Parallel-sequential circuits provide a tunable family of quantum circuit layouts that numerically outperform brickwall, sequential, and log-depth circuits for 1D ground-state preparation under realistic noise models.
Entanglement scaling in matrix product state representation of smooth functions and their shallow quantum circuit approximations
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abstract
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input functions, including probability distributions, with only linear number of gates. We derive rigorous asymptotic expansions for the decay of entanglement across bonds in the MPS representation depending on the smoothness of the input function, real or complex. We also consider the dependence of the entanglement on localization properties and function support. Based on these analytical results we construct an improved MPS-based algorithm yielding shallow and accurate encoding quantum circuits. By using Tensor Cross Interpolation we are able to construct utility-scale quantum circuits in a compute- and memory-efficient way. We validate our methods by loading heavy-tailed distributions, including Levy, important in finance, but they apply to any smooth function inputs. We test the performance of the resulting quantum circuits by executing and sampling from them on IBM quantum devices, for up to 156 qubits.
fields
quant-ph 3years
2025 3verdicts
UNVERDICTED 3representative citing papers
A two-step method minimizes entanglement entropy of target states before using matrix product state representations to achieve high-accuracy quantum state preparation on NISQ devices.
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
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State preparation with parallel-sequential circuits
Parallel-sequential circuits provide a tunable family of quantum circuit layouts that numerically outperform brickwall, sequential, and log-depth circuits for 1D ground-state preparation under realistic noise models.
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Minimizing entanglement entropy for enhanced quantum state preparation
A two-step method minimizes entanglement entropy of target states before using matrix product state representations to achieve high-accuracy quantum state preparation on NISQ devices.
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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.