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

AIP conference proceedings

Adiabatic quantum computation with spin ensembles

Naeimeh Mohseni, Marek Narożniak, Alexey N. Pyrkov, Valentin Ivannikov, Jonathan P. Dowling, Tim Byrnes

Published Jan 1, 2020• 0 citations
Publisher

Abstract

In the standard approach to adiabatic quantum computing (AQC), quantum information stored on qubits are adia- batically evolved to find the lowest energy state of a problem Hamiltonian. Here we investigate a variation of AQC where spin ensembles are used in place of qubits. The use of ensembles duplicates the quantum information, and allows errors to be suppressed during the adiabatic evolution. We show that there are two distinct types of problem Hamiltonians under this mapping, where the first excited state is a single particle perturbation on the ground state (Type I); or a macroscopically distinct fully polarized state (Type II). For Type I problems, we find that the minimum gap for large ensembles is well predicted by mean-field theory and the AQC performance improves with ensemble size, realizing error-suppression. For Type II problems, the performance of the AQC is mixed, and the gap can increase or decrease with ensemble size depending on the problem instance. The incidences of the Type II problems are greatly suppressed with ensemble size, and consequently for randomly chosen problem instances the success probability of the scheme improves with the ensemble size. Our approach shows that it is possible to perform AQC without the necessity of controlling individual qubits, which allows for an alternative route towards implementing AQC.

DOI
10.1063/5.0011393

Related papers

Error suppression in adiabatic quantum computing with qubit ensembles

Naeimeh Mohseni, Marek Narożniak, Alexey N. Pyrkov +3 more

Abstract Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size Nc where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than Nc, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.

arXiv:1909.09947•npj Quantum Information•May 10, 2021•18 citations

An Alternative Approach to Construct the Initial Hamiltonian of the Adiabatic Quantum Computation

Qian-Heng Duan, Shuo Zhang, Wei Wu +1 more

The adiabatic quantum computation (AQC) has been proven to be equivalent to the standard circuit model. Conventionally, AQC evolves from the initial Hamiltonian which has a uniform equal superposition of the computational basis to the final Hamiltonian whose ground state encodes the solution to a computation problem. We propose an alternative approach to construct the initial Hamiltonian of the AQC which has an unequal superposition of the possible solutions to the problem and show that an educated guess can improve the performance of AQC.

Chinese Physics Letters•Jan 1, 2013•18 citations

Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics

Mohan Sarovar, Kevin C Young

While adiabatic quantum computing (AQC) has some robustness to noise and decoherence, it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have established at least two different techniques for error suppression in AQC. In this paper we derive a model for describing the dynamics of encoded AQC and show that previous constructions for error suppression can be unified with this dynamical model. In addition, the model clarifies the mechanisms of error suppression and allows the identification of its weaknesses. In the second half of the paper, we utilize our description of non-equilibrium dynamics in encoded AQC to construct methods for error correction in AQC by cooling local degrees of freedom (qubits). While this is shown to be possible in principle, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, we use our dynamical model to perform a simplified thermal stability analysis of concatenated-stabilizer-code encoded many-body systems for AQC or quantum memories. This work is a companion paper to 'Error suppression and error correction in adiabatic quantum computation: techniques and challenges (2013 Phys. Rev. X 3 041013)', which provides a quantum information perspective on the techniques and limitations of error suppression and correction in AQC. In this paper we couch the same results within a dynamical framework, which allows for a detailed analysis of the non-equilibrium dynamics of error suppression and correction in encoded AQC.

arXiv:1307.5892•New Journal of Physics•Dec 31, 2013•46 citations

A study of heuristic guesses for adiabatic quantum computation

Alejandro Perdomo‐Ortiz, Salvador Elías Venegas-Andraca, Alán Aspuru‐Guzik

Adiabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial Hamiltonians conventionally have a uniform superposition as ground state. We diverge from this practice by introducing a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem. With this goal in mind, we explain the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7 bit random instances of the satisfiability problem (3-SAT), we show how this heuristic approach is possible and we identify that the performance of the particular algorithm proposed is largely determined by the Hamming distance of the chosen initial guess state with respect to the solution. Besides the possibility of introducing educated guesses as initial states, the new strategy allows for the possibility of restarting a failed adiabatic process from the measured excited state as opposed to restarting from the full superposition of states as in CAQC. The outcome of the measurement can be used as a more refined guess state to restart the adiabatic evolution. This concatenated restart process is another heuristic that the CAQC strategy cannot capture.

arXiv:0807.0354•Jul 2, 2008•2 citations

Adiabatic Quantum Computation With Flux Qubits, First Experimental Results

S. H. W. van der Ploeg, A. Izmalkov, M. Grajcar +10 more

Controllable adiabatic evolution of a multi-qubit system can be used for adiabatic quantum computation (AQC). This evolution ends at a configuration where the Hamiltonian of the system encodes the solution of the problem to be solved. As a first steps towards realization of AQC we have investigated two, three and four flux qubit systems. These systems were characterized by making use of a radio-frequency method. We designed two-qubit systems with coupling energies up to several kelvins. For the three-flux-qubit systems we determined the complete ground-state flux diagram in the three dimensional flux space around the qubits common degeneracy point. We show that the system's Hamiltonian can be completely reconstructed from our measurements. Our concept for the implementation of AQC, by making use of flux qubits, is discussed.

arXiv:cond-mat/0702580•IEEE Transactions on Applied Superconductivity•Jun 1, 2007•16 citations

Quasi-Adiabatic Quantum Computing Treated with c-Numbers Using the Local-Field Response

Tatsuya Tomaru

A computational method called the local-field response method is proposed, where spins evolve by responding to an effective field consisting of gradually decreasing external fields and spin–spin interactions, similarly to what is carried out in adiabatic quantum computing (AQC). This method is partly quantum–mechanical. That is, spins are treated as classical variables, but the response function of the spins to the effective field is determined a priori by referring to a quantum–mechanical calculation that was carried out for similar problems. This novel response function improves the performance of the ground state being maintained in the time evolution compared with the case without a priori information. The performance is numerically checked in an eight-qubit system by solving random-interaction problems of finding their ground states. The false probability decreases by about half as a result of using a priori information. The operation of this method is classical, but it has a quantum–mechanical advantage through a priori information. This method is practically useful because obtaining a complete quantum system is difficult as it stands.

