{"total":15,"items":[{"citing_arxiv_id":"2607.01843","ref_index":36,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Low-ancilla block encodings via Hamiltonian simulation","primary_cat":"quant-ph","submitted_at":"2026-07-02T08:06:14+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Single-ancilla approximate block encoding of A = sum alpha_j H_j is achieved via generalized quantum signal processing applied to Hamiltonian simulation, yielding near-optimal depth with one or O(log log(1/epsilon)) ancilla.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.11475","ref_index":19,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Linear Combination of Hamiltonian Simulation with Commutator Scaling","primary_cat":"quant-ph","submitted_at":"2026-06-09T22:12:35+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Using multi-product formulas in LCHS produces commutator-sensitive error bounds and better quadrature scaling than norm-based analyses for dissipative dynamics.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.06442","ref_index":47,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Nanostructure modelling with early fault tolerant quantum computers","primary_cat":"quant-ph","submitted_at":"2026-06-04T17:41:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Quantum simulation framework for ground-state energies of 4- and 8-electron double quantum dots on surface-code fault-tolerant hardware, with resource estimates of 226k-314k physical qubits and 24 hours to 3.4 days runtime at 10^{-3} noise.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.29279","ref_index":36,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Permutation Matrix Representation for Quantum Simulation: Comparative Resource Analysis","primary_cat":"quant-ph","submitted_at":"2026-05-28T02:58:41+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":3.0,"formal_verification":"none","one_line_summary":"Comparative resource analysis finds PMR offers complementary advantages and favorable scaling versus leading methods for time-independent and time-dependent Hamiltonian simulation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.21597","ref_index":32,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series","primary_cat":"quant-ph","submitted_at":"2026-05-20T18:00:49+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"MPO encodings of the Magnus expansion and Dyson series for accurate time evolution of time-dependent 1D quantum Hamiltonians on finite or infinite lattices with long-range interactions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16195","ref_index":123,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems","primary_cat":"quant-ph","submitted_at":"2026-05-15T17:11:07+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.12450","ref_index":61,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Simulation of Non-Hermitian Hamiltonians with Bivariate Quantum Signal Processing","primary_cat":"quant-ph","submitted_at":"2026-05-12T17:40:56+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Bivariate quantum signal processing simulates non-Hermitian Hamiltonians H_eff = H_R + i H_I with query-optimal complexity O((α_R + β_I)T + log(1/ε)/log log(1/ε)) in the separate-oracle model.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"WithH δ >0uniformly, the zero-locus and autocorre- lation obstructions are eliminated. The operator Fejér- Riesz theorem yields an SOS complement with correct bidegree. Theorem VI.2(Degree-bounded SOS factorization). LetH∈ T d1,d2 withH >0onT 2 andH= 1− |P| 2 for someP∈ P + d1,d2 . Then there existR 1, . . . , RL ∈ P + d1,d2 with H= LX ℓ=1 |Rℓ|2 onT 2, L≤min(d 1+1, d 2+1). (61) Proof sketch.The proof proceeds in two stages; the full construction is given in Appendix H. Stage 1: Reduction to a matrix-valued univariate prob- lem.Fixθ 2 and organize theθ 1-Fourier coefficients of Hinto the matrix-valued functionH(θ 2)∈C N1×N1 (N1 =d 1 + 1) with entriesH(θ 2)mm′ = ˆHm−m′(θ2). Each entry is a trigonometric polynomial of degreed 2"},{"citing_arxiv_id":"2604.07704","ref_index":31,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Trotterization with Many-body Coulomb Interactions: Convergence for General Initial Conditions and State-Dependent Improvements","primary_cat":"quant-ph","submitted_at":"2026-04-09T01:47:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Second-order Trotterization of many-body Coulomb Hamiltonians achieves a 1/4 convergence rate for general initial conditions in the Hamiltonian domain with polynomial particle-number scaling, and improves to first or second order under state-dependent conditions such as high-angular-momentum excited","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.07214","ref_index":49,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Quantum Gibbs sampling through the detectability lemma","primary_cat":"quant-ph","submitted_at":"2026-04-08T15:34:49+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"∥A−α(⟨0 m| ⊗I)U(|0 m⟩ ⊗I)∥ ≤ϵ.