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State Engineering of Unsteerable Hamiltonians

T0 review · 2 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper proves that ground-state manifolds of commuting Pauli Hamiltonians are steerable by local measurement sequences, even when the Hamiltonian is frustrated, and bounds how close local steering can come when it is not.

desk verdict Theorem 4 is real and worth citing; the glass-floor temperature bound is a Gibbs ansatz, not a derived cooling limit. read the letter →

arxiv 2505.18393 v2 pith:IFVQSA3K submitted 2025-05-23 quant-ph cond-mat.mes-hallcond-mat.str-el

Yi-Xuan Wang , Yuval Gefen This is my paper · ORCID
classification quant-phcond-mat.mes-hallcond-mat.str-el
keywords passivesteeringground-statemanifoldfrustration-freeHamiltonianscommutingPaulijitteryglassflooreffectivetemperaturedissipativestateengineering
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Passive steering uses predetermined local measurements to push an arbitrary initial state toward a target subspace, typically the ground-state manifold of a many-body Hamiltonian. This paper tries to overturn the long-held expectation that only frustration-free Hamiltonians can be reached this way. It proves that every commuting Pauli Hamiltonian, including classically frustrated examples such as odd-length Ising antiferromagnets, has a steerable ground-state manifold, with the caveat that the state never settles down inside the manifold: it keeps jumping between ground states. For Hamiltonians whose ground states cannot be steered, the paper derives a quantitative "glass floor": any local passive protocol must respect an upper bound on fidelity, a lower bound on energy, and a lower bound on effective temperature, all controlled by the smallest eigenvalue of the local reduced density matrices of the ground states.

What carries the argument

The load-bearing object is the local steering superoperator, built from the Hamiltonian's own local terms: $P^{(i)}_{\pm}(\rho)=\Pi^{(i)}_{\pm}\rho\Pi^{(i)}_{\pm}+\Pi^{(i)}_{\mp}V_\pm^\dagger\rho V_\pm\Pi^{(i)}_{\mp}$, where $\Pi^{(i)}_{\pm}=(1\pm H^{(i)})/2$ and $V_\pm$ is a Pauli operator anticommuting with $H^{(i)}$. Applied repeatedly, these operators cool each commuting term to its local ground value, and the proof tracks the resulting evolution in the Heisenberg picture as linear algebra over $\mathbb{F}_2$; a randomized greedy choice of flip operators guarantees that the system lands in the common ground-state eigenspace and then keeps moving inside it. The classification side is carried by the Subspace Conserved Quantity (SCQ), a local Hermitian operator whose expectation value is conserved inside the ground-state manifold, and by the Parent-Hamiltonian-Frustration-Free (PHFF) condition: the existence of a local frustration-free Hamiltonian sharing the same ground-state manifold. For non-steerable targets, the engine of the "glass floor" is the quantity $p(\Pi_{\mathrm{GS}})$, the smallest eigenvalue of any local reduced density matrix of any ground state; it converts directly into upper bounds on fidelity and lower bounds on energy and effective temperature.

What would settle it

Numerically optimize a finite sequence of local superoperators for a system whose ground state has full local Schmidt rank, such as the spin-1/2 antiferromagnetic Heisenberg chain with $N$ up to 20, and test whether the overlap with the ground-state manifold can exceed $1-p(\Pi_{\mathrm{GS}})$; any success would refute the glass floor. In parallel, reconstruct the asymptotic state produced by the protocol and examine its low-energy spectrum: if it is not well fit by a Gibbs distribution, the effective-temperature bound is not a physical property of the state.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is a revised classification of local Hamiltonians by the steerability of their ground-state manifold. Theorem 1 characterizes steady steerability: a Hamiltonian is steadily steerable exactly when a local frustration-free parent Hamiltonian shares its ground-state manifold. Theorem 4 goes further and shows that the ground-state manifold of any commuting Pauli Hamiltonian is a steerable subspace in the "jittery" sense: local superoperators built from projectors onto eigenstates of the commuting terms, together with Pauli flip operators, drive every initial state into the manifold and then continue to move states around within it, so that no single ground state is a fixed point. For non-steerable targets, the paper establishes that the best overlap of any local passive protocol with the ground-state manifold is at most $1-p(\Pi_{\mathrm{GS}})$, where $p(\Pi_{\mathrm{GS}})$ is the smallest eigenvalue of any local reduced density matrix of any ground state; equivalently, the energy is at least $E_{\mathrm{GS}}+p(\Pi_{\mathrm{GS}})\,\mathrm{gap}[H]$, and the effective temperature is bounded from below once the asymptotic state is modeled as a Gibbs state.

Load-bearing premise

For the temperature bound, the argument assumes that the asymptotic state of any steering protocol can be approximated by a Gibbs state of the target Hamiltonian with ordinary Boltzmann weights for the low-lying states; the target Hamiltonian is not part of the steering dynamics, and nothing in the proof forces the surrogate state to be thermal.

