Deterministic Quantum Phase Estimation with Linear Circuit Complexity in a Photonic System

• URL: http://arxiv.org/abs/2607.13404v1
• Date: Wed, 15 Jul 2026 03:02:14 GMT
• Title: Deterministic Quantum Phase Estimation with Linear Circuit Complexity in a Photonic System
• Abstract summary: Quantum algorithms solve certain computational problems faster than the best known classical algorithms.<n>We introduce a QPE algorithm that successfully reduces the circuit complexity from $mathcalO(n2)$ to $mathcalO(n)$ for a special class of unitary operators.
• Score: 4.969716969054012
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum algorithms solve certain computational problems faster than the best known classical algorithms. Many algorithms, including Shor's for factoring, Grover's for unstructured search, and the HHL for solving linear systems, rely on quantum phase estimation (QPE) as a fundamental subroutine. The QPE protocol proceeds through the initialization of a control register in a uniform superposition, controlled unitary evolution encoding the eigenphase, and a final inverse quantum Fourier transform followed by measurement to extract the phase. Here, we address a special class of unitary operators that frequently appear in quantum Fourier transform-based protocols, cyclic group representations, and periodically evolving quantum systems. We introduce a QPE algorithm that successfully reduces the circuit complexity from $\mathcal{O}(n^2)$ to $\mathcal{O}(n)$ for a special class of unitary operators and implement it on a four-qubit photonic system. The four-qubit system is realised using a photon pair, with two qubits encoded in its polarization degree of freedom and the remaining two in its path modes. In contrast to previous photonic implementations of QPE based on dual-rail encoding and KLM protocol, where controlled operations are inherently probabilistic and thus reduce the overall success probability of phase estimation, our scheme is fully deterministic. Moreover, it is scalable to higher-dimensional unitaries, provided the underlying structure of the unitaries is preserved.

Related papers

• Breaking the Curse of Dimensionality in Quantum PDE Solvers via Gevrey Regularity [4.219859693008517]
  We use the Gevrey hierarchy to stratifies the space between smooth and analytic functions.<n>We show how our Fourier methods do so efficiently at varying target precisions on a quantum computer.<n>As an application, we introduce a hierarchy of many-body quantum simulation pipelines.
  arXiv  Detail & Related papers  (2026-08-08T03:40:25Z)
• Iterative quantum phase estimation with cQED encoding [0.0]
  Quantum phase estimation is a cornerstone algorithm for determining eigenvalues of unitary operators or Hamiltonians.<n>We propose a conceptually simple and experimentally feasible alternative that exploits the toolbox of circuit quantum electrodynamics.<n>A bosonic mode serves as an efficient quantum memory in which the binary digits of the phase are encoded into the direction of phase-space rotations.
  arXiv  Detail & Related papers  (2026-06-20T14:45:05Z)
• Information Propagation in Rydberg Arrays via Analog OTOC Calculations [37.108493798440655]
  Out-of-time-order correlators (OTOCs) are the main tool for probing quantum chaos and scrambling.<n>We develop and implement a randomized measurement protocol to compute OTOCs on Aquila by QuEra Computing.<n>This work establishes the first demonstration of fully analog randomized OTOC measurements in neutral-atom simulators.
  arXiv  Detail & Related papers  (2026-04-06T18:00:05Z)
• Semidefinite Programming for Quantum Channel Learning [35.18016233072556]
  Semidefinite Programming (SDP) can be applied to solve the fidelity optimization problem with respect to the Choi matrix.<n>We have tested several commercially available SDP solvers, all of which allowed for the reconstruction of quantum channels of different forms.<n>This suggests that a relatively small Kraus rank quantum channel is typically sufficient to describe experimentally observed classical data.
  arXiv  Detail & Related papers  (2026-01-18T17:26:45Z)
• Neural Guided Sampling for Quantum Circuit Optimization [26.90377134346014]
  Translating a quantum circuit on a specific hardware topology with a reduced set of available gates, also known as transpilation, comes with a substantial increase in the length of the equivalent circuit.<n>One method to address efficient transpilation is based on approaches known from optimization, e.g. by using random sampling and token replacement strategies.<n>Here, we propose in this work 2D neural guided sampling. Thus, given a 2D representation of a quantum circuit, a neural network predicts groups of gates in the quantum circuit, which are likely reducible.
  arXiv  Detail & Related papers  (2025-10-14T12:09:05Z)
• 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)
• Double-bracket algorithm for quantum signal processing without post-selection [0.0]
  Quantum signal processing (QSP) is a fundamental primitive in various quantum algorithms.<n>Despite its versatility, a potentially underappreciated challenge is that all systematic protocols for implementing QSP rely on post-selection.<n>We introduce a new formula for implementing QSP transformations of Hermitian matrices, which requires neither auxiliary qubits nor post-selection.
  arXiv  Detail & Related papers  (2025-04-01T18:00:04Z)
• Extending Quantum Perceptrons: Rydberg Devices, Multi-Class Classification, and Error Tolerance [67.77677387243135]
  Quantum Neuromorphic Computing (QNC) merges quantum computation with neural computation to create scalable, noise-resilient algorithms for quantum machine learning (QML) At the core of QNC is the quantum perceptron (QP), which leverages the analog dynamics of interacting qubits to enable universal quantum computation.
  arXiv  Detail & Related papers  (2024-11-13T23:56:20Z)
• Halving the Cost of Quantum Algorithms with Randomization [0.138120109831448]
  Quantum signal processing (QSP) provides a systematic framework for implementing a transformation of a linear operator.<n>Recent works have developed randomized compiling, a technique that promotes a unitary gate to a quantum channel.<n>Our algorithm implements a probabilistic mixture of randomizeds, strategically chosen so that the average evolution converges to that of a target function, with an error quadratically smaller than that of an equivalent individual.
  arXiv  Detail & Related papers  (2024-09-05T17:56:51Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• Gradient-descent quantum process tomography by learning Kraus operators [63.69764116066747]
  We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems. We use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes.
  arXiv  Detail & Related papers  (2022-08-01T12:48:48Z)
• 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)

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.