Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2603.28506 · Physical Review A

Open-System Adiabatic Quantum Search under Dephasing

Afaf El Kalai, Peter J. Eder, Christian B. Mendl

On Aqora:Afaf El KalaiAfaf El Kalai
quant-phSubmitted Mar 30, 2026• Announced Mar 31, 2026• 0 citations• Revised Oct 12, 2026 (v2)
v1 · Mar 30, 2026v2 · Oct 12, 2026
arXivHTMLPDF

Abstract

Adiabatic quantum algorithms must evolve slowly enough to suppress non-adiabatic transitions while remaining fast enough to be practical. In open systems, this trade-off is reshaped by decoherence. For Hamiltonians subject to dephasing Lindbladians, Avron et al. [Phys. Rev. A 82, 040304(R) (2010)] showed that a unique timetable exists that maximizes the fidelity with a target state. This optimal schedule is characterized by a constant tunneling rate along the adiabatic path. In this work, we revisit their analysis and apply it to the adiabatic Grover search framework, obtaining closed-form expressions for the optimal evolution schedule, the minimum runtime, and the resulting achievable fidelity. Moreover, by invoking an energy-time uncertainty argument, we identify a critical dephasing threshold beyond which further noise-assisted acceleration is prohibited, showing that the apparent advantage of strong dephasing is a Zeno-type stabilization mechanism rather than a conventional algorithmic speedup over unitary Grover search.

Journal reference
Phys. Rev. A 114, 042411 (2026)
DOI
10.1103/9q9k-92cf

Related papers

Optimal time schedule for adiabatic evolution

J. E. Avron, Martin Fraas, Gian Michele Graf +1 more

We show that, provided dephasing is taken into account, there is a unique timetable which maximizes the fidelity with a target state in adiabatic evolutions. The optimum has constant tunneling rate along the path. Application to quantum search algorithms recovers the Grover result for appropriate scaling of the dephasing with the size of the database. Moreover, the Grover bound imposes constraints on the dephasing rates of systems coupled to a universal Markovian bath.

arXiv:1003.2172•Physical Review A•Oct 22, 2010•23 citations

Adiabatic quantum unstructured search in parallel

Sean A. Adamson, Petros Wallden

We present an optimized adiabatic quantum schedule for unstructured search building on the original approach of Roland and Cerf [Phys. Rev. A 65, 042308 (2002)]. Our schedule adiabatically varies the Hamiltonian even more rapidly at the endpoints of its evolution, preserving Grover's well-known quadratic quantum speedup. In the errorless adiabatic limit, the probability of successfully obtaining the marked state from a measurement increases directly proportional to time, suggesting efficient parallelization. Numerical simulations of an appropriate reduced two-dimensional Schrödinger system confirm adiabaticity while demonstrating superior performance in terms of probability compared to existing adiabatic algorithms and Grover's algorithm, benefiting applications with possible premature termination. We introduce a protocol that ensures a marked-state probability at least $p$ in time of order $\sqrt{N}(1+p/\varepsilon)$, and analyze its implications for realistic bounded-resource scenarios. Our findings suggest that quantum advantage may still be achievable under constrained coherence times (where other algorithms fail), provided the hardware allows for them to be sufficiently long.

arXiv:2502.08594•Feb 12, 2025•0 citations

Fixed-point adiabatic quantum search

Alexander M. Dalzell, Theodore J. Yoder, Isaac L. Chuang

Fixed-point quantum search algorithms succeed at finding one of $M$ target items among $N$ total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property---the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014)] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002)] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.

arXiv:1609.03603•Physical Review A•Jan 11, 2017•26 citations

Grover Speedup from Many Forms of the Zeno Effect

Jesse Berwald, Nicholas Chancellor, Raouf Dridi

It has previously been established that adiabatic quantum computation, operating based on a continuous Zeno effect due to dynamical phases between eigenstates, is able to realise an optimal Grover-like quantum speedup. In other words, is able to solve an unstructured search problem with the same N scaling as Grover's original algorithm. A natural question is whether other manifestations of the Zeno effect can also support an optimal speedup in a physically realistic model (through direct analogue application rather than indirectly by supporting a universal gateset). In this paper we show that they can support such a speedup, whether due to measurement, decoherence, or even decay of the excited state into a computationally useless state. Our results also suggest a wide variety of methods to realise speedup which do not rely on Zeno behaviour. We group these algorithms into three families to facilitate a structured understanding of how speedups can be obtained: one based on phase kicks, containing adiabatic computation and continuous-time quantum walks; one based on dephasing and measurement; and finally one based on destruction of the amplitude within the excited state, for which we are not aware of any previous results. These results suggest that there may be exciting opportunities for new paradigms of analog quantum computing based on these effects.