Journal of the Physical Society of Japan•Feb 10, 2016•3 citations
In the standard approach to adiabatic quantum computing (AQC), quantum information stored on qubits are adia- batically evolved to find the lowest energy state of a problem Hamiltonian. Here we investigate a variation of AQC where spin ensembles are used in place of qubits. The use of ensembles duplicates the quantum information, and allows errors to be suppressed during the adiabatic evolution. We show that there are two distinct types of problem Hamiltonians under this mapping, where the first excited state is a single particle perturbation on the ground state (Type I); or a macroscopically distinct fully polarized state (Type II). For Type I problems, we find that the minimum gap for large ensembles is well predicted by mean-field theory and the AQC performance improves with ensemble size, realizing error-suppression. For Type II problems, the performance of the AQC is mixed, and the gap can increase or decrease with ensemble size depending on the problem instance. The incidences of the Type II problems are greatly suppressed with ensemble size, and consequently for randomly chosen problem instances the success probability of the scheme improves with the ensemble size. Our approach shows that it is possible to perform AQC without the necessity of controlling individual qubits, which allows for an alternative route towards implementing AQC.
Abstract Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size Nc where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than Nc, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.
The adiabatic quantum computation (AQC) has been proven to be equivalent to the standard circuit model. Conventionally, AQC evolves from the initial Hamiltonian which has a uniform equal superposition of the computational basis to the final Hamiltonian whose ground state encodes the solution to a computation problem. We propose an alternative approach to construct the initial Hamiltonian of the AQC which has an unequal superposition of the possible solutions to the problem and show that an educated guess can improve the performance of AQC.
While adiabatic quantum computing (AQC) has some robustness to noise and decoherence, it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have established at least two different techniques for error suppression in AQC. In this paper we derive a model for describing the dynamics of encoded AQC and show that previous constructions for error suppression can be unified with this dynamical model. In addition, the model clarifies the mechanisms of error suppression and allows the identification of its weaknesses. In the second half of the paper, we utilize our description of non-equilibrium dynamics in encoded AQC to construct methods for error correction in AQC by cooling local degrees of freedom (qubits). While this is shown to be possible in principle, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, we use our dynamical model to perform a simplified thermal stability analysis of concatenated-stabilizer-code encoded many-body systems for AQC or quantum memories. This work is a companion paper to 'Error suppression and error correction in adiabatic quantum computation: techniques and challenges (2013 Phys. Rev. X 3 041013)', which provides a quantum information perspective on the techniques and limitations of error suppression and correction in AQC. In this paper we couch the same results within a dynamical framework, which allows for a detailed analysis of the non-equilibrium dynamics of error suppression and correction in encoded AQC.
Adiabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial Hamiltonians conventionally have a uniform superposition as ground state. We diverge from this practice by introducing a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem. With this goal in mind, we explain the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7 bit random instances of the satisfiability problem (3-SAT), we show how this heuristic approach is possible and we identify that the performance of the particular algorithm proposed is largely determined by the Hamming distance of the chosen initial guess state with respect to the solution. Besides the possibility of introducing educated guesses as initial states, the new strategy allows for the possibility of restarting a failed adiabatic process from the measured excited state as opposed to restarting from the full superposition of states as in CAQC. The outcome of the measurement can be used as a more refined guess state to restart the adiabatic evolution. This concatenated restart process is another heuristic that the CAQC strategy cannot capture.
Controllable adiabatic evolution of a multi-qubit system can be used for adiabatic quantum computation (AQC). This evolution ends at a configuration where the Hamiltonian of the system encodes the solution of the problem to be solved. As a first steps towards realization of AQC we have investigated two, three and four flux qubit systems. These systems were characterized by making use of a radio-frequency method. We designed two-qubit systems with coupling energies up to several kelvins. For the three-flux-qubit systems we determined the complete ground-state flux diagram in the three dimensional flux space around the qubits common degeneracy point. We show that the system's Hamiltonian can be completely reconstructed from our measurements. Our concept for the implementation of AQC, by making use of flux qubits, is discussed.
A computational method called the local-field response method is proposed, where spins evolve by responding to an effective field consisting of gradually decreasing external fields and spin–spin interactions, similarly to what is carried out in adiabatic quantum computing (AQC). This method is partly quantum–mechanical. That is, spins are treated as classical variables, but the response function of the spins to the effective field is determined a priori by referring to a quantum–mechanical calculation that was carried out for similar problems. This novel response function improves the performance of the ground state being maintained in the time evolution compared with the case without a priori information. The performance is numerically checked in an eight-qubit system by solving random-interaction problems of finding their ground states. The false probability decreases by about half as a result of using a priori information. The operation of this method is classical, but it has a quantum–mechanical advantage through a priori information. This method is practically useful because obtaining a complete quantum system is difficult as it stands.