Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Love, Peter J.

doi:10.1103/physrevlett.123.200501

Cited by 29 publications

(39 citation statements)

References 83 publications

(159 reference statements)

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“…Then, in Sec. V we show that noncontextual Hamiltonians, defined in [41] (also studied in [42]), are reducible to commuting Hamiltonians under unitary partitioning. We close the paper with discussion and directions for future work.…”

Section: Introductionmentioning

confidence: 91%

“…In Ref. [41], contextuality of a Pauli Hamiltonian is defined as the condition under which it is impossible to consistently assign values to the Pauli terms in the Hamiltonian. Contextuality, if present, is a manifestation of nonclassicality of the Hamiltonian.…”

Section: Noncontextual Hamiltoniansmentioning

confidence: 99%

“…Contextuality, if present, is a manifestation of nonclassicality of the Hamiltonian. Contextuality of a Hamiltonian is determined by the following criterion on the set S of Pauli terms [41]: First, let Z ⊆ S be the set of terms that commute with all other terms, and let T ≡ S \ Z. Then S is noncontextual if and only if commutation is an equivalence relation on T .…”

Section: Noncontextual Hamiltoniansmentioning

confidence: 99%

“…We now show that, using the term reduction technique presented above, we can map any noncontextual Hamiltonian to a commuting Hamiltonian. First, as shown in [41], we can check that the Hamiltonian is noncontextual in O(|S| 3 ) time. Given that the Hamiltonian is noncontextual, we know that it has the structure described above: we can find the cliques C i as well as Z in O(|S| 2 ) time.…”

Section: Noncontextual Hamiltoniansmentioning

confidence: 99%

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Measurement reduction in variational quantum algorithms

et al. 2020

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Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The number of terms can become overwhelmingly large for problems at the scale of NISQ hardware that may soon be available. We use unitary partitioning (developed independently by Izmaylov et al. [J. Chem. Theory Comput. 16, 190 (2020)]) to define variational quantum eigensolver procedures in which additional unitary operations are appended to the ansatz preparation to reduce the number of terms. This approach may be scaled to use all coherent resources available after ansatz preparation. We also study the use of asymmetric qubitization to implement the additional coherent operations with lower circuit depth. Using this technique, we find a constant factor speedup for lattice and random Pauli Hamiltonians. For electronic structure Hamiltonians, we prove that linear term reduction with respect to the number of orbitals, which has been previously observed in numerical studies, is always achievable. For systems represented on 10-30 qubits, we find that there is a reduction in the number of terms by approximately an order of magnitude. Applied to the plane-wave dual-basis representation of fermionic Hamiltonians, however, unitary partitioning offers only a constant factor reduction. Finally, we show that noncontextual Hamiltonians may be reduced to effective commuting Hamiltonians using unitary partitioning.

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Section: Introductionmentioning

confidence: 91%

Section: Noncontextual Hamiltoniansmentioning

confidence: 99%

Section: Noncontextual Hamiltoniansmentioning

confidence: 99%

Section: Noncontextual Hamiltoniansmentioning

confidence: 99%

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Measurement reduction in variational quantum algorithms

et al. 2020

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“…Due to its simplicity, this example has been widely used both experimentally and theoretically [ 8 , 16 , 17 , 18 , 20 , 39 , 41 ]. It was recently shown that this example is in a sense not quantum mechanical, as it lacks measurement contextuality [ 46 ]; however, the simplicity of the system makes it a good candidate for initial studies.…”

Section: Molecular Hydrogenmentioning

confidence: 99%

Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure

Tranter

Love

Mintert

et al. 2019

Entropy

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Trotter-Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error-the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to nd methods of reducing the Trotter error through alternate means.The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, nding an optimal strategy for ordering Trotter sequences is di cult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred.Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We nd that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than kcal/mol.Relative to this, the di ference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising-particularly for systems involving heavy atoms-however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.

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Nothing Will Come of Everything: Software Towers and Quantum Towers

Abramsky

2022

The Frontiers Collection

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Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Cited by 29 publications

References 83 publications

Measurement reduction in variational quantum algorithms

Measurement reduction in variational quantum algorithms

Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure

Nothing Will Come of Everything: Software Towers and Quantum Towers

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