Faster State Preparation with Randomization

• URL: http://arxiv.org/abs/2510.12247v1
• Date: Tue, 14 Oct 2025 07:57:06 GMT
• Title: Faster State Preparation with Randomization
• Abstract summary: We introduce a randomized protocol that improves the accuracy-cost trade-off for states with hierarchical amplitude structures.<n>We rigorously prove that the randomized ensemble achieves a quadratic improvement in trace-distance error over the deterministic truncation method.<n>The method broadens the class of states preparable on near-term and fault-tolerant quantum devices.
• Score: 18.283557976657445
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum state preparation remains a dominant cost in many quantum algorithms. We introduce a randomized protocol that fundamentally improves the accuracy-cost trade-off for states with hierarchical amplitude structures, where amplitudes decay exponentially or by a power law with exponent greater than one. Rather than commonly employed deterministically truncating small amplitudes, we prepare an ensemble of simple circuits: each retains all large amplitudes while amplifying a single small one. We rigorously prove that the randomized ensemble achieves a quadratic improvement in trace-distance error over the deterministic truncation method. This quadratic scaling halves the number of encoded amplitudes for exponential decay and yields polynomial reductions for power-law decay, which directly translates to a reduction in circuit depth. Demonstrations on molecular wavefunctions (LiH), many-body ground states (transverse-field Ising), and machine-learning parameters (ResNet) validate the approach across diverse applications. The method broadens the class of states preparable on near-term and fault-tolerant quantum devices.

Related papers

• The Gain-Engineered Transmon [68.89136228609398]
  We introduce and experimentally realize a noise-biased qubit in a standard transmon-readout resonator circuit.<n>Our results open a path towards using this system as a simple building-block for hardware-efficient quantum error detection and correction schemes.
  arXiv  Detail & Related papers  (2026-08-26T17:00:42Z)
• Scaling Laws for Neural-Network Quantum States [35.51694331707922]
  Scaling laws offer a way to characterize the complexity of a learning problem.<n>We show that scaling laws can be used to benchmark variational anstze.
  arXiv  Detail & Related papers  (2026-06-01T18:59:01Z)
• Algebraic Reduction to Improve an Optimally Bounded Quantum State Preparation Algorithm [0.6875312133832078]
  Preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms.<n>A simpler algebraic decomposition is proposed to separate the preparation of the real part of the desired state from the complex one.<n>The reduction in complexity is due to the use of a single operator $$ for each uniformly controlled gate, instead of the three in the original decomposition.
  arXiv  Detail & Related papers  (2026-02-06T09:40:09Z)
• Preconditioned Multivariate Quantum Solution Extraction [0.0]
  Quantum computers can potentially provide high-degree speed-ups for solving PDEs.<n>Many algorithms simply end with preparing the quantum state encoding the solution in its amplitudes.<n>We present a technique for extracting a smooth positive function encoded in the amplitudes of a quantum state.
  arXiv  Detail & Related papers  (2026-01-08T16:21:49Z)
• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• On the Constant Depth Implementation of Pauli Exponentials [49.48516314472825]
  We decompose $Zotimes n$ exponentials of arbitrary length into circuits of constant depth using $mathcalO(n)$ ancillae and two-body XX and ZZ interactions.<n>We prove the correctness of our approach, after introducing novel rewrite rules for circuits which benefit from qubit recycling.
  arXiv  Detail & Related papers  (2024-08-15T17:09:08Z)
• Quantum quench dynamics as a shortcut to adiabaticity [31.114245664719455]
  We develop and test a quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. Our experiments show that this approach significantly outperforms the adiabatic algorithm.
  arXiv  Detail & Related papers  (2024-05-31T17:07:43Z)
• Attention to Quantum Complexity [21.766643620345494]
  We introduce the Quantum Attention Network (QuAN), a versatile classical AI framework. QuAN treats measurement snapshots as tokens while respecting their permutation invariance. We rigorously test QuAN across three distinct quantum simulation settings.
  arXiv  Detail & Related papers  (2024-05-19T17:46:40Z)
• Non-Linear Transformations of Quantum Amplitudes: Exponential Improvement, Generalization, and Applications [0.0]
  Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. We present a framework for applying a general class of non-linear functions to the amplitudes of quantum states. Our work provides an important and efficient building block with potentially numerous applications in areas such as optimization, state preparation, quantum chemistry, and machine learning.
  arXiv  Detail & Related papers  (2023-09-18T14:57:21Z)
• Refining the weighted subspace-search variational quantum eigensolver: compression of ansätze into a single pure state and optimization of weights [1.0485739694839669]
  The weighted subspace-search variational quantum eigensolver (SSVQE) is a prominent algorithm for calculating excited-state properties of quantum systems. In this work, we elaborate on some of its fundamental features with the aim of improving its practical realization.
  arXiv  Detail & Related papers  (2023-06-20T18:53:09Z)
• Approximate encoding of quantum states using shallow circuits [0.0]
  A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. Here, we aim at creating an approximate encoding of the target state using a limited number of gates. Our work offers a universal method to prepare target states using local gates and represents a significant improvement over known strategies.
  arXiv  Detail & Related papers  (2022-06-30T18:00:04Z)
• Orthogonal-ansatz VQE: Locating excited states without modifying a cost-function [0.0]
  We develop an excited-state VQE solver which trades increasing measurement complexity for increasing circuit complexity. We demonstrate our approach with three distinct ansatze, beginning with a simple single-body example, before generalizing to accommodate the full Hilbert space spanned by all qubits.
  arXiv  Detail & Related papers  (2022-04-09T02:22:09Z)
• Quantum error mitigation via matrix product operators [27.426057220671336]
  Quantum error mitigation (QEM) can suppress errors in measurement results via repeated experiments and post decomposition of data. MPO representation increases the accuracy of modeling noise without consuming more experimental resources. Our method is hopeful of being applied to circuits in higher dimensions with more qubits and deeper depth.
  arXiv  Detail & Related papers  (2022-01-03T16:57:43Z)
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences [41.42601188771239]
  We create non-classical states of light in three-dimensional microwave cavities. These states are useful for quantum computation. We show that this way of creating non-classical states is robust to fluctuations of the system parameters.
  arXiv  Detail & Related papers  (2021-11-15T18:20:38Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.