Editorial extensions

If this is right

  • Any commuting Pauli Hamiltonian, including classically frustrated ones such as an odd-length Ising antiferromagnet, can be steered into its ground-state manifold by discrete local superoperators; within the manifold the protocol keeps generating transitions, so the asymptotic target is a subspace rather than a fixed point.
  • Steady steerability is fully characterized by parent Hamiltonians: a ground-state manifold is steadily steerable when a local frustration-free parent Hamiltonian exists, and such a parent can be assembled from trivial subspace conserved quantities.
  • For non-steerable ground states, every local passive protocol leaves a population of at least $p(\Pi_{\mathrm{GS}})$ outside the target manifold, giving a fidelity bound $1-p(\Pi_{\mathrm{GS}})$, an energy bound $E_{\mathrm{GS}}+p(\Pi_{\mathrm{GS}})\,\mathrm{gap}[H]$, and a lower effective-temperature bound when the asymptotic state is Gibbs-like.
  • Cooling power grows with detector range: for SYK models with $\lfloor N/2\rfloor$-mode detectors the ground-state overlap bound improves as $1-\langle\psi_{\mathrm{GS}}|\tilde\rho_{\mathrm{surr}}|\psi_{\mathrm{GS}}\rangle\gtrsim e^{-O(N)}$, whereas two-mode detectors give a floor around $\tfrac14-O(1/N)$ that worsens with $N$.
  • In the near-superconducting Fermi-Hubbard model the computed minimum effective temperature lies below the estimated critical temperature, so the glass floor does not by itself rule out reaching the d-wave phase by passive steering.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The jittery steering construction suggests a practical way to keep a degenerate encoded subspace populated while deliberately randomizing inside it; the paper notes the error-correction template but does not analyze logical noise or code distance within that subspace.
  • The temperature version of the glass floor is the only place where the argument requires the surrogate state to be thermal; if exact numerics on the Heisenberg or SYK chains show the asymptotic state is non-thermal, the fidelity and energy bounds survive but the temperature bound should be read as a fitting parameter rather than a physical cooling limit.
  • Because the necessary conditions for the NFFJS class are explicitly incomplete and require non-local information, the true boundary between jittery steerable and non-steerable Hamiltonians remains open for systems that satisfy the local conditions; closing the classification would need a non-local entanglement criterion.
  • The same reduced-density-matrix datum $p(\Pi_{\mathrm{GS}})$ can serve as a pre-screening diagnostic for quantum simulators: compute the smallest eigenvalues of few-body reduced density matrices of the target state, and if the value is large, no local blind cooling protocol can prepare that state faithfully.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper studies passive ('blind') steering of many-body quantum states by sequences of local non-unitary superoperators, with the target being the ground-state manifold of a local Hamiltonian. It proposes a four-way classification: frustration-free steerable (FFS), non-frustration-free steadily steerable (NFFSS), non-frustration-free jittery steerable (NFFJS), and non-frustration-free non-steerable (NFFNS). The central positive claims are Theorem 1, that steady steerability is equivalent to the existence of a local frustration-free parent Hamiltonian with the same ground-state manifold, and Theorem 4, that the ground-state manifold of any commuting Pauli Hamiltonian is a steerable subspace (of NFFJS type), with an explicit construction of local superoperators and a randomized greedy steering sequence. For the non-steerable class, the paper derives an upper bound on the fidelity of any 'presumed surrogate' state with the target ground state (Eqs. 11 and 13), a lower bound on the achievable energy (Eq. 15), and a lower bound on an effective temperature interpreted as a 'glass floor' (Eq. 17). These results are applied numerically to the antiferromagnetic Heisenberg model, the Dirac and Majorana SYK models, and the Fermi-Hubbard model. The paper explicitly acknowledges that the necessary conditions for NFFJS steerability are not claimed to be sufficient, and that the Gibbs-state replacement in Sec. VII D is a working approximation.

Significance. If the main claims hold, the paper substantially extends the known scope of dissipative and measurement-based ground-state engineering: the identification of a broad class of frustrated commuting-Pauli Hamiltonians whose ground-state manifolds are steerable overturns the prior belief that only frustration-free Hamiltonians admit passive steering. The fidelity and energy bounds in Sec. VII are clean consequences of the Schmidt decomposition and are not fitted to the numerics, which is a strength. The proofs in Appendix C are explicit and internally coherent, although they are not machine-checked and no code is shipped. The self-identified limitations—the provisional character of the NFFJS necessary conditions and the Gibbs ansatz in Sec. VII D—are important and need to be resolved before the temperature-based 'glass floor' can be regarded as a physical bound.

