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.
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.
We investigate how the stabilizer formalism, in particular highly entangled stabilizer states, can be used to describe the emergence of many-body shape collectivity from individual constituents in a symmetry-preserving and classically efficient way. The method that we adopt is based on determining an optimal separation of the Hamiltonian into a stabilizer component and a residual part inducing nonstabilizerness. The corresponding stabilizer ground state is efficiently prepared using techniques of graph states and stabilizer tableaux. We demonstrate this technique in context of the Lipkin-Meshkov-Glick model, a fully connected spin system presenting a second-order phase transition from spherical to deformed state. The resulting stabilizer ground state is found to capture to a large extent both bipartite and collective multipartite entanglement features of the exact solution in the region of large deformation. We also explore several methods for injecting nonstabilizerness into the system, including adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver and imaginary-time evolution (ITE) techniques. Stabilizer ground states are found to accelerate ITE convergence due to a larger overlap with the exact ground state. While further investigations are required, the present work suggests that collective features may be associated with high but simple large-scale entanglement which can be captured by stabilizer states, while the interplay with single-particle motion may be responsible for inducing nonstabilizerness. This study motivates applications of the proposed approach to more realistic quantum many-body systems, whose stabilizer ground states can be used in combinations with powerful classical many-body techniques and/or quantum methods.
We investigate how the stabilizer formalism, in particular highly entangled stabilizer states, can be used to describe the emergence of many-body shape collectivity from individual constituents in a symmetry-preserving and classically efficient way. The method that we adopt is based on determining an optimal separation of the Hamiltonian into a stabilizer component and a residual part inducing nonstabilizerness. The corresponding stabilizer ground state is efficiently prepared using techniques of graph states and stabilizer tableaux. We demonstrate this technique in context of the Lipkin-Meshkov-Glick model, a fully connected spin system presenting a second-order phase transition from spherical to deformed state. The resulting stabilizer ground state is found to capture to a large extent both bipartite and collective multipartite entanglement features of the exact solution in the region of large deformation. We also explore several methods for injecting nonstabilizerness into the system, including adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver and imaginary-time evolution (ITE) techniques. Stabilizer ground states are found to accelerate ITE convergence due to a larger overlap with the exact ground state. While further investigations are required, the present work suggests that collective features may be associated with high but simple large-scale entanglement which can be captured by stabilizer states, while the interplay with single-particle motion may be responsible for inducing nonstabilizerness. This study motivates applications of the proposed approach to more realistic quantum many-body systems, whose stabilizer ground states can be used in combinations with powerful classical many-body techniques and/or quantum methods.
Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply stabilizer states to tackle quantum many-body ground state problems and introduce the concept of stabilizer ground states. We establish an equivalence formalism for identifying stabilizer ground states of general Pauli Hamiltonians. Moreover, we develop an exact and linear-scaled algorithm to obtain stabilizer ground states of 1D local Hamiltonians and thus free from discrete optimization. This proposed equivalence formalism and linear-scaled algorithm are not only applicable to finite-size systems, but also adaptable to infinite periodic systems. The scalability and efficiency of the algorithms are numerically benchmarked on different Hamiltonians. Finally, we demonstrate that stabilizer ground states are promising tools for not only qualitative understanding of quantum systems, but also cornerstones of more advanced classical or quantum algorithms.
In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations of the Hartree-Fock state, followed by constructing quantum error-detection codes based on this stabilizer state using codeword-stabilized codes. Through various numerical experiments, we confirm that our method finds the best stabilizer approximations to the true ground states of molecules up to 36 qubits in size. Additionally, we construct generalized stabilizer states that offer a better approximation to the true ground states. Furthermore, for a simple noise model, we demonstrate that both the stabilizer and (some) generalized stabilizer states can be prepared with higher fidelity using the error-detection codes we construct. Our work represents a promising step toward designing algorithms for early fault-tolerant quantum computation.
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of s t a b i l i z e r rank , which for a pure state ψ is defined to be the smallest integer χ such that ψ is a superposition of χ stabilizer states. Here we develop a comprehensive mathematical theory of the stabilizer rank and the related approximate stabilizer rank. We also present a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art. A new feature is the capability to simulate circuits composed of Clifford gates and arbitrary diagonal gates, extending the reach of a previous algorithm specialized to the Clifford+T gate set. We implemented the new simulation methods and used them to simulate quantum algorithms with 40-50 qubits and over 60 non-Clifford gates, without resorting to high-performance computers. We report a simulation of the Quantum Approximate Optimization Algorithm in which we process superpositions of χ ∼ 10 6 stabilizer states and sample from the full n -bit output distribution, improving on previous simulations which used ∼ 10 3 stabilizer states and sampled only from single-qubit marginals. We also simulated instances of the Hidden Shift algorithm with circuits including up to 64 T gates or 16 CCZ gates; these simulations showcase the performance gains available by optimizing the decomposition of a circuit's non-Clifford components.
In this work, we develop a variational imaginary-time evolution (ITE) framework based on polynomial filtering, derived from an operator-level action principle, which yields an optimized non-unitary projector expressed as a polynomial in the Hamiltonian. Starting from a single-ancilla, first-order imaginary-time update defined by a Taylor expansion and Trotter-Suzuki (TS) decompositions, we show that replacing these approximations with alternative variational formulas substantially improves both accuracy and stability at larger time steps, leading to up to an order-of-magnitude enhancement in the final success probability. We further derive rigorous error bounds that depend only on static properties of the Hamiltonian, providing practical guidance for selecting the simulation time step. Benchmarks on the transverse-field Ising model demonstrate faster convergence to the ground-state energy and improved robustness compared to standard TS--Taylor ITE, highlighting variational polynomial filtering as a practical route to higher-fidelity ground-state preparation on near-term quantum devices.