clifford_qc is a Python research toolkit for constructing quantum models, comparing variational and subspace eigensolvers, and estimating measurement resources. A common sparse Pauli algebra connects Hamiltonians, density operators, gates, and candidate-selection observables; dedicated interfaces handle circuits, execution, and statistical estimates. A worked gradient example illustrates shared measurements, and a molecular workflow separates reusable preparation, solving, and reference validation. Matrix-element banks support virtual subspaces, exact Ritz residuals, and folded-spectrum roots. Process-isolated benchmarks show that packed coefficients and streaming reduce observed peak memory on the larger tested inputs at increased runtime. Measurement studies separate setting counts, shot requirements, and device cost: fully commuting readout certifies a fixed first-order Ritz functional with fewer shots, while anticommuting cliques help some fixed reference energies and not others. Entangling-gate time and connectivity can offset shot savings or make a protocol inadmissible under illustrative device models. Further studies expose subspace bias, indeterminate encoding comparisons, failed approximate-restriction screens, and high residual-measurement costs under the tested uniform allocations. Generated tables, provenance records, a versioned evidence contract, and manuscript checks connect claims to their inputs. These small-system results support reproducible method development and establish neither hardware performance nor a general simulation speedup.
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18 pages, 5 figures, 12 tables. v2: adds exact Ritz residuals and folded-spectrum roots, process-isolated storage measurements, anticommuting-clique comparisons, and residual-measurement cost studies; clarifies numerical and evidence limits. Companion to arXiv:2607.17443. Code and records: https://github.com/gutama/clifford_qc
clifford_qc is a Python research toolkit for constructing quantum models, comparing variational and subspace eigensolvers, and estimating measurement resources. A common sparse Pauli algebra connects Hamiltonians, density operators, gates, and candidate-selection observables; dedicated interfaces handle circuits, execution, and statistical estimates. A worked gradient example illustrates shared measurements, and a molecular workflow separates reusable preparation, solving, and reference validation. Matrix-element banks support virtual subspaces, exact Ritz residuals, and folded-spectrum roots. Process-isolated benchmarks show that packed coefficients and streaming reduce observed peak memory on the larger tested inputs at increased runtime. Measurement studies separate setting counts, shot requirements, and device cost: fully commuting readout certifies a fixed first-order Ritz functional with fewer shots, while anticommuting cliques help some fixed reference energies and not others. Entangling-gate time and connectivity can offset shot savings or make a protocol inadmissible under illustrative device models. Further studies expose subspace bias, indeterminate encoding comparisons, failed approximate-restriction screens, and high residual-measurement costs under the tested uniform allocations. Generated tables, provenance records, a versioned evidence contract, and manuscript checks connect claims to their inputs. These small-system results support reproducible method development and establish neither hardware performance nor a general simulation speedup.
Quantum subspace methods are often compared by basis dimension or energyerror, although their dominant experimental costs arise from different statepreparations, measurement settings, and shot allocations. We present theDyadic Adaptive Clifford-Algebra Subspace Eigensolver (DA-CASE), whose basisstates are virtual directions Ai∣ψ⟩ generated from one reference.Overlap, Hamiltonian, and observable matrices are reconstructed from onecached set of Pauli expectations on that reference. The method thereforetrades multiple prepared basis states for a potentially wide measurement bank.We make that trade explicit on a frozen eight-qubit H4 Hamiltonian. Twogenerator resolutions reach the same nine-dimensional subspace and the sameenergy to machine precision, while the retained bank changes from 7371 to 2240Pauli words. A reference-conditioned symmetry test certifies the narrower spanwithout asserting that its individual Pauli words conserve the sector asabstract operators. Independently, a dyadic commuting hierarchy reduces thedeterminant bank from 913 qubit-wise-commuting settings to 64 fully commutingsettings, while exposing the added logical-CX cost. In a separate four-qubitfinite-shot diagnostic, covariance-aware allocation reduces theprojected-matrix variance target by 68.9%. Mode-wise overlap regularizationremoves the observed catastrophic energy estimates and lowers RMSE, butdoubles the median error relative to a fixed cutoff. These are small-instanceexact and Monte Carlo results, not a hardware demonstration, scaling result,or quantum advantage claim. The contribution is a single-referencemeasurement architecture and a resource ledger that keeps contexts, settings,shots, circuit depth, and post-selection retries in their proper units.
We develop a sparse operator-centric realization of n-qubit variational quantum algorithms in the complex Clifford algebra Cl(2n,C)≅M(2n,C). Density operators, gates, observables, channels, fermionic modes, and adaptive-selection observables are represented in one Pauli-word algebra, with the Jordan--Wigner map providing the exact bridge to anticommuting Clifford generators. We distinguish general Pauli-word rotations from Spin-group rotors and formulate the familiar odd-Y restriction for real-state adaptive ansatzes as an exact transpose-parity statement: for real Hamiltonians and real states, every candidate Pauli word containing an even number of Y factors has zero ADAPT gradient, while odd-Y rotations preserve the real sector. For the critical open transverse-field Ising chain, a depth-three Hamiltonian variational ansatz gives relative energy errors 4.84×10−5, 2.19×10−3, and 3.67×10−3 for n=4,5,6. A compact local ADAPT pool is exact at n=4 but leaves residual errors at larger sizes; a systematic contiguous three-local odd-Y pool reaches relative errors below 1.3×10−12 for n≤6. In 100-seed finite-shot tests at n=4, fixed-shot selection succeeds in 0/100 runs, whereas uniform escalation and confidence-bound racing each succeed in 84/100 runs; racing lowers median shots by 34%. We claim no asymptotic speedup over matrix methods. The contribution is a corrected algebraic formulation, a density-operator derivation and implementation of the real-sector pool filter, and a reproducible study of measurement-limited adaptive selection.