arXiv:2305.11146•Quantum•Nov 20, 2024•7 citations

Quantum search with hybrid adiabatic–quantum-walk algorithms and realistic noise

James G. Morley, Nicholas Chancellor, Sougato Bose +1 more

Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near term. Adiabatic quantum computing, quantum annealing, computation by a continuous-time quantum walk, and special purpose quantum simulators all use this strategy. In this work, we carry out a detailed examination of adiabatic and quantum-walk implementation of the quantum search algorithm, using the more physically realistic hypercube connectivity, rather than the complete graph, for our base Hamiltonian. We calculate optimal adiabatic schedules both analytically and numerically for the hypercube and then interpolate between adiabatic and quantum-walk searching, obtaining a family of hybrid algorithms. We show that all of these hybrid algorithms provide the quadratic quantum speedup when run with optimal parameter settings, which we determine and discuss in detail. We incorporate the effects of multiple runs of the same algorithm, noise applied to the qubits, and two types of problem misspecification, determining the optimal hybrid algorithm for each case. Our results reveal a rich structure of how these different computational mechanisms operate and should be balanced in different scenarios. For large systems with low noise and good control, a quantum walk is the best choice, while hybrid strategies can mitigate the effects of many shortcomings in hardware and problem misspecification.

arXiv:1709.00371•Physical Review A•Feb 28, 2019•46 citations

Grover search under localized dephasing

Daniel Reitzner, Mark S. Hillery

Decoherence in quantum searches, and in the Grover search, in particular, has already been extensively studied, leading very quickly to the loss of the quadratic speedup over the classical case, when searching for some target (marked) element within a set of size $N$. The noise models used were, however, almost always global. In this paper, we study Grover search under the influence of localized partially dephasing noise of rate $p$. We find that, in the case when the size $k$ of the affected subspace is much smaller than $N$ and the target is unaffected by the noise, namely when $kp\ensuremath{\ll}\sqrt{N}$, the quadratic speedup is retained. Once these restrictions are not met, the quadratic speedup is lost. If the target is affected by the noise, the noise rate needs to scale as $1/\sqrt{N}$ to keep the speedup. We also observe an intermediate region, where if $k\ensuremath{\sim}{N}^{\ensuremath{\mu}}$ and the target is unaffected, the speedup seems to obey ${N}^{\ensuremath{\mu}}$, which for $\ensuremath{\mu}>0.5$ is worse than the quantum, but better than the classical case. We also put obtained results for quantum searches into perspective of quantum walks and searches on graphs.

