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EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

Ramin Ayanzadeh, Poulami Das, Swamit Tannu, Moinuddin K. Qureshi

Published Mar 2, 2022• 2 citations
Publisher

Abstract

Abstract Quantum Annealers (QAs) are single-instruction quantum machines that can only sample from the ground state of an energy function, called Hamiltonian. To execute a program, the problem is cast to a Hamiltonian, embedded on the hardware, and a single quantum machine instruction (QMI) is run. Noise and imperfections in hardware result in sub-optimal solutions on QAs even if the QMI is run for thousands of trials. Owing to the limited programmability of QAs, users execute the same QMI for all trials. This subjects all trials to a similar noise profile throughout the execution, resulting in a systematic bias. We observe that systematic bias leads to sub-optimal solutions and cannot be alleviated by executing more trials or using existing error-mitigation schemes. To address this challenge, we propose EQUAL (Ensemble QUantum AnneaLing). EQUAL generates an ensemble of QMIs by adding controlled perturbations to the program QMI. When executed on the QA, the ensemble of QMIs steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions. Our evaluations using the D-Wave 2000Q machine show that EQUAL bridges the difference between the baseline and the ideal by an average of 14% (and up to 26%), without requiring any additional trials. EQUAL can be combined with existing error mitigation schemes to bridge further the difference between the baseline and ideal by an average of 55% (and up to 68%).

DOI
10.21203/rs.3.rs-1343360/v1

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EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

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Abstract Quantum Annealers (QAs) are single-instruction quantum machines that can only sample from the ground state of an energy function, called Hamiltonian. To execute a program, the problem is cast to a Hamiltonian, embedded on the hardware, and a single quantum machine instruction (QMI) is run. Noise and imperfections in hardware result in sub-optimal solutions on QAs even if the QMI is run for thousands of trials. Owing to the limited programmability of QAs, users execute the same QMI for all trials. This subjects all trials to a similar noise profile throughout the execution, resulting in a systematic bias. We observe that systematic bias leads to sub-optimal solutions and cannot be alleviated by executing more trials or using existing error-mitigation schemes. To address this challenge, we propose EQUAL (Ensemble QUantum AnneaLing). EQUAL generates an ensemble of QMIs by adding controlled perturbations to the program QMI. When executed on the QA, the ensemble of QMIs steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions. Our evaluations using the D-Wave 2000Q machine show that EQUAL bridges the difference between the baseline and the ideal by an average of 14% (and up to 26%), without requiring any additional trials. EQUAL can be combined with existing error mitigation schemes to bridge further the difference between the baseline and ideal by an average of 55% (and up to 68%).
Quantum computing is an information processing paradigm that uses quantum-mechanical properties to speedup computationally hard problems. Gate-based quantum computers and Quantum Annealers (QAs) are two commercially available hardware platforms that are accessible to users today. Although promising, existing gate-based quantum computers consist of only a few dozen qubits and are not large enough for most applications. On the other hand, existing QAs with few thousand qubits have the potential to solve some domain-specific optimization problems. QAs are single instruction machines and to execute a program, the problem is cast to a Hamiltonian, embedded in the hardware, and a single quantum machine instruction (QMI) is run. Unfortunately, noise and imperfections in hardware result in sub-optimal solutions on QAs even if the QMI is run for thousands of trials.Due to the limited programmability of QAs users execute the same QMI for all trials. This subjects all trials to a similar noise profile throughout the execution, resulting in a systematic bias. We observe that systematic bias leads to sub-optimal solutions and cannot be alleviated by executing more trials or using existing error-mitigation schemes. To address this challenge, we propose EQUAL (Ensemble QUantum AnneaLing). EQUAL generates an ensemble of QMIs by adding controlled perturbations to the program QMI. When executed on the QA, the ensemble of QMIs steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions. Our evaluations using the 2041-qubit D-Wave QA show that EQUAL bridges the difference between the baseline and the ideal by an average of 14% (and up to 26%) without requiring any additional trials. EQUAL can be combined with existing error mitigation schemes to further bridge the difference between the baseline and ideal by an average of 55% (and up to 68%).
Quantum computing is an information processing paradigm that uses quantum-mechanical properties to speedup computationally hard problems. Although promising, existing gate-based quantum computers consist of only a few dozen qubits and are not large enough for most applications. On the other hand, existing QAs with few thousand of qubits have the potential to solve some domain-specific optimization problems. QAs are single instruction machines and to execute a program, the problem is cast to a Hamiltonian, embedded on the hardware, and a single quantum machine instruction (QMI) is run. Unfortunately, noise and imperfections in hardware result in sub-optimal solutions on QAs even if the QMI is run for thousands of trials. The limited programmability of QAs mean that the user executes the same QMI for all trials. This subjects all trials to a similar noise profile throughout the execution, resulting in a systematic bias. We observe that systematic bias leads to sub-optimal solutions and cannot be alleviated by executing more trials or using existing error-mitigation schemes. To address this challenge, we propose EQUAL (Ensemble Quantum Annealing). EQUAL generates an ensemble of QMIs by adding controlled perturbations to the program QMI. When executed on the QA, the ensemble of QMIs steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions. Our evaluations using the 2041-qubit D-Wave QA show that EQUAL bridges the difference between the baseline and the ideal by an average of 14% (and up to 26%), without requiring any additional trials. EQUAL can be combined with existing error mitigation schemes to further bridge the difference between the baseline and ideal by an average of 55% (and up to 68%).
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.
We leverage the idea of a statistical ensemble to improve the quality of quantum annealing based binary compressive sensing. Since executing quantum machine instructions on a quantum annealer can result in an excited state, rather than the ground state of the given Hamiltonian, we use different penalty parameters to generate multiple distinct quadratic unconstrained binary optimization (QUBO) functions whose ground state(s) represent a potential solution of the original problem. We then employ the attained samples from minimizing all corresponding (different) QUBOs to estimate the solution of the problem of binary compressive sensing. Our experiments, on a D-Wave 2000Q quantum processor, demonstrated that the proposed ensemble scheme is notably less sensitive to the calibration of the penalty parameter that controls the trade-off between the feasibility and sparsity of recoveries.
We leverage the idea of a statistical ensemble to improve the quality of quantum annealing based binary compressive sensing. Since executing quantum machine instructions on a quantum annealer can result in an excited state, rather than the ground state of the given Hamiltonian, we use different penalty parameters to generate multiple distinct quadratic unconstrained binary optimization (QUBO) functions whose ground state(s) represent a potential solution of the original problem. We then employ the attained samples from minimizing all corresponding (different) QUBOs to estimate the solution of the problem of binary compressive sensing. Our experiments, on a D-Wave 2000Q quantum processor, demonstrated that the proposed ensemble scheme is notably less sensitive to the calibration of the penalty parameter that controls the trade-off between the feasibility and sparsity of recoveries.
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.