Logarithmic-depth quantum state preparation of polynomials

• URL: http://arxiv.org/abs/2603.16527v3
• Date: Wed, 25 Mar 2026 11:11:25 GMT
• Title: Logarithmic-depth quantum state preparation of polynomials
• Abstract summary: This work introduces a method for preparing quantum states whose amplitudes are given by a degree$-d$ using circuits with logarithmic depth in the number $n$ of qubits.<n>Because approximations are ubiquitous in scientific computing, this construction provides a scalable and resource-efficient approach to quantum state preparation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum state preparation is a central primitive in many quantum algorithms, yet it is generally resource intensive, with efficient constructions known only for structured families of states. This work introduces a method for preparing quantum states whose amplitudes are given by a degree$-d$ polynomial, using circuits with logarithmic depth in the number $n$ of qubits and only $\mathcal O(n)$ ancilla qubits, improving previous approaches that required linear-depth circuits. The construction first relies on a block-encoding of an affine diagonal operator based on its Pauli-basis decomposition, which involves only $n$ terms. A modified linear-combination-of-unitaries (LCU) technique is introduced to implement this decomposition in logarithmic depth, together with a novel circuit for the EXACT-one oracle that flags basis states in which exactly one qubit is in the state $|1\rangle$. It then uses a generalized quantum eigenvalue transformation (GQET) to promote this affine operator to an arbitrary degree polynomial. Theoretical analysis and numerical simulations are reported along with a proof-of-principle implementation on a trapped-ion quantum processor using $14$ qubits and more than $500$ primitive quantum gates. Because polynomial approximations are ubiquitous in scientific computing, this construction provides a scalable and resource-efficient approach to quantum state preparation, further improving the potential of quantum algorithms in fields such as chemistry, physics, engineering, and finance.

Related papers

• Verifiable quantum advantage in extremely low depth [52.51019642214249]
  We give a problem that is solvable by shallow quantum circuits, hard for computation in time under lattice-based assumptions.<n>We prove that shallow quantum circuits have sufficient structure to solve certain classically hard tasks whose solutions can be verified efficiently.
  arXiv  Detail & Related papers  (2026-09-01T15:54:34Z)
• Analytical construction of $(n, n-1)$ quantum random access codes saturating the conjectured bound [0.0]
  Quantum Random Access Codes (QRACs) embody the fundamental trade-off between the compressibility of information into limited quantum resources.<n>We establish an analytical construction method for $(n, n-1)$-QRACs by using an explicit operator formalism.<n>We present a systematic algorithm to decompose the derived optimal POVM into standard quantum gates.
  arXiv  Detail & Related papers  (2026-01-27T04:43:43Z)
• Efficient Quantum State Preparation with Bucket Brigade QRAM [47.72095699729477]
  Preparation of data in quantum states is a critical component in the design of quantum algorithms.<n>One of the main approaches to achieve efficient state preparation is through the use of Quantum Random Access Memory (QRAM)<n>We present a framework that integrates the physical model of the Bucket Brigade QRAM (BBQRAM) with the classical data structure of the Segment Tree to achieve efficient state preparation.
  arXiv  Detail & Related papers  (2025-10-17T18:50:07Z)
• Randomized Quantum Singular Value Transformation [18.660349597156266]
  We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT)<n>Standard implementations of QSVT rely on block encodings of the Hamiltonian, requiring a logarithmic number of ancilla qubits, intricate multi-qubit control, and circuit depth scaling linearly with the number of Hamiltonian terms.<n>Our algorithms use only a single ancilla qubit and entirely avoid block encodings.
  arXiv  Detail & Related papers  (2025-10-08T10:14:15Z)
• Quantum Krylov Algorithm for Szegö Quadrature [0.8158532237212478]
  We present a quantum algorithm to evaluate matrix elements of functions of unitary operators.<n>The method is based on calculating quadrature nodes and weights using data collected from a quantum processor.
  arXiv  Detail & Related papers  (2025-09-23T16:13:08Z)
• EHands: Quantum Protocol for Polynomial Computation on Real-Valued Encoded States [0.08209843760716957]
  We present EHands, a quantum-native protocol for implementing multivariable transformations on quantum processors.<n>EHands operates directly on vectorized real-valued inputs prepared in the initial state.<n>The protocol's effectiveness is demonstrated through experimental validation on IBM's Heron-class quantum processors.
  arXiv  Detail & Related papers  (2025-02-21T20:52:16Z)
• Efficient explicit circuit for quantum state preparation of piece-wise continuous functions [0.6906005491572401]
  We propose a method to upload a function $f(x)$ on the interval $x in [-1,1]$ into a pure quantum state consisting of qubits.<n>The preparation cost has $mathcalO(nlog n)$ scaling in the number of qubits $n$ and linear scaling with the degree of the $Q$.<n>We introduce an explicit algorithm for uploading such functions using four reals that meet specific parity and boundedness conditions.
  arXiv  Detail & Related papers  (2024-11-02T04:20:31Z)
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
  Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2023-10-11T15:59:54Z)
• Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians [0.7332146059733189]
  We propose a method for constructing $textttPREPARE$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry.<n>The $textttPREPARE$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes.
  arXiv  Detail & Related papers  (2023-08-26T05:32:38Z)
• Iterative Qubit Coupled Cluster using only Clifford circuits [36.136619420474766]
  An ideal state preparation protocol can be characterized by being easily generated classically. We propose a method that meets these requirements by introducing a variant of the iterative qubit coupled cluster (iQCC) We demonstrate the algorithm's correctness in ground-state simulations and extend our study to complex systems like the titanium-based compound Ti(C5H5)(CH3)3 with a (20, 20) active space.
  arXiv  Detail & Related papers  (2022-11-18T20:31:10Z)
• K-sparse Pure State Tomography with Phase Estimation [1.2183405753834557]
  Quantum state tomography (QST) for reconstructing pure states requires exponentially increasing resources and measurements with the number of qubits. QST reconstruction for any pure state composed of the superposition of $K$ different computational basis states of $n$bits in a specific measurement set-up is presented.
  arXiv  Detail & Related papers  (2021-11-08T09:43:12Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)
• 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)

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.