Variational Quantum Eigensolvers in the Era of Distributed Quantum Computers

Khait, Ilia; Tham, Edwin; Segal, Dvira; Brodutch, Aharon

doi:10.48550/arxiv.2302.14067

Cited by 3 publications

(3 citation statements)

References 38 publications

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“…by landing in a local minimum or stalling in a barren plateau. A balance should be struck between these complications: the first error source can be mitigated by considering larger fragments with a larger number of auxiliary qubits or possibly by limiting the number of inter-fragment unitaries, as done in [102], while the second can be mitigated by considering smaller fragments with fewer circuit parameters.…”

Section: Solving Maxcut With Mean-field Termsmentioning

confidence: 99%

Near-term distributed quantum computation using mean-field corrections and auxiliary qubits

McClain Gomez,

Patti,

Anandkumar

et al. 2024

Quantum Sci. Technol.

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Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such exchange of quantum information itself poses unique engineering challenges, requiring high gate fidelity and costly non-local operations. To mitigate this, we propose near-term distributed quantum computing, focusing on approximate approaches that involve limited information transfer and conservative entanglement production. We first devise an approximate distributed computing scheme for the time evolution of quantum systems split across any combination of classical and quantum devices. Our procedure harnesses mean-field corrections and auxiliary qubits to link two or more devices classically, optimally encoding the auxiliary qubits to both minimize short-time evolution error and extend the approximate scheme's performance to longer evolution times. We then expand the scheme to include limited quantum information transfer through selective qubit shuffling or teleportation, broadening our method's applicability and boosting its performance. Finally, we build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms. To characterize our technique, we introduce a non-linear perturbation theory that discerns the critical role of our mean-field corrections in optimization and may be suitable for analyzing other non-linear quantum techniques. This fragmented pre-training is remarkably successful, reducing algorithmic error by orders of magnitude while requiring fewer iterations.

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Section: Solving Maxcut With Mean-field Termsmentioning

confidence: 99%

Near-term distributed quantum computation using mean-field corrections and auxiliary qubits

McClain Gomez,

Patti,

Anandkumar

et al. 2024

Quantum Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…We are working in the noisy intermediate-scale quantum (NISQ) era [10]. One class of algorithms that is expected to unlock the computational potential of NISQ devices is variational quantum algorithms (VQAs) [11][12][13] as they only require the implementation of shallow circuits and simple measurements. Two of representative VQAs are the variations quantum eigensolver (VQE) which is a hybrid algorithm to approximate the ground state eigenvalues for chemical systems [14,15] and the quantum approximate optimization algorithm (QAOA) for finding an approximate solution of an optimization problem [4,16].…”

Section: Introductionmentioning

confidence: 99%

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Zhang,

Qin,

Zhou

et al. 2024

New J. Phys.

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Variational quantum algorithms (VQAs) are among the most promising algorithms to achieve quantum advantages in the NISQ era. One important challenge in implementing such algorithms is to construct an effective parameterized quantum circuit (also called an ansatz). In this work, we propose a single entanglement connection architecture (SECA) for a bipartite hardware-efficient ansatz (HEA) by balancing its expressibility, entangling capability, and trainability. Numerical simulations with a one-dimensional Heisenberg model and quadratic unconstrained binary optimization (QUBO) issues were conducted. Our results indicate the superiority of SECA over the common full entanglement connection architecture (FECA) in terms of computational performance. Furthermore, combining SECA with gate-cutting technology to construct distributed quantum computation (DQC) can efficiently expand the size of NISQ devices under low overhead. We also demonstrated the effectiveness and scalability of the DQC scheme. Our study is a useful indication for understanding the characteristics associated with an effective training circuit.

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“…CI assumes that measurement errors between distant qubits are uncorrelated. This assumption is especially relevant for quantum devices with limited connectivity among physical qubits, such as those constrained by nearest-neighbor couplings [26] or employing distributed modular architectures [27][28][29][30][31]. By incorporating this assumption, we are able to exponentially reduce the size of neural networks used for QMEM.…”

Section: Introductionmentioning

confidence: 99%

Scalable quantum measurement error mitigation via conditional independence and transfer learning

Lee,

Park

2023

Mach. Learn.: Sci. Technol.

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Mitigating measurement errors in quantum systems without relying on quantum error correction is of critical importance for the practical development of quantum technology. Deep learning-based quantum measurement error mitigation (QMEM) has exhibited advantages over the linear inversion method due to its capability to correct non-linear noise. However, scalability remains a challenge for both methods. In this study, we propose a scalable QMEM method that leverages the conditional independence (CI) of distant qubits and incorporates transfer learning (TL) techniques. By leveraging the CI assumption, we achieve an exponential reduction in the size of neural networks used for error mitigation. This enhancement also offers the benefit of reducing the number of training data needed for the machine learning model to successfully converge. Additionally, incorporating TL provides a constant speedup. We validate the effectiveness of our approach through experiments conducted on IBM quantum devices with 7 and 13 qubits, demonstrating excellent error mitigation performance and highlighting the efficiency of our method.

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Variational Quantum Eigensolvers in the Era of Distributed Quantum Computers

Cited by 3 publications

References 38 publications

Near-term distributed quantum computation using mean-field corrections and auxiliary qubits

Near-term distributed quantum computation using mean-field corrections and auxiliary qubits

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Scalable quantum measurement error mitigation via conditional independence and transfer learning

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