major comments (2)
  1. [Sec. VII D, Eq. (17)] The temperature lower bound ('glass floor') is not derived from the steering dynamics. Equation (17) replaces the asymptotic surrogate state by a Gibbs state of the target Hamiltonian H, writing Tr(ρ_surr Π_GS) ≈ deg(H)e^{-βE_GS}/Z(β). But H is not part of the dynamics, and the local superoperators are chosen only from the target manifold; nothing in the derivation rules out a non-thermal asymptotic state with the same ground-state population and an arbitrary distribution over excited states. In that case the quantity T_eff is merely a re-parameterization of 1-p(Π_GS) under an unjustified Boltzmann ansatz, and the numerical values reported in Sec. VIII inherit that ansatz. The fidelity bound (Eq. 13) and the energy bound (Eq. 15) survive, but the claim of a lower bound on an achievable physical temperature does not. The authors should either prove that the steering protocol thermalizes with respect to H, or explicitly define T_eff as the temperature of the Gibbs state that best fits the ground-state population and adjust the abstract and Sec. IX accordingly.
  2. [Appendix C 4 and Theorem 4] The locality reduction for arbitrary commuting Pauli Hamiltonians is not fully established. Lemma 3 shows that for every g_VH in the right null space of C_H there exists a Pauli operator V with the required commutation relations, but this V can have support that scales with the system size. The manuscript then states that a non-local g_VH 'can be decomposed into a sum of local components, each corresponding to a local operator V_k', and that replacing a single superoperator by a product of local superoperators resolves the issue. However, no argument is given that the sequential application of the local superoperators reproduces the same energy update v_E → v_E + e_CVH A_0,C, nor that the greedy convergence proof of Appendix C 3 remains valid after this replacement. Since Definition 1 requires each steering operation to be local, this step is load-bearing for Theorem 4. A rigorous locality reduction, or a restricted statement of Theorem 4 to the cases where the construction is explicitly local, is needed.
minor comments (3)
  1. [Sec. VI, paragraph after Eq. (4)] The stated Heisenberg-picture identity P(i)†(H_{i-1}) = -1 is incorrect; direct calculation from Eq. (4) gives P(i)†(H_{i-1}) = -H_{i-1}H_i, not -1. The assertion that one application brings all states to the local ground state of H_{i-1} therefore needs revision. This does not affect the general proof in Appendix C, but the example's explanation should be corrected.
  2. [Sec. VII B, Eq. (14)] The displayed derivation of the local fidelity contains a typo in the summation index: one line reads 'i̸=' without a lower limit or an index name, and the surrounding indices are inconsistent. Please fix the notation so that the expression matches Eq. (10).
  3. [Sec. VIII A] The SU(2)-symmetry argument for the absence of SCQs in the antiferromagnetic Heisenberg model is heuristic, especially the sentence 'For the scenario (ii), one also expects the absence of local SCQ'. Since this model is used as a numerical example of the NFFNS class, the argument should invoke the precise criterion of Corollary 4.1 or otherwise give a verifiable condition rather than an expectation.

Circularity Check

1 steps flagged · score 2.0 of 10

Central steerability theorems are self-contained; the temperature 'glass floor' is a definitional re-parameterization of the fidelity/energy bound, not an independent prediction.

  1. self definitional [Sec. VII D, Eq. (17)]
    "Our working approximation is to replace the presumed surrogate state by a thermal state, with thermal Boltzmann weights of the low-lying states. ... 1 − p(ΠGS) ≥ Tr(˜ρsurrΠGS) ≥ Tr(ρsurrΠGS) = deg(H)e^{−βEGS}/Z(β), where β = 1/Teff,min."

    The claimed lower bound on effective temperature is not extracted from the steering dynamics; Teff,min is fixed by inverting the already-derived RDM bound 1 − p(ΠGS) against the Gibbs weight of the target Hamiltonian H, which is not part of the steering dynamics. Thus the 'glass floor' temperature is a re-parameterization of p(ΠGS) under a Gibbs ansatz, rather than a predicted thermalization temperature. If the asymptotic state is not Gibbs, the temperature label carries no independent physical content; the substantive results are the fidelity and energy bounds, which do not rely on the Gibbs replacement. This is a definitional conversion, not a fitted-parameter circularity, so it does not undermine Theorems 1 and 4.

full rationale

The main load-bearing claims are Theorem 1 (steady steerability iff a local frustration-free parent Hamiltonian exists) and Theorem 4 (ground-state manifolds of commuting Pauli Hamiltonians are steerable). Both are supported by explicit constructions rather than by fitting or by definitional identity: Theorem 1 is proved by building the parent Hamiltonian from the invariant subspaces of the local superoperators and conversely by using the FF parent to construct the steering protocol; Theorem 4 supplies explicit superoperators (Eq. C3) and a randomized greedy sequence, with locality addressed in Appendix C.4. The numerical examples compute p(ΠGS) from exact ground-state reduced density matrices, independently of the bounds they illustrate. The paper's self-citations (e.g., Refs. [8,22]) are background or peripheral and are not load-bearing; no uniqueness theorem is imported from the authors' prior work. The only step with a definitional character is Eq. (17), where the effective temperature lower bound is defined by equating the ground-state population bound with a Gibbs weight of the target Hamiltonian. This is an interpretive re-labeling of the fidelity/energy bound rather than an independent dynamical prediction, giving a mild circularity score of 2. The central theorems and the fidelity/energy bounds are self-contained and not circular.

Assumptions & free parameters 1 free parameters · 6 assumptions · 3 invented entities

The central claims rest on the steering framework of passive local superoperators, on the standard open-systems structure of invariant subspaces, and (for the temperature floor) on an explicit Gibbs-state ansatz. No parameters are fitted to data; the only hand-chosen quantity is the support size of the steering operators in the examples. The paper introduces new mathematical constructs (SCQ, surrogate states) but no new physical degrees of freedom.

