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IEEE International Conference on Quantum Computing and Engineering (QCE)

Quantum Annealing Error Mitigation Using Mirror Symmetries on Different Generations of Quantum Annealers

Bhavika Bhalgamiya, Dilina Perera, M. A. Novotny

Published Sep 1, 2022• 1 citation
Publisher

Abstract

We present an effective method of error mitigation on adiabatic quantum annealing machines. This method involves a mirror symmetric property of the adiabatic quantum device underlying graph. The methodology is tested on different generations of D-Wave annealing devices. An initial Hamiltonian is formed with two mirror- symmetric graphs k = k′, coupled with either ferromagnetic (M > 0) or antiferromagnetic (M < 0) graph edges, and then implemented on the underlying D-Wave Chimera graph. Examining the returned solution states at the end of annealing process, allows one to discard returned states that are not the ground state of the problem Hamiltonian. The approach is applicable to any quantum adiabatic device. We used the method to compare the performances of different generations of adiabatic devices.

DOI
10.1109/qce53715.2022.00140

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We present an effective method of error mitigation on adiabatic quantum annealing machines. This method involves a mirror symmetric property of the adiabatic quantum device underlying graph. The methodology is tested on different generations of D-Wave annealing devices. An initial Hamiltonian is formed with two mirror- symmetric graphs k = k′, coupled with either ferromagnetic (M > 0) or antiferromagnetic (M < 0) graph edges, and then implemented on the underlying D-Wave Chimera graph. Examining the returned solution states at the end of annealing process, allows one to discard returned states that are not the ground state of the problem Hamiltonian. The approach is applicable to any quantum adiabatic device. We used the method to compare the performances of different generations of adiabatic devices.
We present a generic approach for checking the validity of the solutions returned by quantum annealing devices to aid in the analysis of whether the solution is the true ground state of the desired problem. The underlying principle is to embed a mirrored graph G' of the original graph G, and connect the two graphs via strong ferromagnetic/antiferromagnetic couplings that span across the mirror plane. This allows one to dismiss solutions that do not agree with the underlying mirror symmetry inherent to the true ground state of the composite graph. Using a 1000 qubit D-Wave 2X device, we demonstrate this method by applying it to spin glass problems defined on the device's native Chimera architecture.
Quantum annealers like those from D-Wave Systems implement adiabatic quantum computing to solve optimization problems, but their analog nature and limited control functionalities present challenges to correcting or mitigating errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing. In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is suited for available noisy intermediate-scale quantum (NISQ) annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being compatible with a much wider range of hardware connectivity patterns. In comparisons against standard quantum annealing without error mitigation, RBM consistently improves the energies and ground state probabilities across parameterized problem sets.
Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.
Quantum annealing (QA) is one of the methods to prepare a ground state of a problem Hamiltonian. In the absence of noise, QA can accurately estimate the ground-state energy if the adiabatic condition is satisfied. However, in practice, systems are known to suffer from decoherence. Meanwhile, considerable research effort has been devoted to noisy intermediate-scale quantum (NISQ) computation. For practical NISQ computation, many error-mitigation (EM) methods have been proposed to mitigate the effects of noise. This paper proposes a QA strategy combined with an EM method, namely, dual-state purification, to suppress the effects of decoherence. Our protocol consists of four parts: the conventional dynamics, single-qubit projective measurements, the Hamiltonian dynamics corresponding to an inverse map of the first dynamics, and postprocessing of the measurement results. Importantly, our protocol works without two-qubit gates that require pulse operations; hence, it is suitable for devices designed for practical QA. In addition, we present numerical calculations to show that our protocol is more accurate than the conventional QA in estimating the ground-state energy under decoherence.
Abstract We present a general error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. Given any Ising model optimization problem, the encoding replaces each logical qubit by a complete graph of degree C, representing the distance of the error-correcting code. A subsequent minor-embedding step then implements the encoding on the underlying hardware graph of the quantum annealer. We demonstrate experimentally that the performance of a D-Wave Two quantum annealing device improves as C grows. We show that the performance improvement can be interpreted as arising from an effective increase in the energy scale of the problem Hamiltonian or, equivalently, an effective reduction in the temperature at which the device operates. The number C thus allows us to control the amount of protection against thermal and control errors, and, in particular, to trade qubits for a lower effective temperature that scales as C−η, with η⩽2. This effective temperature reduction is an important step towards scalable quantum annealing.
Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a key challenge in QA. The choice of the drive Hamiltonian is known to affect the performance of QA because of the possible suppression of non-adiabatic transitions. Here, we propose the use of a drive Hamiltonian that preserves the symmetry of the problem Hamiltonian for more efficient QA. Owing to our choice of the drive Hamiltonian, the solution is searched in an appropriate symmetric subspace during QA. As non-adiabatic transitions occur only inside the specific subspace, our approach can potentially suppress unwanted non-adiabatic transitions. To evaluate the performance of our scheme, we employ the XY model as the drive Hamiltonian in order to find the ground state of problem Hamiltonians that commute with the total magnetization along the zzz axis. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.