arXiv:1712.06558•Physical Review A•Jan 23, 2019•20 citations
Adiabatic quantum algorithms must evolve slowly enough to suppress non-adiabatic transitions while remaining fast enough to be practical. In open systems, this trade-off is reshaped by decoherence. For Hamiltonians subject to dephasing Lindbladians, Avron et al. [Phys. Rev. A 82, 040304(R) (2010)] showed that a unique timetable exists that maximizes the fidelity with a target state. This optimal schedule is characterized by a constant tunneling rate along the adiabatic path. In this work, we revisit their analysis and apply it to the adiabatic Grover search framework, obtaining closed-form expressions for the optimal evolution schedule, the minimum runtime, and the resulting achievable fidelity. Moreover, by invoking an energy-time uncertainty argument, we identify a critical dephasing threshold beyond which further noise-assisted acceleration is prohibited, showing that the apparent advantage of strong dephasing is a Zeno-type stabilization mechanism rather than a conventional algorithmic speedup over unitary Grover search.
We present an optimized adiabatic quantum schedule for unstructured search building on the original approach of Roland and Cerf [Phys. Rev. A 65, 042308 (2002)]. Our schedule adiabatically varies the Hamiltonian even more rapidly at the endpoints of its evolution, preserving Grover's well-known quadratic quantum speedup. In the errorless adiabatic limit, the probability of successfully obtaining the marked state from a measurement increases directly proportional to time, suggesting efficient parallelization. Numerical simulations of an appropriate reduced two-dimensional Schrödinger system confirm adiabaticity while demonstrating superior performance in terms of probability compared to existing adiabatic algorithms and Grover's algorithm, benefiting applications with possible premature termination. We introduce a protocol that ensures a marked-state probability at least ppp in time of order N(1+p/ε)\sqrt{N}(1+p/\varepsilon)N​(1+p/ε), and analyze its implications for realistic bounded-resource scenarios. Our findings suggest that quantum advantage may still be achievable under constrained coherence times (where other algorithms fail), provided the hardware allows for them to be sufficiently long.
Fixed-point quantum search algorithms succeed at finding one of MMM target items among NNN total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property---the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014)] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002)] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.
It has previously been established that adiabatic quantum computation, operating based on a continuous Zeno effect due to dynamical phases between eigenstates, is able to realise an optimal Grover-like quantum speedup. In other words, is able to solve an unstructured search problem with the same N scaling as Grover's original algorithm. A natural question is whether other manifestations of the Zeno effect can also support an optimal speedup in a physically realistic model (through direct analogue application rather than indirectly by supporting a universal gateset). In this paper we show that they can support such a speedup, whether due to measurement, decoherence, or even decay of the excited state into a computationally useless state. Our results also suggest a wide variety of methods to realise speedup which do not rely on Zeno behaviour. We group these algorithms into three families to facilitate a structured understanding of how speedups can be obtained: one based on phase kicks, containing adiabatic computation and continuous-time quantum walks; one based on dephasing and measurement; and finally one based on destruction of the amplitude within the excited state, for which we are not aware of any previous results. These results suggest that there may be exciting opportunities for new paradigms of analog quantum computing based on these effects.
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near term. Adiabatic quantum computing, quantum annealing, computation by a continuous-time quantum walk, and special purpose quantum simulators all use this strategy. In this work, we carry out a detailed examination of adiabatic and quantum-walk implementation of the quantum search algorithm, using the more physically realistic hypercube connectivity, rather than the complete graph, for our base Hamiltonian. We calculate optimal adiabatic schedules both analytically and numerically for the hypercube and then interpolate between adiabatic and quantum-walk searching, obtaining a family of hybrid algorithms. We show that all of these hybrid algorithms provide the quadratic quantum speedup when run with optimal parameter settings, which we determine and discuss in detail. We incorporate the effects of multiple runs of the same algorithm, noise applied to the qubits, and two types of problem misspecification, determining the optimal hybrid algorithm for each case. Our results reveal a rich structure of how these different computational mechanisms operate and should be balanced in different scenarios. For large systems with low noise and good control, a quantum walk is the best choice, while hybrid strategies can mitigate the effects of many shortcomings in hardware and problem misspecification.
Decoherence in quantum searches, and in the Grover search, in particular, has already been extensively studied, leading very quickly to the loss of the quadratic speedup over the classical case, when searching for some target (marked) element within a set of size NNN. The noise models used were, however, almost always global. In this paper, we study Grover search under the influence of localized partially dephasing noise of rate ppp. We find that, in the case when the size kkk of the affected subspace is much smaller than NNN and the target is unaffected by the noise, namely when $kp\ensuremath{\ll}\sqrt{N}$, the quadratic speedup is retained. Once these restrictions are not met, the quadratic speedup is lost. If the target is affected by the noise, the noise rate needs to scale as 1/N1/\sqrt{N}1/N​ to keep the speedup. We also observe an intermediate region, where if $k\ensuremath{\sim}{N}^{\ensuremath{\mu}}$ and the target is unaffected, the speedup seems to obey ${N}^{\ensuremath{\mu}}$, which for $\ensuremath{\mu}>0.5$ is worse than the quantum, but better than the classical case. We also put obtained results for quantum searches into perspective of quantum walks and searches on graphs.