Simulating non-native cubic interactions on noisy quantum machines

Shi, Yuan; Castelli, Alessandro; Wu, Xian; Joseph, I.; Geyko, V. I.; Graziani, Frank; Libby, Stephen B.; Parker, Jeffrey B.; Rosen, Yaniv; Martinez, Luis A.; Dubois, Jonathan

doi:10.1103/physreva.103.062608

Cited by 16 publications

(15 citation statements)

References 43 publications

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“…Other near term platforms that use superconductors, trapped ions, neutral atoms, or photons may have more favorable trade offs in terms of gate depth, connectivity, crosstalk, and other factors that could help to reach the Lyapunov regime more quickly. One such example is the optimal control approach used by the LLNL Quantum Design and Integration Testbed (Qu-DIT) [53,54], which was shown to outperform Rigetti by over an order of magnitude in simulation depth, in proportion to the length of the native gate decomposition [55]. However the Qu-DIT platform is currently limited to a single fourlevel qudit, with plans to scale up.…”

Section: Discussionmentioning

confidence: 99%

Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations

Porter¹,

Joseph²

2021

Preprint

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In this work, the observation of the Lyapunov exponent in noisy quantum simulation experiments is shown to be bounded by three conditions that together make it presently out of reach. These conditions form a triangular region in parameter space with an area dependent on the number of qubits used. We predict that at least six qubits and 2.5 − 13x less error per CNOT gate on IBM-Q or 0.87 − 9.6x less error per Mølmer-Sørensen gate on IonQ are needed for the Lyapunov exponent to become experimentally observable. This prediction is achieved through close study of the quantum sawtooth map (QSM), which is the most efficiently simulated quantum system with a provably chaotic classical counterpart and rich dynamics.

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Section: Discussionmentioning

confidence: 99%

Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations

Porter¹,

Joseph²

2021

Preprint

Self Cite

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“…However, only δI 2 and δI 3 grow exponentially with time. Equations ( 1) and (14) indicate that for the unstable eigenmode of the linearized system, δI 1 and δA 1 remain constant.…”

Section: A Classical Theory For Three-wave Interaction and Instabilitymentioning

confidence: 99%

“…by quantizing the classical fields A j as quantum operators Âj on the occupation number states. The resulting Hamiltonian for a homogeneous (spatially independent) quantum three-wave interaction with complex coupling constant g is [14,21,27,28]…”

Section: B Quantum Theory For Three-wave Interactionmentioning

confidence: 99%

“…Characterizing such quantum instabilities is not only of academic interest, but also has practical value for identifying when they can be realized or inevitably occur on quantum systems. The three-wave interaction, which experiences a classical instability, was recently simulated on a quantum computer [14]. Although the simulation was not of high enough dimension to allow for the instability, it demonstrates the importance of the present work.…”

Section: Introductionmentioning

confidence: 96%

“…The instability transfers energy-momentum from the large wave to the two smaller waves. Although this interaction and instability are well-known [22][23][24][25], its quantum description is less studied [14,21,[26][27][28], and the correspondence between the classical instability and its quantum counterpart has not been established. Section II will focus on providing background to the classical three-wave instability and the quantum theory of three-wave interaction by Shi et al [14,21,27,28].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum Instability

Q.¹,

Qin²

2022

Preprint

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The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a unitary quantum description. Using the example of three-wave interactions, we describe how a time-independent, finite-dimensional quantum system, which is Hermitian with all real eigenvalues, can give rise to a linear instability corresponding to that in the classical system. We show that the instability is realized in the quantum theory as a cascade of the wave function in the space of occupation number states, and an unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.The conditions for quantum instability are described.

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Simulating nonlinear optical processes on a superconducting quantum device

Shi,

Evert,

Brown

et al. 2024

J. Plasma Phys.

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Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be modelled as wave–wave interactions. In this paper, we develop a quantization approach to convert nonlinear wave–wave interaction problems to Hamiltonian simulation problems. We demonstrate our approach using two qubits on a superconducting device. Unlike a photonic device, a superconducting device does not naturally have the desired interactions in its native Hamiltonian. Nevertheless, Hamiltonian simulations can still be performed by decomposing required unitary operations into native gates. To improve experimental results, we employ a range of error-mitigation techniques. Apart from readout error mitigation, we use randomized compilation to transform undiagnosed coherent errors into well-behaved stochastic Pauli channels. Moreover, to compensate for stochastic noise, we rescale exponentially decaying probability amplitudes using rates measured from cycle benchmarking. We carefully consider how different choices of product-formula algorithms affect the overall error and show how a trade-off can be made to best utilize limited quantum resources. This study provides an example of how plasma problems may be solved on near-term quantum computing platforms.

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Simulating non-native cubic interactions on noisy quantum machines

Cited by 16 publications

References 43 publications

Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations

Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations

Quantum Instability

Simulating nonlinear optical processes on a superconducting quantum device

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