free parameters (1)
  • Steering operator support size m = m = 2 or m = floor(N/2) per example
    The range of the local superoperator is chosen by hand for each model (two-body vs half-system). It is a protocol parameter, not fitted to data, but it directly controls how tight the glass-floor bound is (Sec. VIII B).
assumptions (6)
  • standard math Invariant subspace of Lindbladians has a block-diagonal distorted C*-algebra structure, used for steady states (Appendix A).
    Utilized without proof, citing Refs. [16,25,57]; standard in open quantum systems.
  • domain assumption Steering superoperators are strong and have no unitary dynamics in their invariant subspace (Appendix A 2).
    Explicitly assumed to avoid ambiguity of infinite-time limits; if violated, the classification into FFS/NFFSS/NFFJS could change.
  • domain assumption The target Hamiltonian H is not part of the dynamics; dynamics are solely due to local steering superoperators (Sec. II).
    Foundation of the steering definition; relaxing it (adding system Hamiltonian) may improve the glass floor as noted in Sec. IX B.
  • ad hoc to paper The asymptotic surrogate state can be approximated as a Gibbs state of the target Hamiltonian at an effective temperature (Sec. VII D).
    Used to convert the fidelity bound into a temperature lower bound, Eq. (17); no dynamical derivation is provided.
  • domain assumption For the NFFJS necessary conditions, local superoperators must preserve the GS manifold and are assumed strong; bipartite indistinguishability is required (Appendix B 2, Prop. 1).
    These conditions are derived from local preservation of the manifold; the authors note global information may be needed for sufficiency.
  • standard math Exact diagonalization results for SYK and Hubbard provide the ground states from which local RDMs are computed (Appendix D 3).
    Numerical method; no code or data shipped.
invented entities (3)
  • Subspace Conserved Quantity (SCQ)
    purpose: Formal criterion for steerability; local Hermitian operator conserved within a subspace defined by a projector.
    New definition (Def. 2) used to formulate Theorems 1 and necessary conditions for NFFJS; not independently observable, derived from the target subspace and Hamiltonian.
  • Presumed surrogate state
    purpose: State closest to the target state among the complementary set of class D; used to bound steerability distance when the true surrogate is unknown.
    Defined in Sec. VII A and Fig. 4; a conceptual construct rather than a physical entity.
  • p-approximate steerable subspace
    purpose: Formalizes approximate steering with a guaranteed population p in the target subspace.
    Def. 4 in Sec. VII A; quantifies the 'glass floor'.

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Cite this review

Pith. "Pith review of State Engineering of Unsteerable Hamiltonians." pith.science (2026). https://pith.science/paper/IFVQSA3K

@misc{pith2026250518393,
  author       = {Pith},
  title        = {Pith review of: State Engineering of Unsteerable Hamiltonians},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IFVQSA3K}},
  note         = {Machine review of arXiv:2505.18393}
}
read the original abstract

Lindbladian dynamics of open systems may be employed to steer a many-body system towards a non-trivial ground state of a local Hamiltonian. Such protocols provide us with tunable platforms facilitating the engineering and study of non-trivial many-body states. Steering towards a degenerate ground state manifold provides us with a protected platform to employ many-body states as a resource for quantum information processing. Notably, ground states of frustrated local Hamiltonians have been known not to be amenable to steering protocols. Revisiting this intricate physics we report two new results: (i) we find a broad class of (geometrically) frustrated local Hamiltonians for which steering of the ground state manifold is possible through a sequence of discrete steering steps. Following the steering dynamics, states within the degenerate ground-state manifold keep evolving in a non-stationary manner. (ii) For the class of Hamiltonians with ground states which are non-steerable through local superoperators, we derive a "glass floor" on how close to the ground state one can get implementing a steering protocol. This is expressed invoking the concept of cooling-by-steering (a lower bound of the achievable temperature), or through an upper bound of the achievable fidelity. Our work provides a systematic outline for studying quantum state manipulation of a broad class of strongly correlated states.

Figures

Figures reproduced from arXiv: 2505.18393 by the authors.

