Every quantum algorithm worth knowing about, written down the same way: what it takes, what it returns, what it costs, and who proved it.
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The defining behavior was checked exactly: a mathematical identity, a full statevector or stabilizer simulation, or an exhaustive basis-state truth table.
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45 public entries
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Find quantum circuits that diagonalize a given input Hamiltonian, that is, approximate its eigenstates, without resorting to brute-force optimization of an unstructured variational circuit, which runs into barren plateaus.
A ground-state preparation method that projects non-unitary imaginary-time evolution onto a parameterized quantum circuit.
Given a target position for a robot manipulator's end effector, find joint angles that reach it — the inverse kinematics problem, which has no analytical solution for a general 6-degree-of-freedom arm and admits many joint configurations at once for a redundant one.
A quantum algorithm that produces approximate solutions for combinatorial optimization problems, tunable by a positive integer p.
Predict the three-dimensional structure a protein takes from its primary sequence of amino acids, posed here on the model Hamiltonian the paper defines for a chain of N monomers placed on a tetrahedral lattice.
A hybrid chemistry workflow that compares a quantum expectation loop with classical eigensolvers.
Determine the ground state of weakly-interacting, non-covalently bonded molecules — the weakly-bound intermolecular regime that variational quantum algorithms applied to strongly-bound, covalently-bonded systems with full molecular-orbital bases had left largely unexplored — using a coarse-grained representation of the electronic response suited to a VQA.
Simulate strongly correlated chemical systems on near-term quantum hardware, whose noise and limited size otherwise confine such simulations to small chemical systems, by embedding a quantum treatment of a strongly correlated fragment within a larger classical calculation.
Frozen-core and active-orbital choices define the Hamiltonian size before variational optimization.
An adaptive ansatz grows one operator at a time using measured energy gradients from a predefined pool.
Several high-gradient operators are appended per adaptive iteration to reduce optimization and measurement rounds.
Randomized measurements are reused to estimate many observables from a shared data set.
Conditional value-at-risk averages only a selected low-energy tail of samples for combinatorial objectives.
Minimizing the squared shifted Hamiltonian targets eigenstates near a chosen energy shift.
Generalized singles and doubles relax occupied-to-virtual restrictions to enlarge the variational manifold.
Parameter-shift or analytic derivative measurements supply gradients to a classical optimizer.
Alternating native one-qubit rotations and entanglers reduce compilation overhead but can change trainability.
McLachlan-style projected imaginary-time dynamics update parameters toward low-energy states.
Iterative QCC repeatedly dresses the Hamiltonian and selects new entanglers instead of fixing one deep circuit.
Repeated paired generalized doubles with generalized singles trade expressivity against shallower chemistry circuits.
Circuit depth grows in stages so each newly introduced layer can be initialized and optimized locally.
A contracted reference subspace is jointly entangled before a small effective Hamiltonian is diagonalized.
Commuting Pauli terms are partitioned into compatible bases to reduce distinct measurement circuits.
The Fubini–Study metric preconditions parameter updates according to circuit-state geometry.
The canonical hybrid loop: prepare an ansatz, estimate a Hamiltonian expectation, and update parameters classically.
Orbital rotations are optimized alongside circuit parameters to improve compact active-space descriptions.
Givens-style or excitation-preserving blocks keep evolution inside a fixed-particle-number sector.
Orthogonality or symmetry penalties augment the energy objective to exclude previously identified sectors.
Qubit coupled-cluster uses Pauli-word entanglers and a product-state reference directly in qubit space.
Commutator matrix elements over a VQE reference produce excitation energies through an equation-of-motion problem.
Measured response operators around a VQE state define a generalized eigenproblem for excitations and mitigation.
Qubit-space Pauli generators replace fermionic excitation operators to seek shorter adaptive circuits.
Known Z2 symmetries remove qubits and constrain the variational search to a selected sector.
Calibrated assignment errors are inverted or regularized before Pauli expectations are assembled.
Spin-complemented generators reduce leakage from a target total-spin sector.
Simultaneous perturbation estimates a stochastic gradient with two objective evaluations per iteration.
One shared unitary transforms several orthogonal inputs while a weighted objective orders multiple eigenstates.
The ansatz is constrained to preserve selected particle-number, parity, or spin symmetries.
Samples outside conserved symmetry sectors are rejected or reweighted as an error-mitigation step.
Operators with disjoint support are packed into the same adaptive layer to reduce circuit depth.
A chemistry-inspired unitary coupled-cluster ansatz truncated to single and double excitations.
Hamiltonian variance supplements or replaces energy to target eigenstates and diagnose convergence.
Overlap penalties against previously found states turn excited-state search into a sequence of VQE objectives.
Classical approximations, smaller active spaces, or nearby geometries initialize the variational parameters.
Energy estimates at amplified noise levels are extrapolated toward an inferred zero-noise limit.