Are there Traps in Quantum Control Landscapes?

Pechen, Alexander; Tannor, David J.

doi:10.1103/physrevlett.106.120402

Cited by 100 publications

(68 citation statements)

References 20 publications

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“…This result suggests that the traps in [36][37][38] are at most an extremely rare occurrence on the landscape, and possibly a null set. Another consideration is that many practical OCT and OCE studies may be considered as quite successful upon even reaching moderate yields when operating with various constraints.…”

Section: Testing For the Presence Of Traps On The Landscapementioning

confidence: 80%

“…The vast OCT literature supports the ability to reach excellent yields [1-3, 6-19, 39-59], although these works are not definitive with regard to the landscape due to control field constraints typically being present. The recent identification of trapping conditions [36][37][38] under unusual circumstances necessitates a more explicit investigation of whether traps can be expected when performing normal optimizations.…”

Section: Resultsmentioning

confidence: 99%

“…However, traps may arise for so-called singular control fields where the above Jacobian is significantly rank-deficient. Such situations have been known to occur when ε(t) = constant is employed [36][37][38], but this situation is generally not physically relevant in the laboratory. Thus, one goal of the simulations in this work is to establish whether traps may be encountered in optimizations starting from physically reasonable control fields.…”

Section: Formulation Of the Control Objectivementioning

confidence: 99%

“…Considering a controllable target system under reasonable physical assumptions [32], the topology of the dynamical quantum control landscape can be shown to have no suboptimal local maxima or traps [31,[33][34][35]. Exceptions to this favorable topology have been found under unusual circumstances, e.g., when constant control fields ε(t) are employed [36][37][38]. An important objective is to either affirm the attractive theoretical landscape findings or identify the likelihood of encountering landscape traps in the course of typical optimizations under reasonable physical conditions.…”

Section: Introductionmentioning

confidence: 99%

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Exploring quantum control landscapes: Topology, features, and optimization scaling

2011

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Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic iterations) required to find an optimal control field appears to be essentially invariant to the complexity of the system. The present work explores this matter in a series of systematic optimizations of the state-to-state transition probability on model quantum systems with the number of states N ranging from 5 through 100. The optimizations occur over a landscape defined by the transition probability as a function of the control field. Previous theoretical studies on the topology of quantum control landscapes established that they should be free of sub-optimal traps under reasonable physical conditions. The simulations in this work include nearly 5000 individual optimization test cases, all of which confirm this prediction by fully achieving optimal population transfer of at least 99.9% upon careful attention to numerical procedures to ensure that the controls are free of constraints. Collectively, the simulation results additionally show invariance of required search effort to system dimension N . This behavior is rationalized in terms of the structural features of the underlying control landscape. The very attractive observed scaling with system complexity may be understood by considering the distance traveled on the control landscape during a search and the magnitude of the control landscape slope. Exceptions to this favorable scaling behavior can arise when the initial control field fluence is too large or when the target final state recedes from the initial state as N increases.

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Section: Testing For the Presence Of Traps On The Landscapementioning

confidence: 80%

Section: Resultsmentioning

confidence: 99%

Section: Formulation Of the Control Objectivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploring quantum control landscapes: Topology, features, and optimization scaling

2011

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“…The question of whether traps exist in unitary control using the standard gate fidelity has been well studied [39][40][41], and the conclusion is that generic quantum control landscapes are almost always trap free. This may also apply to the local estimator of the fidelity; traps were not a problem for the numerical simulations we performed and found no evidence of any new traps in Fig.3 or elsewhere.…”

Section: Discussionmentioning

confidence: 99%

In situ upgrade of quantum simulators to universal computers

Dive

Pitchford

Mintert

et al. 2018

Quantum

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Quantum simulators, machines that can replicate the dynamics of quantum systems, are being built as useful devices and are seen as a stepping stone to universal quantum computers. A key difference between the two is that computers have the ability to perform the logic gates that make up algorithms. We propose a method for learning how to construct these gates efficiently by using the simulator to perform optimal control on itself. This bypasses two major problems of purely classical approaches to the control problem: the need to have an accurate model of the system, and a classical computer more powerful than the quantum one to carry out the required simulations. Strong evidence that the scheme scales polynomially in the number of qubits, for systems of up to 9 qubits with Ising interactions, is presented from numerical simulations carried out in different topologies. This suggests that this in situ approach is a practical way of upgrading quantum simulators to computers.Recent and ongoing work on building large quantum systems is leading to simulators that are able to model physical phenomena, allowing questions about the underlying science to be answered [1][2][3]. These machines contain a register of quantum particles, typically two level quantum systems (qubits) storing quantum information. The presence of interactions between these leads to dynamics that, by varying control parameters in the system Hamiltonian, can replicate the quantum behaviour of systems of interest. This, however, is less general than a quantum computer which is able is to perform a universal set of logic gates on the qubits [4].Provided some control parameters can be varied in time, it is in principle possible to do an arbitrary gate on a quantum many-body system such as a quantum simulator [5][6][7]. Finding the right time-dependency however relies almost exclusively on numerical methods, especially when physical constraints on the control fields are taken into account [8,9]. These methods require a very precise knowledge of the parameters of a system, a daunting task for a machine with a huge number of degrees of freedom. Furthermore, they are intractable on a classical computer if the quantum simulator we want to solve the problem for is large enough to do something beyond the capabilities of classical computers. These two difficulties provide a major obstacle in using quantum simulators to perform arbitrary computation.We circumvent these problems by showing how well-known existing numerical methods can be translated to run in situ on the quantum simulator itself, as illustrated in Fig.1. A mix of an-

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From Coherent to Incoherent Dynamical Control of Open Quantum Systems

Kurizki

Zwick

2016

Advances in Chemical Physics Volume 159

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Are there Traps in Quantum Control Landscapes?

Cited by 100 publications

References 20 publications

Exploring quantum control landscapes: Topology, features, and optimization scaling

Exploring quantum control landscapes: Topology, features, and optimization scaling

In situ upgrade of quantum simulators to universal computers

From Coherent to Incoherent Dynamical Control of Open Quantum Systems

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