Figure 2
Figure 2. Steerability of ground states of the underlying Hamiltonians (which are made up of local operators). A: (Frustration Free steerable (FFS)) Hamiltonians: the Hamiltonian is Frustration Free. B: (Non-Frustration-Free Steadily Steerable (NFFSS)) the Hamiltonian is not Frustration Free, but there exists a Frustration Free Parent Hamiltonian. C: (Non-FF Jittery Steerable (NFFJS)) and C + D (classification is unknown) sat… view at source ↗
Figure 3
Figure 3. Steering trajectories of two situations in Def. 1. (a) Steering towards the GS manifold of an FFS/NFFSS Hamiltonian. Once it is mapped onto Htarget, the system’s states remain stationary. (b) Steering employing towards the GS manifold of an NFFJS Hamiltonian. Even within Htarget, the system’s state keeps ”jumping” around. Note that for the latter case there exists at least one GS, that is invariant for each Pn. To s… view at source ↗
Figure 4
Figure 4. Schematics of the distances from target states to surrogate states. ρtar and σtar are two non-steerable target states defined in the class D, cf [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figures from the paper (10 more)
Figure 5
Figure 5. Figure 5: Anti-ferromagnetic Heisenberg model with N-long chains (periodic boundary conditions) of spin s = 1/2, 1, 3/2, 2. (a) The function p(ΠGS), which is 1 minus the fidelity upper bound (cf. Eq. (13)), calculated with the GS (manifold) of the above models. (b) Lower bound o…
Figure 6
Figure 6. Figure 6: Temperature lower bound for short-range system-detector interaction, m = 2. Shown are normalized histograms of the lower bound of the normalized effective temperature Teff,min/ gap[HD SYK] computed for SYK model for Dirac fermions, for different disorder configurations…
Figure 7
Figure 7. Figure 7: Temperature lower bound for long-range system-detector interaction, m = ⌊N/2⌋. (a) Normalized histograms of Teff,min/ gap[HD SYK] for Dirac-Fermionic SYK model with different numbers of fermion modes N. Note that it behaves like Gaussian distributions. (b) Mean and sta…
Figure 9
Figure 9. Figure 9: Temperature lower bound for long-range system-detector interaction, m = ⌊N/2⌋. (a)Normalized histograms of Teff,min/ gap[HM SYK] for Majorana-Fermionic SYK model with different numbers of fermion modes N. Note that it behaves like Gaussian distributions. (b) Mean and s…
Figure 10
Figure 10. Figure 10: (a)Lattice of the two dimensional Fermi-Hubbard model, showing single electron fermionic modes. Each mode may be filled by electrons of spin up (blue) or down (red). The boxed (marked by dashed green lines) represents the support of the reduced density matrices employ…
Figure 11
Figure 11. Figure 11: Schematics of the fixed points and block-diagonal structure. be decomposed up to an isomorphism as H ≃ M k Ak ⊗ 1dk , where {Ak} are linear spaces, and {1dk } are dk￾dimensional identity matrices [57]. Consequently, the states in As(H) must have the form ρ = X k pkρk,…
Figure 12
Figure 12. Figure 12: SYK model for Dirac Fermion. Shown are normalized histograms of several physical quantities for different numbers of fermionic modes N. Here the occupation (number of Dirac fermions) is ⌊N/2⌋. Steering operators consist of the detector’s degree of freedom and m = ⌊N/2…
Figure 13
Figure 13. Figure 13: SYK model for Dirac fermions: shown are normalized histograms of several physical quantities for different numbers of fermionic modes N. Here the occupation (number of Dirac fermions) is ⌊N/2⌋. Steering operators consist of the detector’s degree of freedom and m = 2 f…
Figure 14
Figure 14. Figure 14: SYK model for Majorana Fermion. Shown are normalized histograms of several physical quantities for different numbers of fermionic modes N. Steering operators consist of the detector’s degree of freedom and m = ⌊N/2⌋ fermionic degrees of freedom. Hence phalf (|ψ⟩GS) (E…
Figure 15
Figure 15. Figure 15: SYK model for Fermion fermions: shown are normalized histograms of several physical quantities for different numbers of fermionic modes N. Steering operators consist of the detector’s degree of freedom and m = 2 fermionic degrees of freedom. (a) Maximal overlap of the…

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Works this paper leans on

74 extracted references · 63 canonical work pages

  1. [1]

    Commuting Pauli Hamiltonians are n-qubit Hamiltonians of the form H = P i H (i), where each term H (i) belongs to the Pauli group and satisfies [ H (i), H(j)] = 0 for all i, j

    Spectrum of Commuting Pauli Hamiltonians In the following, to establish the steerability of commuting Pauli Hamiltonians, we first intro- duce a lemma regarding their spectrum. Commuting Pauli Hamiltonians are n-qubit Hamiltonians of the form H = P i H (i), where each term H (i) belongs to the Pauli group and satisfies [ H (i), H(j)] = 0 for all i, j. Sin...

    work page

  2. [2]

    Our focus is on the evolution of the energy ex- pectation value throughout the steering process

    Steering operators In this section, we introduce the set of steering operators for commuting Pauli Hamiltonians and analyze their effects in the Heisenberg picture. Our focus is on the evolution of the energy ex- pectation value throughout the steering process. We begin by characterizing the evolution of the Hamiltonian group, denoted H (cf. Eq. (C1)), un...

    work page

  3. [3]

    Proof of steerability In this section, we present and prove the main theorem regarding the steerability of commuting Pauli Hamiltonians. Additionally, we provide a randomized algorithm for generating a sequence of steering operators, such that these operators ensure that the energy of the system is non- increasing, hence driving the system toward the grou...

    work page

  4. [4]

    To demonstrate this locality, we begin by proving Lemma 3, which is stated in Appendix C 2

    Locality of superoperator Another important aspect of steerability is the locality of the superoperators introduced above. To demonstrate this locality, we begin by proving Lemma 3, which is stated in Appendix C 2. Lemma 3. For arbitrary Pauli operator V , with its commuting relation with H (i) represented by vector gVH, must satisfy that CH×gT VH = 0, wh...

    work page

  5. [5]

    Alternative superoperators In addition to the family of steering operators discussed above, we now consider an alternative class of steering operators. Above we have chosen the the superoperators such that the system is always stabilized in sub- space with definite local energy ⟨H (i)⟩ = ±1, which works just like flipping spins classically. In general, st...

    work page

  6. [6]

    (C3), can be physically realized through the following procedure

    Realization of superoperator with Clifford unitary We now explain how the superoperators P (i) ± , defined in Eq. (C3), can be physically realized through the following procedure. First, we in- troduce an auxiliary qubit (serving as a ”detec- tor”), and then apply a Clifford unitary oper- ation [7]—which maps Pauli operators to Pauli operators—on a segmen...

    work page

  7. [7]

    This suppression is evident from the fact that the system does not leak out of the GS man- ifold, as shown previously

