Quantum algorithms for Uhlmann transformation

• URL: http://arxiv.org/abs/2509.03619v3
• Date: Mon, 03 Nov 2025 09:51:33 GMT
• Title: Quantum algorithms for Uhlmann transformation
• Authors: Takeru Utsumi, Yoshifumi Nakata, Qisheng Wang, Ryuji Takagi,
• Abstract summary: We propose quantum algorithms that realize the Uhlmann transformation in query and access models.<n>Our algorithms can be-time for low-rank states, exhibiting an exponential improvement over the previous approach.<n>We apply our algorithms to fidelity estimation between two states, and substantially improve the previous best query and sample complexities.
• Score: 10.701270379190106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Uhlmann's theorem is a central result in quantum information theory, which associates the closeness of two quantum states with that of their purifications. The theorem also well characterizes a fundamental task: how close a pure quantum state can be transformed into another state via local operations acting only on its subsystem. The optimal transformation for this task is called the Uhlmann transformation, which has broad applications in various information-processing tasks. However, its quantum circuit implementation and computational cost have remained unclear, limiting the utility of the transformation. In this work, we fill this gap by proposing quantum algorithms that realize the Uhlmann transformation in query and sample access models. Notably, our Uhlmann transformation algorithms can be polynomial-time for low-rank states, exhibiting an exponential improvement over the previous approach and other naive approaches based on quantum state tomography. In addition, we derive a lower bound on the query and sample complexities of the Uhlmann transformation for a deeper understanding of its algorithmic features. We apply our Uhlmann transformation algorithms to fidelity estimation between two states, and substantially improve the previous best query and sample complexities. We further discuss other applications to several information-theoretic tasks, including entanglement transmission, quantum state merging, and the algorithmic implementation of the Petz recovery map, providing a comprehensive evaluation of their computational costs. These results, hence, contribute to the practical realization of such widely recognized and useful protocols.

Related papers

• Quantum Approximate Optimization Algorithm for MIMO with Quantized b-bit Beamforming [47.98440449939344]
  Multiple-input multiple-output (MIMO) is critical for 6G communication, offering improved spectral efficiency and reliability.<n>This paper explores the use of the Quantum Approximate Optimization Algorithm (QAOA) and alternating optimization to address the problem of b-bit quantized phase shifters both at the transmitter and the receiver.<n>We demonstrate that the structure of this quantized beamforming problem aligns naturally with hybrid-classical methods like QAOA, as the phase shifts used in beamforming can be directly mapped to rotation gates in a quantum circuit.
  arXiv  Detail & Related papers  (2025-10-07T17:53:02Z)
• Advancing Quantum State Preparation Using Decision Diagram with Local Invertible Maps [5.328178128965817]
  We propose a family of efficient Quantum State Preparation (QSP) algorithms tailored to different numbers of available ancilla qubits.<n>Our approach exploits the power of Local Invertible Map Decision Diagrams (LimTDDs) to reduce quantum circuit complexity.
  arXiv  Detail & Related papers  (2025-07-23T03:34:44Z)
• Classical post-processing approach for quantum amplitude estimation [0.0]
  We propose an approach for quantum amplitude estimation (QAE) designed to enhance computational efficiency while minimizing the reliance on quantum resources.<n>Our method leverages quantum computers to generate a sequence of signals, from which the quantum amplitude is inferred through classical post-processing techniques.
  arXiv  Detail & Related papers  (2025-02-08T15:51:31Z)
• Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers [39.58317527488534]
  This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic non-relativistic elastic scattering processes on a quantum computer.
  arXiv  Detail & Related papers  (2024-07-04T21:11:05Z)
• Fast Quantum Process Tomography via Riemannian Gradient Descent [3.1406146587437904]
  Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data.
  arXiv  Detail & Related papers  (2024-04-29T16:28:14Z)
• Surrogate optimization of variational quantum circuits [1.0546736060336612]
  Variational quantum eigensolvers are touted as a near-term algorithm capable of impacting many applications. Finding algorithms and methods to improve convergence is important to accelerate the capabilities of near-term hardware for VQE.
  arXiv  Detail & Related papers  (2024-04-03T18:00:00Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval [1.6421520075844793]
  A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable problem. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems.
  arXiv  Detail & Related papers  (2024-02-09T15:01:56Z)
• Hamiltonian Encoding for Quantum Approximate Time Evolution of Kinetic Energy Operator [2.184775414778289]
  The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers. We have proposed a new encoding method, namely quantum approximate time evolution (QATE) for the quantum implementation of the kinetic energy operator.
  arXiv  Detail & Related papers  (2023-10-05T05:25:38Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Unitary Complexity and the Uhlmann Transformation Problem [39.6823854861458]
  We introduce a framework for unitary synthesis problems, including notions of reductions and unitary complexity classes.<n>We use this framework to study the complexity of transforming one entangled state into another via local operations.<n>Our framework for unitary complexity thus provides new avenues for studying the computational complexity of many natural quantum information processing tasks.
  arXiv  Detail & Related papers  (2023-06-22T17:46:39Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Quantum Phase Processing and its Applications in Estimating Phase and Entropies [10.8525801756287]
  "quantum phase processing" can directly apply arbitrary trigonometric transformations to eigenphases of a unitary operator. Quantum phase processing can extract the eigen-information of quantum systems by simply measuring the ancilla qubit. We propose a new quantum phase estimation algorithm without quantum Fourier transform, which requires the fewest ancilla qubits and matches the best performance so far.
  arXiv  Detail & Related papers  (2022-09-28T17:41:19Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Detailed Account of Complexity for Implementation of Some Gate-Based Quantum Algorithms [55.41644538483948]
  In particular, some steps of the implementation, as state preparation and readout processes, can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of quantum algorithms for solving linear systems of equations and linear system of differential equations.
  arXiv  Detail & Related papers  (2021-06-23T16:33:33Z)

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.