Hamiltonian Decoded Quantum Interferometry

• URL: http://arxiv.org/abs/2510.07913v1
• Date: Thu, 09 Oct 2025 08:06:15 GMT
• Title: Hamiltonian Decoded Quantum Interferometry
• Authors: Alexander Schmidhuber, Jonathan Z. Lu, Noah Shutty, Stephen Jordan, Alexander Poremba, Yihui Quek,
• Abstract summary: We introduce Hamiltonian Decoded Quantum Interferometry (HDQI)<n>HDQI utilizes coherent measurements and the symplectic representation of the Pauli group to reduce Gibbs sampling and Hamiltonian Bellians.<n>We show that HDQI efficiently prepares Gibbs states at arbitrary temperatures for a class of physically motivated commuting Hamiltonians.
• Score: 69.7049555871155
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce Hamiltonian Decoded Quantum Interferometry (HDQI), a quantum algorithm that utilizes coherent Bell measurements and the symplectic representation of the Pauli group to reduce Gibbs sampling and Hamiltonian optimization to classical decoding. For a signed Pauli Hamiltonian $H$ and any degree-$\ell$ polynomial ${P}$, HDQI prepares a purification of the density matrix $\rho_{P}(H) \propto {P}^2(H)$ by solving a combination of two tasks: decoding $\ell$ errors on a classical code defined by $H$, and preparing a pilot state that encodes the anti-commutation structure of $H$. Choosing $P(x)$ to approximate $\exp(-\beta x/2)$ yields Gibbs states at inverse temperature $\beta$; other choices prepare approximate ground states, microcanonical ensembles, and other spectral filters. For local Hamiltonians, the corresponding decoding problem is that of LDPC codes. Preparing the pilot state is always efficient for commuting Hamiltonians, but highly non-trivial for non-commuting Hamiltonians. Nevertheless, we prove that this state admits an efficient matrix product state representation for Hamiltonians whose anti-commutation graph decomposes into connected components of logarithmic size. We show that HDQI efficiently prepares Gibbs states at arbitrary temperatures for a class of physically motivated commuting Hamiltonians -- including the toric code and Haah's cubic code -- but we also develop a matching efficient classical algorithm for this task. For a non-commuting semiclassical spin glass and commuting stabilizer Hamiltonians with quantum defects, HDQI prepares Gibbs states up to a constant inverse-temperature threshold using polynomial quantum resources and quasi-polynomial classical pre-processing. These results position HDQI as a versatile algorithmic primitive and the first extension of Regev's reduction to non-abelian groups.

Related papers

• Hamiltonian Decoded Quantum Interferometry for General Pauli Hamiltonians [6.4675604105664]
  We study the Hamiltonian Decoded Quantum Interferometry (HDQI) for the general Hamiltonians $H=sum_ic_iP_i$ on an $n$-qubit system.<n>We show that, given access to an appropriate decoding oracle, there exist efficient quantum algorithms for preparing the state $_mathcal P(H) = fracmathcal P(H)textTr[$cal P(H)]$, where $mathcal P(H)textTr[$
  arXiv  Detail & Related papers  (2026-01-26T18:44:59Z)
• New random compiler for Hamiltonians via Markov Chains [0.07499722271664146]
  We develop a new compiler, similar to the first order randomized Trotter, or qDRIFT, but with an arguably simpler framework.<n>We first present the model and derive its governing equations. We then define and analyze the simulation error for a sum of two Hamiltonians, and generalize it to a sum of $Q$ Hamiltonians.
  arXiv  Detail & Related papers  (2024-11-10T14:57:25Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma.<n>This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles.<n>We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• 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)
• Gibbs state preparation for commuting Hamiltonian: Mapping to classical Gibbs sampling [0.2764448420478315]
  We show that our Gibbs sampler is able to replicate state-of-the-art results.<n>We demonstrate that our Gibbs sampler is able to prepare the Gibbs state in regimes which were previously unknown.
  arXiv  Detail & Related papers  (2024-10-07T10:52:23Z)
• Hamiltonian simulation for low-energy states with optimal time dependence [45.02537589779136]
  We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. We present a quantum algorithm that uses $O(tsqrtlambdaGamma + sqrtlambda/Gammalog (1/epsilon))$ queries to the block-encoding for any $Gamma$.
  arXiv  Detail & Related papers  (2024-04-04T17:58:01Z)
• A polynomial-time dissipation-based quantum algorithm for solving the ground states of a class of classically hard Hamiltonians [4.500918096201963]
  We give a complexity-time quantum algorithm for solving the ground states of a class of classically hard Hamiltonians. We show that the Hamiltonians that can be efficiently solved by our algorithms contain classically hard instances.
  arXiv  Detail & Related papers  (2024-01-25T05:01:02Z)
• An efficient and exact noncommutative quantum Gibbs sampler [0.0]
  We construct the first efficiently implementable and exactly detailed-balanced Lindbladian for Gibbs states of arbitrary noncommutative Hamiltonians. Our construction can also be regarded as a continuous-time quantum analog of the Metropolis-Hastings algorithm.
  arXiv  Detail & Related papers  (2023-11-15T18:51:24Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Average-case Speedup for Product Formulas [69.68937033275746]
  Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states. Our results open doors to the study of quantum algorithms in the average case.
  arXiv  Detail & Related papers  (2021-11-09T18:49:48Z)
• Variational quantum eigensolvers for sparse Hamiltonians [0.0]
  Hybrid quantum-classical variational algorithms such as the variational quantum eigensolver (VQE) are promising applications for noisy, intermediate-scale quantum computers. We extend VQE to general sparse Hamiltonians.
  arXiv  Detail & Related papers  (2020-12-13T22:36:51Z)
• 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.