On low-depth algorithms for quantum phase estimation

• URL: http://arxiv.org/abs/2302.02454v4
• Date: Sat, 28 Oct 2023 18:37:12 GMT
• Title: On low-depth algorithms for quantum phase estimation
• Authors: Hongkang Ni, Haoya Li, Lexing Ying
• Abstract summary: For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to use a minimal number of ancilla qubits. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. We propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.
• Score: 11.678822620192438
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.

Related papers

• Quantum-Centric Algorithm for Sample-Based Krylov Diagonalization [0.6512657417859998]
  We introduce a quantum diagonalization algorithm which combines two key ideas on quantum subspaces. We prove that our algorithm converges under working assumptions of Krylov quantum diagonalization and sparseness of ground state. We then show numerical investigations of lattice Hamiltonians, which indicate that our method can outperform existing Krylov quantum diagonalization in presence of shot noise.
  arXiv  Detail & Related papers  (2025-01-16T17:56:19Z)
• One-Shot Min-Entropy Calculation Of Classical-Quantum States And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state. It offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme. It gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• 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)
• A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity [50.387179833629254]
  We introduce a collaborative classical-quantum architecture called co-TenQu. Co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. It outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.
  arXiv  Detail & Related papers  (2024-02-23T14:09:41Z)
• Mitigating Errors on Superconducting Quantum Processors through Fuzzy Clustering [38.02852247910155]
  A new Quantum Error Mitigation (QEM) technique uses Fuzzy C-Means clustering to specifically identify measurement error patterns. We report a proof-of-principle validation of the technique on a 2-qubit register, obtained as a subset of a real NISQ 5-qubit superconducting quantum processor. We demonstrate that the FCM-based QEM technique allows for reasonable improvement of the expectation values of single- and two-qubit gates based quantum circuits.
  arXiv  Detail & Related papers  (2024-02-02T14:02:45Z)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• Quantum Thermal State Preparation [39.91303506884272]
  We introduce simple continuous-time quantum Gibbs samplers for simulating quantum master equations. We construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time.
  arXiv  Detail & Related papers  (2023-03-31T17:29:56Z)
• Achieving metrological limits using ancilla-free quantum error-correcting codes [1.9265037496741413]
  Existing quantum error-correcting codes generally exploit entanglement between one probe and one noiseless ancilla of the same dimension. Here we construct two types of multi-probe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla-free.
  arXiv  Detail & Related papers  (2023-03-02T00:51:02Z)
• Unbiased quantum phase estimation [5.324438395515079]
  Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. We find that the PEA is not an unbiased estimation, which prevents the estimation error from achieving an arbitrarily small level. We propose an unbiased phase estimation algorithm (A) based on the original PEA, and study its application in quantum counting.
  arXiv  Detail & Related papers  (2022-10-01T09:38:20Z)
• Improved maximum-likelihood quantum amplitude estimation [0.0]
  Quantum estimation is a key subroutine in a number of powerful quantum algorithms, including quantum-enhanced Monte Carlo simulation and quantum machine learning. In this article, we deepen the analysis of Maximum-likelihood quantum amplitude estimation (MLQAE) to put the algorithm in a more prescriptive form, including scenarios where quantum circuit depth is limited. We then propose and numerically validate a modification to the algorithm to overcome this problem, bringing the algorithm even closer to being useful as a practical subroutine on near- and mid-term quantum hardware.
  arXiv  Detail & Related papers  (2022-09-07T17:30:37Z)
• Quantum Speedup for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection [2.5272389610447856]
  We propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization problem. The proposed algorithm is capable of reducing the query complexity in the classical domain and providing a quadratic speedup in the quantum domain.
  arXiv  Detail & Related papers  (2022-05-31T00:14:49Z)
• 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)
• Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation [50.591267188664666]
  Quantum chemistry and materials is one of the most promising applications of quantum computing. Much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them.
  arXiv  Detail & Related papers  (2022-03-14T16:51:36Z)
• Quantum mean value approximator for hard integer value problems [19.4417702222583]
  We show that an optimization can be improved substantially by using an approximation rather than the exact expectation. Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems.
  arXiv  Detail & Related papers  (2021-05-27T13:03:52Z)
• Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers [3.7747526957907303]
  We propose an alternative method to estimate the ground state energy of a Hamiltonian with Heisenberg-limited precision scaling. Our algorithm also produces an approximate cumulative distribution function of the spectral measure.
  arXiv  Detail & Related papers  (2021-02-22T20:21:56Z)
• Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets [47.00474212574662]
  Variational quantum algorithms are believed to be promising for solving computationally hard problems. In this paper, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
  arXiv  Detail & Related papers  (2020-05-11T17:20:51Z)

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.