    Stability against heating In this section, we explain how environmental heating can be suppressed with the superoper- ators. This suppression is evident from the fact that the system does not leak out of the GS man- ifold, as shown previously. Here, we focus on il- lustrating the dynamical process by which this elimination of environmental errors (i.e., h...

    work page

  8. [8]

    II, a prerequisite for steer- ability is that the target GS can either be sta- bilized by certain non-trivial steering operations or be transformed from other intermediate states

    Non-steerability for states with full-Schmidt-rank As discussed in Sec. II, a prerequisite for steer- ability is that the target GS can either be sta- bilized by certain non-trivial steering operations or be transformed from other intermediate states. In this section, we demonstrate that for GSs with full Schmidt rank, such steering operations do not exis...

    work page

Show all 74 references
  1. [9]

    (12) in Sec

    Calculation of function p(ΠGS) In this section, we consider the calculation of 1 − p(ΠGS), as introduced in Eq. (12) in Sec. VII B. We then illustrate the necessity of computing this quantity exactly by examining the example of Dicke states. Let us first discuss the calculatio...

  2. [10]

    We then present the numerical calculation of the ef- fective temperature lower bound introduced in Sec

    Implementation of examples In this section, we first discuss the notion of locality for indistinguishable particles. We then present the numerical calculation of the ef- fective temperature lower bound introduced in Sec. VII D, for the SYK and Fermi–Hubbard models discussed in...

    2000

  3. [11]

    Verstraete, M

    F. Verstraete, M. M. Wolf, and J. I. Cirac, Quan- tum computation and quantum-state engineer- ing driven by dissipation, Nature physics 5, 633 (2009)

    2009

  4. [12]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quan- tum simulation, Reviews of Modern Physics 86, 153 (2014)

    2014

  5. [13]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computa- tional chemistry, Reviews of Modern Physics 92, 015003 (2020)

    2020

  6. [14]

    Kempe, A

    J. Kempe, A. Kitaev, and O. Regev, The com- plexity of the local hamiltonian problem, Siam journal on computing 35, 1070 (2006)

    2006

  7. [15]

    Lucas, Ising formulations of many np prob- lems, Frontiers in physics 2, 5 (2014)

    A. Lucas, Ising formulations of many np prob- lems, Frontiers in physics 2, 5 (2014)

    2014

  8. [16]

    A. Y. Kitaev, Fault-tolerant quantum computa- tion by anyons, Annals of Physics 303, 2 (2003)

    2003

  9. [17]

    Gottesman, Theory of fault-tolerant quantum computation, Phys

    D. Gottesman, Theory of fault-tolerant quantum computation, Phys. Rev. A 57, 127 (1998)

    1998

  10. [18]

    S. Roy, J. T. Chalker, I. V. Gornyi, and Y. Gefen, Measurement-induced steering of quantum sys- tems, Phys. Rev. Research 2, 033347 (2020)

    2020

  11. [19]

    Herasymenko, I

    Y. Herasymenko, I. Gornyi, and Y. Gefen, Measurement-driven navigation in many-body hilbert space: Active-decision steering, PRX 45 Quantum 4, 020347 (2023)

    2023

  12. [20]

    Morales, Y

    S. Morales, Y. Gefen, I. Gornyi, A. Zazunov, and R. Egger, Engineering unsteerable quantum states with active feedback, Phys. Rev. Res. 6, 013244 (2024)

    2024

  13. [21]

    Ticozzi and L

    F. Ticozzi and L. Viola, Stabilizing entangled states with quasi-local quantum dynamical semi- groups, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engi- neering Sciences 370, 5259 (2012)

    2012

  14. [22]

    Affleck, T

    I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 59, 799 (1987)

    1987

  15. [23]

    Kumar, K

    P. Kumar, K. Snizhko, Y. Gefen, and B. Rosenow, Optimized steering: Quantum state engineering and exceptional points, Phys. Rev. A 105, L010203 (2022)

    2022

  16. [24]

    Preskill, Lecture notes for physics 229: Quan- tum information and computation, California In- stitute of Technology 16, 1 (1998)

    J. Preskill, Lecture notes for physics 229: Quan- tum information and computation, California In- stitute of Technology 16, 1 (1998)

    1998

  17. [25]

    R. Uola, A. C. Costa, H. C. Nguyen, and O. G¨ uhne, Quantum steering, Reviews of Mod- ern Physics 92, 015001 (2020)

    2020

  18. [26]

    V. V. Albert, B. Bradlyn, M. Fraas, and L. Jiang, Geometry and response of lindbladians, Phys. Rev. X 6, 041031 (2016)

    2016

  19. [27]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al., Quantum supremacy using a programmable superconduct- ing processor, Nature 574, 505 (2019)

    2019

  20. [28]

    McArdle, T

    S. McArdle, T. Jones, S. Endo, Y. Li, S. C. Ben- jamin, and X. Yuan, Variational ansatz-based quantum simulation of imaginary time evolution, npj Quantum Information 5, 1 (2019)

    2019

  21. [29]

    J. T. Barreiro, M. M¨ uller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, and R. Blatt, An open-system quan- tum simulator with trapped ions, Nature 470, 486 (2011)

    2011

  22. [30]

    Y. Lin, J. Gaebler, F. Reiter, T. R. Tan, R. Bowler, A. Sørensen, D. Leibfried, and D. J. Wineland, Dissipative production of a maximally entangled steady state of two quantum bits, Na- ture 504, 415 (2013)

