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arXiv:1810.04817 · Physical Review A

Ultrafast variational simulation of nontrivial quantum states with long-range interactions

Wen Wei Ho, Cheryne Jonay, Timothy H. Hsieh

Published May 22, 2019• 32 citations
arXivHTMLPDF

Abstract

State preparation protocols ideally require as minimal operations as possible in order to be implemented in near-term, potentially noisy quantum devices. Motivated by long-range interactions (LRIs) intrinsic to many present-day experimental platforms (trapped ions, Rydberg atom arrays, etc.), we investigate the efficacy of variationally simulating nontrivial quantum states using the variational quantum-classical simulation (VQCS) protocol explored recently [W. W. Ho and T. H. Hsieh, SciPost Phys. 6, 29 (2019)], in the presence of LRIs. We show that this approach leads to extremely efficient state preparation: for example, Greenberger-Horne-Zeilinger (GHZ) states can be prepared with $O(1)$ iterations of the protocol, and a quantum critical point of the long-range transverse-field Ising model (TFIM) can be prepared with $>99%$ fidelity on a 100-qubit system with only one iteration. Furthermore, we show that VQCS with LRIs is a promising route for exploring generic points in the phase diagram of the long-range TFIM. Our approach thus provides concrete, ultrafast protocols for quantum simulators equipped with long-range interactions.

DOI
10.1103/physreva.99.052332

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State preparation protocols ideally require as minimal operations as possible in order to be implemented in near-term, potentially noisy quantum devices. Motivated by long-range interactions (LRIs) intrinsic to many present-day experimental platforms (trapped ions, Rydberg atom arrays, etc.), we investigate the efficacy of variationally simulating nontrivial quantum states using the variational quantum-classical simulation (VQCS) protocol explored recently [W. W. Ho and T. H. Hsieh, SciPost Phys. 6, 29 (2019)], in the presence of LRIs. We show that this approach leads to extremely efficient state preparation: for example, Greenberger-Horne-Zeilinger (GHZ) states can be prepared with O(1)O(1)O(1) iterations of the protocol, and a quantum critical point of the long-range transverse-field Ising model (TFIM) can be prepared with >99>99%>99 fidelity on a 100-qubit system with only one iteration. Furthermore, we show that VQCS with LRIs is a promising route for exploring generic points in the phase diagram of the long-range TFIM. Our approach thus provides concrete, ultrafast protocols for quantum simulators equipped with long-range interactions.
State preparation protocols ideally require as minimal operations as possible, in order to be implemented in near-term, potentially noisy quantum devices. Motivated by long range interactions (LRIs) intrinsic to many present-day experimental platforms (trapped ions, Rydberg atom arrays, etc.), we investigate the efficacy of variationally simulating non-trivial quantum states using the Variational Quantum-Classical Simulation (VQCS) protocol explored recently in [SciPost Phys. 6, 029 (2019)], in the presence of LRIs. We show that this approach leads to extremely efficient state preparation: for example, Greene-Horne-Zeilinger (GHZ) states can be prepared with O(1) iterations of the protocol, and a quantum critical point of the long range transverse field Ising model (TFIM) can be prepared with > 99% fidelity on a 100 qubit system with only one iteration. Furthermore, we show that VQCS with LRIs is a promising route for exploring generic points in the phase diagram of the long-range TFIM. Our approach thus provides concrete, ultrafast protocols for quantum simulators equipped with long range interactions.
In variational Monte Carlo (VMC) calculations of NNN-site quantum systems with arbitrary all-to-all two-body interactions, evaluating the local energy generally costs O(N3)O(N^3)O(N3). We introduce a new framework that reduces this cost to O(N)O(N)O(N) for tensor network states, capable of scalable and accurate computation of real-time dynamics and ground states. As a result, we obtain accurate simulations of the adiabatic real-time protocol of a 10×1010\times1010×10 dipolar XY model realized in a Rydberg simulator [C. Chen et al., Nature 616, 691 (2023)], which was previously beyond the reach of classical simulation. Going beyond quantum experiments, we also directly perform ground state VMC to compare with the adiabatic state preparation. Our work demonstrates tensor network VMC as a powerful classical simulator for long-range quantum platforms such as Rydberg and ion-trap simulators, which are currently in urgent need of scalable classical benchmarking tools. As a separate technical contribution, we resolve the pathology of evolving from product states within of tensor network VMC.
We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with \bm{L} 𝐋 variational parameters and physical runtimes \bm{T} 𝐓 that scale linearly with the system size \bm{L} 𝐋 . We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational Ansätze as good descriptions of non-trivial states of matter.
Abstract Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the performance. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology.
Long-range interactions are the source of many equilibrium and out-of-equilibrium quantum many-body phenomena. Analog simulators based on ionic, atomic, superconducting, and molecular systems provide a natural platform to obtain these interactions using vibration- and photon-mediated processes. Recent experimental advances, such as their integration in multi-mode cavities and waveguides, or the use of Raman-assisted transitions, enable dynamical control over both the strength and the spatial range of these interactions, thereby rendering them programmable. Here, we develop a hybrid classical-quantum toolbox that exploits this tunability to enhance many-body state preparation in analog simulators beyond fixed-connectivity architectures. Our approach is based on classical pre-compilation in homogeneous small systems, whose optimized parameters are extrapolated iteratively to larger system sizes, and then refined on the quantum hardware using noise-aware hybrid re-optimization and error-mitigation techniques. We benchmark this strategy across several fermionic, spin-1/2, and spin-1 models, demonstrating orders-of-magnitude improvements in fidelity and energy estimation for system sizes ranging from 100 to 1000 particles. Finally, we show that the combination of such high-fidelity programmable state preparation techniques with tunable-range out-of-equilibrium dynamics enables controlled studies of many-body thermalization in regimes accessible to current experimental platforms. Our results establish programmable long-range interactions as a powerful resource for next-generation analog quantum simulators.
Preparing finite-temperature states in quantum simulators of spin systems, such as trapped ions or Rydberg atoms in optical tweezers, is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality and equivalent to the one in Lu et al., PRX Quantum 2, 020321 (2021). It consists of classical importance sampling of initial states and a measurement of the Loschmidt echo with a quantum simulator. We use the method as a quantum-inspired classical algorithm and simulate the protocol with matrix product states to analyze the requirements on a quantum simulator. This way, we show that a finite-temperature phase transition in the long-range transverse-field Ising model can be characterized in trapped ion quantum simulators. We propose a concrete measurement protocol for the Loschmidt echo and discuss the influence of measurement noise, dephasing, as well as state preparation and measurement errors. We argue that the algorithm is robust against those imperfections under realistic conditions.