(12) An equivalent way to express (12) is U= \u0012eA/α∗ ∗ ∗ \u0013 , where∗can be any block matrices of the correct sizes and∥eA−A∥ ≤ϵ. We first note that, because eachPm can be implemented via its(1, 1, 0)-block encoding, these block encodings can be composed to implement a(1, M, 0)-block encoding of DL(H). Using the compression gadget in [49,50] we can further reduce the number of ancilla qubit toO(log(M)), thus resulting in a(1,O (log(M)), 0)-block encoding ofDL(H). Note that each implementation ofPm may involve exponentially small errors due to unitary synthesis, but these errors can be suppressed with polylogarithmic overhead, and their accumulation throughout the algorithm is well-controlled, as will"},{"citing_arxiv_id":"2602.09575","ref_index":61,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Quantum Simulation of Non-Unitary Dynamics via Amplitude-Phase Separation","primary_cat":"quant-ph","submitted_at":"2026-02-10T09:23:55+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Introduces Amplitude-Phase Separation (APS) decomposition for quantum simulation of non-unitary dynamics, with complementary error scaling advantages in time-independent cases and unification of prior methods like LCHS and NDME.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2511.10267","ref_index":43,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition","primary_cat":"quant-ph","submitted_at":"2025-11-13T12:52:52+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2510.07380","ref_index":45,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Quantum simulation of electronic structure via quantum fast multipole method","primary_cat":"quant-ph","submitted_at":"2025-10-08T18:00:01+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Quantum fast multipole method yields electronic structure simulation gate complexity t(η^{4/3}N^{1/3} + η^{1/3}N^{2/3})(η N t / ε)^{o(1)}, providing roughly O(η) speedup over prior work for N < η^7.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2509.19709","ref_index":129,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State","primary_cat":"physics.chem-ph","submitted_at":"2025-09-24T02:36:30+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"Review of quantum computing methods and potential for non-ground-state quantum chemistry including reaction dynamics, mechanisms, and finite temperatures.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"[127] have demonstrated improved performance for simple systems including the jellium model, H3 molecule, and Heisenberg spin models [128]. 6. Summary As one of the most promising quantum chemistry applications of quantum computers beyond the ground state, we emphasize the need for developing quantum computing methods 23 that can simulate spinful electronic dynamics, possibly with relativistic effects [129]. While our review mostly focused on asymptotic scaling, there are concrete gate counts estimated for many of the algorithms in the above (for example, Ref. [107]). We expect a combination of circuit optimization, faithful algorithmic approximation, and steady progress on fault- tolerant hardware development in the near future to push the limit of these Hamiltonian"},{"citing_arxiv_id":"2509.03586","ref_index":67,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Quantum simulation of out-of-equilibrium dynamics in gauge theories","primary_cat":"quant-ph","submitted_at":"2025-09-03T18:00:29+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"The paper reviews advances in quantum simulation of out-of-equilibrium dynamics in gauge theories, covering particle production, string breaking, thermalization, and related phenomena.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2312.05344","ref_index":175,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Quantum Algorithms for Simulating Nuclear Effective Field Theories","primary_cat":"quant-ph","submitted_at":"2023-12-08T20:09:28+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Resource estimates for quantum simulation of pionless and pionful nuclear lattice EFTs, including time evolution and energy estimation, with new error bounds from symmetries and locality yielding orders-of-magnitude improvements for the pionless case.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Empirical studies suggest that, for certain problems, product formulae perform better for instances of modest size [166], as mentioned above, but it might still be worth studying whether such approaches can be valuable for nuclear-EFT simulations in some regimes. Alternatively, techniques such as Trotter-error extrapolation might be used to reduce the error [175]. Ultimately, knowledge of the simulation's input state may improve the product-formula error bounds, as studied in Refs. [77-80], which should be explored further in the context of nuclear-EFT simulations. h. Different quantum-phase-estimation routines. The phase estimation routine used in Section VIIB is a standard variant of QPE. However, there are many alternative QPE methods that may improve the gate"}],"limit":50,"offset":0}