Variational fast forwarding for quantum simulation beyond the coherence time

Cirstoiu, Cristina; Holmes, Zoë; Iosue, Joseph T.; Cincio, Łukasz; Coles, Patrick J.; Sornborger, Andrew

doi:10.1038/s41534-020-00302-0

Cited by 219 publications

(158 citation statements)

References 46 publications

(73 reference statements)

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“…Figure 5 shows representative results of our numerical implementations of the quantum autoencoder in ref. 11 obtained by training V(θ) with the global and local cost functions respectively given by (22) and (23). Specifically, while we train with finite sampling, in the figures we show the exact cost-function values versus the number of iterations.…”

Section: Corollarymentioning

confidence: 99%

“…In VQE, the cost function is obviously the energy C ¼ ψjHjψ h iof the trial state ψ j i. However, VQAs have been proposed for other applications, like quantum data compression 11 , quantum error correction 12 , quantum metrology 13 , quantum compiling [14][15][16][17] , quantum state diagonalization 18,19 , quantum simulation [20][21][22][23] , fidelity estimation 24 , unsampling 25 , consistent histories 26 , and linear systems [27][28][29] . For these applications, the choice of C is less obvious.…”

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confidence: 99%

“…In this work, we connect the trainability of VQAs to the choice of C. For the abstract applications in refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] , it is important for C to be operational, so that small values of C imply that the task is almost accomplished. Consider an example of state preparation, where the goal is to find a gate sequence that prepares a target state ψ 0…”

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confidence: 99%

“…While our work is for general VQAs, barren plateaus for global cost functions were noted for specific VQAs and for a very specific tensor-product example by our research group 14,18 , and more recently in 29 . This motivated the proposal of local cost functions 14,16,18,22,[25][26][27] , where one compares objects (states or operators) with respect to each individual qubit, rather than in a global sense, and therein it was shown that these local cost functions have indirect operational meaning.…”

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confidence: 99%

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Cost function dependent barren plateaus in shallow parametrized quantum circuits

et al. 2021

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Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is $${\mathcal{O}}(\mathrm{log}\,n)$$ O ( log n ) . Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

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Section: Corollarymentioning

confidence: 99%

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Cost function dependent barren plateaus in shallow parametrized quantum circuits

et al. 2021

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“…It has been shown, however, that quadratic Hamiltonians can be fast forwarded, meaning the evolution of the systems under such Hamiltonians can be simulated with circuits whose depths do not grow significantly with the simulation time [25]. A recent work took advantage of this to variationally compile approximate circuits with a hybrid classical-quantum algorithm for fast-forwarded simulations [26]. The circuits, however, are approximate, with error that grows with increasing fast-forwarding time.…”

Section: Introductionmentioning

confidence: 99%

Domain-specific compilers for dynamic simulations of quantum materials on quantum computers

Bassman¹,

Gulania²,

Powers³

et al. 2020

Quantum Sci. Technol.

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Dynamic simulation of materials is a promising application for noisy intermediate-scale quantum (NISQ) computers. The difficulty in carrying out such simulations is that a quantum circuit must be executed for each time-step, and in general, these circuits grow in size with the number of time-steps simulated. NISQ computers can only produce high-fidelity results for circuits up to a given size due to gate error rates and qubit decoherence times, limiting the number of time-steps that can be successfully simulated. Here, we present a method for producing circuits that are constant in depth with increasing number of simulated time-steps for dynamic simulations of quantum materials for a specialized set of Hamiltonians derived from the one-dimensional Heisenberg model. We show how to build the constant-depth circuit structure for each system size, where the number of CNOT gates in the N -qubit constant-depth circuit structure grows only quadratically with N . The constantdepth circuits, which comprise an array of two-qubit matchgates on nearest-neighbor qubits, are constructed based on a set of multi-matchgate identities that we introduce as conjectures. Tutorials with the full code for generating our constant-depth circuits for the XY and transverse field Ising models are included. Using our constant-depth circuits, we are successfully able to demonstrate longtime dynamic simulations of quantum systems with up to five spins on available quantum hardware. Such constant-depth circuits could enable simulations of long-time dynamics for scientifically and technologically relevant quantum materials, enabling the observation of interesting and important atomic-level physics.

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Deep Ising Born Machine

Cao

2023

Adv Quantum Tech

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A quantum neural network (QNN) is a method to find patterns in quantum data and has a wide range of applications including quantum chemistry, quantum computation, quantum metrology, and quantum simulation. Efficiency and universality are two desirable properties of a QNN but are unfortunately contradictory. In this work, we examine a deep Ising Born machine (DIBoM), and show it has a good balance between efficiency and universality. More precisely, the DIBoM has a flexible number of parameters to be efficient, and achieves provable universality with sufficient parameters. The architecture of the DIBoM is based on generalized controlled-Z gates, conditional gates, and some other ingredients. To compare the universality of the DIBoM with other QNNs, we propose a fidelity-based expressivity measure, which may be of independent interest. Extensive empirical evaluations corroborate that the DIBoM is both efficient and expressive.

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Variational fast forwarding for quantum simulation beyond the coherence time

Cited by 219 publications

References 46 publications

Cost function dependent barren plateaus in shallow parametrized quantum circuits

Cost function dependent barren plateaus in shallow parametrized quantum circuits

Domain-specific compilers for dynamic simulations of quantum materials on quantum computers

Deep Ising Born Machine

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