    2013

  23. [31]

    J. T. Barreiro, P. Schindler, O. G¨ uhne, T. Monz, M. Chwalla, C. F. Roos, M. Hennrich, and R. Blatt, Experimental multiparticle entangle- ment dynamics induced by decoherence, Nature Physics 6, 943 (2010)

    2010

  24. [32]

    Langbehn, K

    J. Langbehn, K. Snizhko, I. Gornyi, G. Morigi, Y. Gefen, and C. P. Koch, Dilute measurement- induced cooling into many-body ground states, PRX Quantum 5, 030301 (2024)

    2024

  25. [33]

    Kishony, M

    G. Kishony, M. S. Rudner, A. Rosch, and E. Berg, Gauged cooling of topological excita- tions and emergent fermions on quantum simu- lators, Phys. Rev. Lett. 134, 086503 (2025)

    2025

  26. [34]

    Sugiura and M

    S. Sugiura and M. Ueda, Quantum feedback cooling of a trapped nanoparticle by using a low-pass filter, arXiv preprint arXiv:2505.10157 (2025)

    2025

  27. [35]

    Watrous, The Theory of Quantum Informa- tion (Cambridge University Press, 2018)

    J. Watrous, The Theory of Quantum Informa- tion (Cambridge University Press, 2018)

    2018

  28. [36]

    Perez-Garcia, F

    D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quantum Info. Comput. 7, 401–430 (2007)

    2007

  29. [37]

    Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321, 2 (2006)

    A. Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321, 2 (2006)

    2006

  30. [38]

    Haah, Commuting pauli hamiltonians as maps between free modules, Communications in Math- ematical Physics 324, 351 (2013)

    J. Haah, Commuting pauli hamiltonians as maps between free modules, Communications in Math- ematical Physics 324, 351 (2013)

    2013

  31. [39]

    Poulin, Stabilizer formalism for operator quantum error correction, Phys

    D. Poulin, Stabilizer formalism for operator quantum error correction, Phys. Rev. Lett. 95, 230504 (2005)

    2005

  32. [40]

    M. Hein, J. Eisert, and H. J. Briegel, Multiparty entanglement in graph states, Physical Review A 69, 10.1103/physreva.69.062311 (2004)

    2004 doi

  33. [41]

    H. W. Bl¨ ote and M. P. Nightingale, Antiferro- magnetic triangular ising model: Critical behav- ior of the ground state, Physical Review B 47, 15046 (1993)

    1993

  34. [42]

    This can be verified by noting the effect of P (i) − in Heisenberg picture

  35. [43]

    Gottesman, The heisenberg representation of quantum computers, arXiv preprint quant- ph/9807006 (1998)

    D. Gottesman, The heisenberg representation of quantum computers, arXiv preprint quant- ph/9807006 (1998)

    1998

  36. [44]

    Raussendorf, D

    R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A 68, 022312 (2003)

    2003

  37. [45]

    Mazurenko, C

    A. Mazurenko, C. S. Chiu, G. Ji, M. F. Par- sons, M. Kan´ asz-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold- atom fermi–hubbard antiferromagnet, Nature 545, 462 (2017)

    2017

  38. [46]

    M. Xu, L. H. Kendrick, A. Kale, Y. Gang, G. Ji, R. T. Scalettar, M. Lebrat, and M. Greiner, Frustration-and doping-induced magnetism in a fermi–hubbard simulator, Nature 620, 971 (2023)

    2023

  39. [47]

    X. Li, S. Wang, X. Luo, Y.-Y. Zhou, K. Xie, H.- C. Shen, Y.-Z. Nie, Q. Chen, H. Hu, Y.-A. Chen, and J.-W. Pan, Observation and quantification of the pseudogap in unitary fermi gases, Nature 626, 288 (2024)

    2024

  40. [48]

    Shao, Y.-X

    H.-J. Shao, Y.-X. Wang, D.-Z. Zhu, Y.-S. Zhu, H.-N. Sun, S.-Y. Chen, C. Zhang, Z.-J. Fan, Y. Deng, X.-C. Yao, Y.-A. Chen, and J.-W. Pan, Antiferromagnetic phase transition in a 3d fermionic hubbard model, Nature 632, 267 (2024)

    2024

  41. [49]

    M. Xu, L. H. Kendrick, A. Kale, Y. Gang, C. Feng, S. Zhang, A. W. Young, M. Lebrat, and M. Greiner, A neutral-atom hubbard quan- tum simulator in the cryogenic regime, Nature (2025), published online 11 June 2025

    2025

  42. [50]

    Bravyi, Efficient algorithm for a quantum ana- logue of 2-sat, arXiv preprint quant-ph/0602108 (2006)

    S. Bravyi, Efficient algorithm for a quantum ana- logue of 2-sat, arXiv preprint quant-ph/0602108 (2006)

    2006 arXiv

  43. [51]

    Gosset and D

    D. Gosset and D. Nagaj, Quantum 3-sat is qma 1-complete, SIAM Journal on Computing 45, 1080 (2016)

    2016

  44. [52]

    Kitaev, A simple model of quantum holog- raphy, http://online.kitp.ucsb.edu/online/ entangled15/ (2015)