This work presents QiliSim, the native C++ simulation backend of QiliSDK, an open-source Python framework for digital and analog quantum computing. QiliSim supports quantum circuits, Hamiltonian time evolution, and analog-digital quantum reservoirs through a common interface, allowing users to test quantum algorithms before executing them on quantum hardware. The simulator provides statevector and density-matrix methods for digital workloads, alongside fixed-step and adaptive Runge–Kutta integrators, Krylov-subspace methods, and direct matrix exponentiation for analog evolution. Monte Carlo trajectories, mid-circuit measurements, and Kraus and Lindbladian noise models support the simulation of noisy quantum systems. Numerical methods and execution settings are selected through structured configuration objects, allowing the same quantum program to run with different simulation strategies without modifying its definition. The poster includes a circuit simulation example and performance comparisons for digital circuit sampling and quantum annealing. The reported benchmarks show competitive CPU performance against Qiskit Aer and Cirq for small to medium circuits, and faster execution than QuTiP and CUDA-Q dynamics for the tested annealing task at a target fidelity of 99%.
Exact classical simulation of fault-tolerant quantum circuits remains limited by a tradeoff between exponential state vector scaling, exponential T-count scaling in stabilizer-rank approaches, and per-shot tracking overhead in sparse generalized stabilizer simulators. In this work, we introduce Clifft, an open-source simulator that shifts the dominant exponential cost from the total qubit count to a dynamic active subspace by factoring the quantum state into an offline Clifford frame, an online Pauli frame, and a dynamically sized active state vector. This architecture resolves deterministic Clifford coordinate transformations ahead of time, generalizing Stim's compile-once, sample-many execution model to circuits with non-Clifford operations. Consequently, exponential simulation costs are determined by the peak active virtual dimension, which expands during non-Clifford operations and contracts during measurements. Clifft remains within a constant factor of standard tools in the pure-Clifford and non-Clifford limits, while delivering up to orders-of-magnitude throughput gains over GPU-accelerated near-Clifford simulators on low-magic fault-tolerant benchmarks. Executing on commodity CPUs and exposing a Stim-like API, Clifft enables, to our knowledge, the first exact end-to-end simulation of magic state cultivation including the escape stage, over hundreds of billions of shots. These simulations show that escape-stage failures suppress the discrepancy between the true T-gate circuit and its S-proxy at low decoder-gap thresholds, while at high thresholds the full-protocol behavior approaches the larger discrepancy observed in the cultivation stages alone.
Recent years have seen a rapid growth in literature presenting new methods for simulating non-Clifford quantum circuits with classical hardware. These methods span a range of approaches, including stabiliser decomposition and tensor contraction techniques, varying in efficiency depending on circuit class, depth, non-Clifford gate count, and other metrics. A notable limitation of this literature is the lack of a standardised approach to benchmarking, with each new paper outlining its own specification, simulating its own set of circuits on the authors' own hardware. This paper seeks to address this issue by presenting a standardised and canonical benchmark suite and infrastructure for quantifying the efficiency of non-Clifford classical simulators, with a consistent dataset of circuits and providing consistent (virtual) hardware, thereby enabling a fair comparison of results.
Electronic-structure and embedding workflows terminate in effective many-body Hamiltonians, whereas quantum eigensolver studies often start from hand-built qubit models. We present the Adaptive Clifford-Algebra Subspace Eigensolver (A-CASE), a single-reference, operator-generated Rayleigh--Ritz method. Overlap, Hamiltonian, observable, and response matrices are reconstructed from one shared Pauli-expectation bank, while adaptive growth scores overlap-aware local pencils and rejects symmetry leakage or near-linear dependence. A strict FCIDUMP adapter supplies the active-space boundary. For linear H4 in STO-3G with CAS(4e,4o), the mapped sector agrees with independent determinant FCI to 3.1×10−15 Ha. At a nine-vector budget A-CASE has a 3.019 mHa error; replacing the determinant reference by a two-operator ADAPT-VQE state reduces it to 0.342 mHa, without implying a matched total-cost advantage. Under a matched contract, the fixed-reference route uses one state preparation versus ADAPT-VQE's ninety but measures roughly an order of magnitude more Pauli words. Exact fixed-angle ADAPT-GCIM gives 13.364 mHa at the nearest size match and 10.674 mHa at the iteration match, with its transition-pair burden reported separately. Across a broader benchmark ladder, fixed Krylov bases are generally more accurate and often narrower but substantially less well conditioned. A grouped bootstrap propagates finite-shot variability through thresholding, diagonalization, root matching, spectral weights, susceptibility, and broadening; its bands are explicitly heuristic and conditional, not finite-sample confidence certificates. The work establishes an executable path from an interchange Hamiltonian to energies, correlations, and response, without claiming materials accuracy, favorable scaling, or quantum advantage.