Accurately computing the electronic properties of a quantum ring

Neill, C.; McCourt, Trevor; Mi, Xiao; Zhang, Jiang; Niu, Murphy Yuezhen; Mruczkiewicz, Wojciech; Aleǐner, I. L.; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C.; Barends, R.; Bengtsson, Andreas; Bourassa, Alexandre; Broughton, Michael; Buckley, Bob B.; Buell, David A.; Burkett, Brian; Bushnell, Nicholas; Campero, Juan; Chen, Z.; Chiaro, Benjamin; Collins, Roberto; Courtney, William; Demura, Sean; Derk, Alan R.; Dunsworth, A.; Eppens, Daniel; Erickson, Catherine; Farhi, Edward; Fowler, Austin G.; Foxen, Brooks; Gidney, Craig; Giustina, Marissa; Gross, Jonathan A.; Harrigan, Matthew P.; Harrington, Sean D.; Hilton, Jeremy; Ho, Alan; Hong, Sabrina; Huang, Trent; Huggins, William J.; Isakov, Sergei V.; Jacob-Mitos, M.; Jeffrey, E.; Jones, Cody; Kafri, Dvir; Kechedzhi, Kostyantyn; Kelly, J.; Kim, S.; Klimov, Paul V.; Korotkov, Alexander N.; Kostritsa, Fedor; Landhuis, David; Laptev, Pavel; Lucero, Erik; Martin, Orion; McClean, Jarrod R.; McEwen, Matt; Megrant, A.; Miao, Kevin C.; Mohseni, Masoud; Mutus, J.; Naaman, Ofer; Neeley, M.; Newman, Michael; O’Brien, Thomas E.; Opremcak, Alex; Ostby, Eric; Pató, Bálint; Petukhov, A.; Quintana, Chris; Redd, Nicholas; Rubin, Nicholas C.; Sank, D.; Satzinger, Kevin J.; Shvarts, Vladimir; Strain, Doug; Szalay, Marco; Trevithick, Matthew D.; Villalonga, Benjamin; White, Theodore C.; Yao, Z. Jamie; Yeh, P.; Zalcman, Adam; Neven, Hartmut; Boixo, Sergio; Ioffe, L. B.; Roushan, P.; Chen, Y.; Smelyanskiy, Vadim

doi:10.1038/s41586-021-03576-2

Cited by 61 publications

(48 citation statements)

References 25 publications

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“…In this work we have evaluated the use of a Loschmidt Echo diagnostic on a specific selection of circuits employing only readout error mitigation, and so the optimal qubit assignments determined in this work may not remain optimal when employing platform-specific error mitigation. In particular, control errors which may go undetected by (see Appendix A 2 b) can be mitigated using Floquet Calibration [55], thereby strengthening the relationship between F LE and F . Therefore such devicespecific calibration procedures should be combined with qubit assignment based on F LE to maximize the final assignment performance.…”

Section: Discussionmentioning

confidence: 99%

Qubit assignment using time reversal

Peters,

Shyamsundar,

et al. 2022

Preprint

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As the number of qubits available on noisy quantum computers grows, it will become necessary to efficiently select a subset of physical qubits to use in a quantum computation. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while relying on standard device benchmarks provides incomplete information about the performance of any specific program. Furthermore, the number of possible assignments grows combinatorially in the number of qubits on the device and in the program, motivating the use of heuristic optimization techniques. We approach this problem using simulated annealing with a cost function based on the Loschmidt Echo, a diagnostic that measures the reversibility of a quantum process. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal qubit assignment based on state fidelity in the weak error limit, and we provide experimental justification using diagnostics performed on Google's superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices as well as optimization experiments performed on a quantum processor. Our results demonstrate that the use of Loschmidt Echoes and simulated annealing provides a scalable and flexible approach to optimizing qubit assignment on near-term hardware.

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Section: Discussionmentioning

confidence: 99%

Qubit assignment using time reversal

Peters,

Shyamsundar,

et al. 2022

Preprint

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“…This obstacle has motivated many materials scientists to consider quantum computation, which enables extensions to the the band structure approach which more accurately account for electron-electron interactions. The literature is full of distinct algorithms which treat periodic systems, including hybrid quantum-classical DMFT, [1][2][3][4] cyclic qubit arrays, 5 and "holographic" VQE. 6 Other methods developed for quantum chemistry are also readily applied to periodic systems expanded in a basis of plane waves 7 or Bloch atomic orbitals.…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for band structures with local tight-binding orbitals

Sherbert

Jayaraj

Nardelli

2022

Preprint

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While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum ``toolbox''. With this in mind, we consider the quantum calculation of a periodic system's single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire band-structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.

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“…Application of VQAs to the tight-binding Hamiltonian in absence of electron-electron correlations was studied 19 and experimentally demonstrated with 18 qubits. 20 Modifications to Unitary Coupled Cluster Singles and Doubles (UCCSD) variational ansatz to incorporate periodic boundary conditions 21 and orbital optimization 22 were examined. The UCCSD method adapted for periodic boundary conditions was used together with translational Quantum Subspace expansion methods.…”

Section: Introductionmentioning

confidence: 99%