    A. Kitaev, A simple model of quantum holog- raphy, http://online.kitp.ucsb.edu/online/ entangled15/ (2015)

    2015

  45. [53]

    Fu and S

    W. Fu and S. Sachdev, Numerical study of fermion and boson models with infinite-range 46 random interactions, Phys. Rev. B 94, 035135 (2016)

    2016

  46. [54]

    Zyczkowski and H.-J

    K. Zyczkowski and H.-J. Sommers, Induced mea- sures in the space of mixed quantum states, Jour- nal of Physics A: Mathematical and General 34, 7111 (2001)

    2001

  47. [55]

    Sachdev and J

    S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum heisenberg magnet, Phys. Rev. Lett. 70, 3339 (1993)

    1993

  48. [56]

    Imada, A

    M. Imada, A. Fujimori, and Y. Tokura, Metal- insulator transitions, Rev. Mod. Phys. 70, 1039 (1998)

    1998

  49. [57]

    Tarruell and L

    L. Tarruell and L. Sanchez-Palencia, Quantum simulation of the hubbard model with ultra- cold fermions in optical lattices, Comptes Ren- dus Physique 19, 365 (2018)

    2018

  50. [58]

    Sigrist, Introduction to unconventional su- perconductivity, in AIP Conference Proceedings, Vol

    M. Sigrist, Introduction to unconventional su- perconductivity, in AIP Conference Proceedings, Vol. 789 (American Institute of Physics, 2005) pp. 165–243

    2005

  51. [59]

    Or´ us, A practical introduction to tensor net- works: Matrix product states and projected en- tangled pair states, Annals of physics 349, 117 (2014)

    R. Or´ us, A practical introduction to tensor net- works: Matrix product states and projected en- tangled pair states, Annals of physics 349, 117 (2014)

    2014

  52. [60]

    Ding, C.-F

    Z. Ding, C.-F. Chen, and L. Lin, Single-ancilla ground state preparation via lindbladians, Phys. Rev. Res. 6, 033147 (2024)

    2024

  53. [61]

    Langbehn, G

    J. Langbehn, G. Mouloudakis, E. King, R. Menu, I. Gornyi, G. Morigi, Y. Gefen, and C. P. Koch (2025), in preparation

    2025

  54. [62]

    M. B. Plenio and P. L. Knight, The quantum- jump approach to dissipative dynamics in quan- tum optics, Reviews of Modern Physics 70, 101 (1998)

    1998

  55. [63]

    Minganti, A

    F. Minganti, A. Miranowicz, R. W. Chhajlany, I. I. Arkhipov, and F. Nori, Hybrid-liouvillian formalism connecting exceptional points of non- hermitian hamiltonians and liouvillians via post- selection of quantum trajectories, Phys. Rev. A 101, 062112 (2020)

    2020

  56. [64]

    Z. K. Minev, S. O. Mundhada, S. Shankar, P. Reinhold, R. Guti´ errez-J´ auregui, R. J. Schoelkopf, M. Mirrahimi, H. J. Carmichael, and M. H. Devoret, To catch and reverse a quantum jump mid-flight, Nature 570, 200 (2019)

    2019

  57. [65]

    Berlekamp, R

    E. Berlekamp, R. McEliece, and H. van Tilborg, On the inherent intractability of certain cod- ing problems, IEEE Transactions on Information Theory 24, 384 (1978)

    1978

  58. [66]

    Manzano, A short introduction to the lind- blad master equation, Aip Advances 10, 025106 (2020)

    D. Manzano, A short introduction to the lind- blad master equation, Aip Advances 10, 025106 (2020)

    2020

  59. [67]

    Blume-Kohout, H

    R. Blume-Kohout, H. K. Ng, D. Poulin, and L. Viola, Information-preserving structures: A general framework for quantum zero-error infor- mation, Phys. Rev. A 82, 062306 (2010)

    2010

  60. [68]

    T. W. Hungerford, Algebra, Vol. 73 (Springer Sci- ence & Business Media, 2012)

    2012

  61. [69]

    Goyeneche, D

    D. Goyeneche, D. Alsina, J. I. Latorre, A. Riera, and K. ˙Zyczkowski, Absolutely maximally entan- gled states, combinatorial designs, and multiuni- tary matrices, Phys. Rev. A 92, 032316 (2015)

    2015

  62. [70]

    R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954)

    1954

  63. [71]

    Valatin, Comments on the theory of supercon- ductivity, Il Nuovo Cimento (1955-1965) 7, 843 (1958)

    J. Valatin, Comments on the theory of supercon- ductivity, Il Nuovo Cimento (1955-1965) 7, 843 (1958)

    1958

  64. [72]

    Masuhara, J

    N. Masuhara, J. M. Doyle, J. C. Sandberg, D. Kleppner, T. J. Greytak, H. F. Hess, and G. P. Kochanski, Evaporative cooling of spin- polarized atomic hydrogen, Phys. Rev. Lett. 61, 935 (1988)

    1988

  65. [73]

    Jordan and E

    P. Jordan and E. Wigner, ¨Uber das paulische ¨ aquivalenzverbot, Zeitschrift f¨ ur Physik47, 631 (1928)

    1928

  66. [74]

    P. W. Anderson et al., Twenty-five years of high-temperature superconductivity–a personal review, in J Phys Conf Ser, Vol. 449 (2013) p. 012001

    2013

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