control pulses needed to execute a quantum circuit or subcircuit by following a gradient descent procedure [10,25]. We use the Tensorflow implementation of GRAPE described in [27]. In contrast to the gate based approach, GRAPE does not have the limitation incurred by the gate decomposition.…”

Section: Grapementioning

confidence: 99%

“…The gate-based compilation model is known to fall short of the GRadient Ascent Pulse Engineering (GRAPE) [17,25] compilation technique, which compiles directly to the level of the machinelevel control pulses that a quantum computer actually executes. In past work [1,27,44], GRAPE has been used to achieve 2-5x pulse speeedups over gate-based compilation for a range of quantum algorithms. Since fidelity decreases exponentially in time, with respect to the extremely short lifetimes of qubits, reducing the pulse duration is critical to ensuring that a computation completes before being completely scrambled by quantum decoherence effects.…”

Section: Introductionmentioning

confidence: 99%

Partial Compilation of Variational Algorithms for Noisy Intermediate-Scale Quantum Machines

Gokhale

Ding

Propson

et al. 2019

Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture

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Quantum computing is on the cusp of reality with Noisy Intermediate-Scale Quantum (NISQ) machines currently under development and testing. Some of the most promising algorithms for these machines are variational algorithms that employ classical optimization coupled with quantum hardware to evaluate the quality of each candidate solution. Recent work used GRadient Descent Pulse Engineering (GRAPE) to translate quantum programs into highly optimized machine control pulses, resulting in a significant reduction in the execution time of programs. This is critical, as quantum machines can barely support the execution of short programs before failing.However, GRAPE suffers from high compilation latency, which is untenable in variational algorithms since compilation is interleaved with computation. We propose two strategies for partial compilation, exploiting the structure of variational circuits to pre-compile optimal pulses for specific blocks of gates. Our results indicate significant pulse speedups ranging from 1.5x-3x in typical benchmarks, with only a small fraction of the compilation latency of GRAPE. CCS CONCEPTS• Computer systems organization → Quantum computing. KEYWORDS quantum computing, optimal control, variational algorithms ACM Reference Format:

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“…amplitude and bandwidth constraints for the control waveform [34], (iv) it can account for deterministic control distortions due to control hardware [35], and (v) it stands a better chance of yielding control sequences that are closer to being time optimal given (iii) and (iv). Furthermore, recent technical advances such as the use of graphics processing units and automatic differentiation [36] hold promise of significantly improving efficiency, and streamlining the implementation of numerical control engineering routines.…”

Section: T T T U T a T U T U T A T U Tmentioning

confidence: 99%

Engineering effective Hamiltonians

et al. 2019

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In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilizes perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we provide a general framework for computing arbitrary timedependent perturbation theory terms, as well as their gradients with respect to control variations, enabling the use of gradient methods for optimizing these terms. In particular, we show that effective Hamiltonian engineering is an instance of a bilinear control problem-the same general problem class as that of standard unitary design-and hence the same optimization algorithms apply. We demonstrate this method in various examples, including decoupling, recoupling, and robustness to control errors and stochastic errors. We also present a control engineering example that was used in experiment, demonstrating the practical feasibility of this approach.

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Speedup for quantum optimal control from automatic differentiation based on graphics processing units

Cited by 143 publications

References 84 publications

Differentiable Programming Tensor Networks

Differentiable Programming Tensor Networks

Partial Compilation of Variational Algorithms for Noisy Intermediate-Scale Quantum Machines

Engineering effective Hamiltonians

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