Algorithms · Hamiltonian simulation · model systems
Quantum simulation of the kicked rotator model
Simulate the quantum kicked rotator model — used to study quantum chaos, localization and the Anderson transition — with a quantum algorithm that scales better than classical simulation of the same model.
Attested & literatureUpdated
Open on the mapView frozen graph
- Record typeLiterature reference
- Reference implementationquantum_chaos
- Reported costExponentially faster than classical algorithms, for simulating the quantum kicked rotator model — a statement about the cost of simulating that one dynamical system, not a bound on solving a decision, search, or optimization problem. The abstract gives no big-O expression, no base for the exponential, no qubit or gate count, and no error dependence; a second, separate claim — that a similar algorithm simulates classical chaos in certain area-preserving maps efficiently — is likewise unquantified.
- Papers1
Simulate the quantum kicked rotator model — used to study quantum chaos, localization and the Anderson transition — with a quantum algorithm that scales better than classical simulation of the same model. Georgeot and Shepelyansky present a quantum algorithm that simulates the quantum kicked rotator model exponentially faster than classical algorithms. They state that this result shows that important physical problems of quantum chaos, localization and the Anderson transition can be modelled efficiently on a quantum computer. They also report a second, related result: a similar algorithm simulates efficiently classical chaos in certain area-preserving maps. The abstract states both results at the level of an asymptotic comparison — exponentially faster, and efficiently — without describing how either algorithm is built, what resource it is measured in, or what base or regime the exponential or the efficient scaling holds over; those specifics, if given at all, are in the paper and not in the abstract read for this record.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
Georgeot and Shepelyansky present a quantum algorithm that simulates the quantum kicked rotator model exponentially faster than classical algorithms. They state that this result shows that important physical problems of quantum chaos, localization and the Anderson transition can be modelled efficiently on a quantum computer. They also report a second, related result: a similar algorithm simulates efficiently classical chaos in certain area-preserving maps. The abstract states both results at the level of an asymptotic comparison — exponentially faster, and efficiently — without describing how either algorithm is built, what resource it is measured in, or what base or regime the exponential or the efficient scaling holds over; those specifics, if given at all, are in the paper and not in the abstract read for this record. Reported cost: Exponentially faster than classical algorithms, for simulating the quantum kicked rotator model — a statement about the cost of simulating that one dynamical system, not a bound on solving a decision, search, or optimization problem. The abstract gives no big-O expression, no base for the exponential, no qubit or gate count, and no error dependence; a second, separate claim — that a similar algorithm simulates classical chaos in certain area-preserving maps efficiently — is likewise unquantified..
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
- Record type
- Literature reference
- Reference implementation
- quantum_chaos
- Reported cost
- Exponentially faster than classical algorithms, for simulating the quantum kicked rotator model — a statement about the cost of simulating that one dynamical system, not a bound on solving a decision, search, or optimization problem. The abstract gives no big-O expression, no base for the exponential, no qubit or gate count, and no error dependence; a second, separate claim — that a similar algorithm simulates classical chaos in certain area-preserving maps efficiently — is likewise unquantified.
- Complexity basis
- The abstract of arXiv:quant-ph/0010005 states no big-O expression, qubit count, or gate count. Its cost claim is: "We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms." That is a claim about simulating a model, not about solving a decision or optimization problem, and the abstract does not say faster in which resource or with what base. The abstract separately states "important physical problems of quantum chaos, localization and Anderson transition can be modelled efficiently on a quantum computer", which names the problems the simulation bears on without attaching a bound to any of them, and "We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps", whose efficiently is likewise left undefined. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field.
- Circuit
- Not supplied
This record is not a concrete circuit.
Quantum vs classical
Classical baseline
Compare Hamiltonian simulation · model systems with the strongest classical method for the same instance, input budget, and output metric.
Quantum claim
This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.
How to compare
Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.
Nobody has reviewed this record for gaps yet.
ALGORITHM: Quantum simulation of the kicked rotator model
PROBLEM: Simulate the quantum kicked rotator model — used to study quantum chaos, localization and the Anderson transition — with a quantum algorithm that scales better than classical simulation of the same model.
IDEA: Georgeot and Shepelyansky present a quantum algorithm that simulates the quantum kicked rotator model exponentially faster than classical algorithms. They state that this result shows that important physical problems of quantum chaos, localization and the Anderson transition can be modelled efficiently on a quantum computer. They also report a second, related result: a similar algorithm simulates efficiently classical chaos in certain area-preserving maps. The abstract states both results at the level of an asymptotic comparison — exponentially faster, and efficiently — without describing how either algorithm is built, what resource it is measured in, or what base or regime the exponential or the efficient scaling holds over; those specifics, if given at all, are in the paper and not in the abstract read for this record.
REPORTED COST: Exponentially faster than classical algorithms, for simulating the quantum kicked rotator model — a statement about the cost of simulating that one dynamical system, not a bound on solving a decision, search, or optimization problem. The abstract gives no big-O expression, no base for the exponential, no qubit or gate count, and no error dependence; a second, separate claim — that a similar algorithm simulates classical chaos in certain area-preserving maps efficiently — is likewise unquantified.
BASIS: The abstract of arXiv:quant-ph/0010005 states no big-O expression, qubit count, or gate count. Its cost claim is: "We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms." That is a claim about simulating a model, not about solving a decision or optimization problem, and the abstract does not say faster in which resource or with what base. The abstract separately states "important physical problems of quantum chaos, localization and Anderson transition can be modelled efficiently on a quantum computer", which names the problems the simulation bears on without attaching a bound to any of them, and "We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps", whose efficiently is likewise left undefined. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field.
PRIMARY SOURCE: B. Georgeot, D. L. Shepelyansky (2000), Exponential Gain in Quantum Computing of Quantum Chaos and Localization — https://arxiv.org/abs/quant-ph/0010005
This is a literature reference record, not an executable circuit.A reference record, not runnable source. Leona cannot execute it, so it cannot be saved to your Library as a circuit.
Where this sits
This record is named by the layer graph at:
- Simulate Hamiltonian evolution Slot
Takes An access model for — a sum of efficiently exponentiable terms, sparse-access oracles, or a block-encoding — plus an evolution time and a target error . Returns A circuit approximating to within , with a stated query or gate count, an ancilla count, and the norm parameter — sparsity times , or the LCU 1-norm — that the cost is measured against.
Related entries
- Trotter–Suzuki Hamiltonian simulation
Algorithms
- Transverse-field Ising simulation
Algorithms
- Quantum adiabatic evolution
Algorithms
- Quantum Fourier Transform
Algorithms
References
- Exponential Gain in Quantum Computing of Quantum Chaos and Localization
B. Georgeot, D. L. Shepelyansky · 2000
Primary source: it presents the quantum algorithm that simulates the quantum kicked rotator model exponentially faster than classical algorithms, states that this makes quantum chaos, localization and the Anderson transition efficiently modellable on a quantum computer, and reports a related algorithm for efficiently simulating classical chaos in certain area-preserving maps. Consult it for how either algorithm is constructed, what resource the speedup is measured in, and any qubit, gate or error bound, none of which the abstract states.