Self-verifying variational quantum simulation of lattice models

Kokail, Christian; Maier, C.; Bijnen, Rick van; Brydges, Tiff; Joshi, Manoj K.; Jurcevic, Petar; Muschik, Christine A.; Silvi, Pietro; Blatt, R.; Roos, C. F.; Zoller, P.

doi:10.1038/s41586-019-1177-4

Cited by 643 publications

(595 citation statements)

References 51 publications

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“…This greatly restricts the number of noncontextual subsets we have to consider, and renders the optimization tractable. We expect this heuristic to give a good approximation to the largest noncontextual subset when the approximate largest noncontextual subsets thus found are of comparable size to the full set of terms: this is the case for the Hamiltonians in [17,21,23]. We also find that for the Hamiltonians in [11,18,20], for which we obtained the exact largest noncontextual subsets, our heuristic approach also finds the exact solutions.…”

Section: Appendix D: Vqe Experiments To Datementioning

confidence: 60%

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Love

2019

Phys. Rev. Lett.

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Contextuality is an indicator of non-classicality, and a resource for various quantum procedures. In this paper, we use contextuality to evaluate the variational quantum eigensolver (VQE), one of the most promising tools for near-term quantum simulation. We present an efficiently computable test to determine whether or not the objective function for a VQE procedure is contextual. We apply this test to evaluate the contextuality of experimental implementations of VQE, and determine that several, but not all, fail this test of quantumness.

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Section: Appendix D: Vqe Experiments To Datementioning

confidence: 60%

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Love

2019

Phys. Rev. Lett.

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“…The condition in (18) implies that the overall channel consisting of global Pauli channels acting on system A during the implementation of  is mathematically equivalent (although physically inequivalent) to a Pauli channel followed by  . Therefore, corollary 1 follows from theorem 1.…”

Section: Noise Resilience Of Full Unitary Matrix Compilingmentioning

confidence: 99%

Noise resilience of variational quantum compiling

et al. 2020

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Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the costevaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

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“…First, a 20‐qubit register has been shown to reliably allow for the creation of multi‐qubit entangled states, thus opening the door to quantum simulations of larger spin systems. The same quantum hardware has been used to show a hybrid quantum‐classical approach to the simulation of the Schwinger model . The latter belongs to the class of variational optimization algorithms commonly employed in quantum chemistry, an approach now commonly defined Variational Quantum Eigensolver (VQE).…”

Section: Experimental Achievements and Prospective Technologiesmentioning

confidence: 99%

“…Using an evolution of the VQE algorithm, nuclear physics quantum simulations have also been reported in superconducting quantum hardware, with the cloud computing of the deuteron binding energy . Along the same lines of trapped ions quantum simulators, a similar quantum classical algorithm has been used to solve for the Schwinger model dynamics on a superconducting quantum hardware …”

Section: Experimental Achievements and Prospective Technologiesmentioning

confidence: 99%

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

et al. 2019

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The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present Review aims at giving a comprehensive outlook on the state‐of‐the‐art capabilities offered from these near‐term noisy devices as universal quantum simulators, that is, programmable quantum computers potentially able to calculate the time evolution of many physical models. First, a pedagogic overview on the basic theoretical background pertaining digital quantum simulations is given, with a focus on hardware‐dependent mapping of spin‐type Hamiltonians into the corresponding quantum circuit as a key initial step toward simulating more complex models. Then, the main experimental achievements obtained in the last decade are reviewed, focusing on the digital quantum simulation of such spin models by employing two leading quantum architectures. Their performances are compared, and future challenges are outlined, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long‐sought quantum advantage for the simulation of complex many‐body models in the physical sciences.

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Self-verifying variational quantum simulation of lattice models

Cited by 643 publications

References 51 publications

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Noise resilience of variational quantum compiling

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

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