The stabilizer ground state and applications to quantum simulation

• URL: http://arxiv.org/abs/2603.06286v1
• Date: Fri, 06 Mar 2026 13:46:37 GMT
• Title: The stabilizer ground state and applications to quantum simulation
• Abstract summary: The optimal stabilizer ground state is defined as the stabilizer ground state which has the highest fidelity with the true ground state.<n>We show applications of this state in the context of measurement-based deterministic imaginary time evolution.
• Score: 13.248696881014924
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground state as the stabilizer ground state which has the highest fidelity with the true ground state. This is useful in quantum simulation contexts as it allows for a Clifford circuit approximation of a ground state that can be further refined towards the true ground state. We show how the optimal stabilizer ground state may be evaluated. We show applications of this state in the context of measurement-based deterministic imaginary time evolution (MITE), which converges to the ground state with high efficiency. By classically selecting the optimal stabilizer generator group and employing the stabilizer tableaux formalism, the method prepares the corresponding stabilizer ground state with maximal fidelity. The identification and refinement of this generator group are performed using a genetic algorithm tailored to the structure of the target Hamiltonian. The complexity analysis further demonstrates that algorithm's quantum resource cost scales polynomially with system size, highlighting its high efficiency and potential quantum advantage.

Related papers

• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation [0.0]
  We investigate how the stabilizer formalism, in particular highly-entangled stabilizer states, can be used to describe the emergence of many-body shape collectivity.<n>The resulting stabilizer ground state is found to capture to a large extent both bi-partite and collective multi-partite entanglement features.
  arXiv  Detail & Related papers  (2025-05-05T18:01:20Z)
• General detectability measure [45.85698554568285]
  Distinguishing resource states from resource-free states is a fundamental task in quantum information.<n>We derived the optimal exponential decay rate of the failure probability for detecting a given $n$-tensor product state.
  arXiv  Detail & Related papers  (2025-01-16T05:39:22Z)
• Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications [0.5735035463793009]
  We apply stabilizer states to tackle quantum many-body ground state problems.<n>We develop an exact and linear-scaled algorithm to obtain stabilizer ground states of 1D local Hamiltonians.
  arXiv  Detail & Related papers  (2024-03-13T11:54:25Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)
• Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array [55.41644538483948]
  We present and analyze a protocol for driven-dissipatively preparing and stabilizing a manifold of quantum manybody entangled states. We perform theoretical modeling of this platform via pulse-level simulations based on physical features of real devices. Our work shows the capacity of driven-dissipative superconducting cQED systems to host robust and self-corrected quantum manybody states.
  arXiv  Detail & Related papers  (2023-03-21T18:02:47Z)
• 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)
• Spectral stabilizability [0.0]
  We develop conditions for stabilizability based on the target state's eigendecomposition. We use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios.
  arXiv  Detail & Related papers  (2022-12-23T10:38:31Z)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• Stabilizing Preparation of Quantum Gaussian States via Continuous Measurement [2.6663319869017523]
  The evolution of the open quantum system is described in terms of the quantum master equation. We present necessary and sufficient conditions for the system to have a unique stabilizing steady Gaussian state.
  arXiv  Detail & Related papers  (2021-09-27T01:18:04Z)
• Improved Graph Formalism for Quantum Circuit Simulation [77.34726150561087]
  We show how to efficiently simplify stabilizer states to canonical form. We characterize all linearly dependent triplets, revealing symmetries in the inner products. Using our novel controlled-Pauli $Z$ algorithm, we improve runtime for inner product computation from $O(n3)$ to $O(nd2)$ where $d$ is the maximum degree of the graph.
  arXiv  Detail & Related papers  (2021-09-20T05:56:25Z)
• Stabilizer extent is not multiplicative [1.491109220586182]
  Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. An important open problem is to decide whether the extent is multiplicative under tensor products.
  arXiv  Detail & Related papers  (2020-07-08T18:41:59Z)

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.