Algorithmic Shadow Spectroscopy

Chan, Hans Hon Sang; Meister, Richard; Goh, Matthew L.; Koczor, Bálint

doi:10.48550/arxiv.2212.11036

Cited by 6 publications

(9 citation statements)

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“…Classical shadows, a scheme introduced in [9] based on the shadow tomography proposal [48], can predict many properties of a quantum system from very few measurements. Since its publication, various flavors [12][13][14] and applications to hybrid quantum-classical algorithms have been developed [10,49,50]. QC-AFQMC provides a natural application of the classical shadow framework when one has only limited quantum resources because the algorithm requires the calculation of many observables of the same state in the form of overlaps of the quantum trial wavefunction and classically computed walker states ⟨Ψ T |ϕ z ⟩.…”

Section: Classical Shadowsmentioning

confidence: 99%

Classical and quantum cost of measurement strategies for quantum-enhanced auxiliary field quantum Monte Carlo

Kiser,

Schroeder,

Anselmetti

et al. 2024

New J. Phys.

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Quantum-enhanced auxiliary field quantum Monte Carlo (QC-AFQMC) uses output from a quantum computer to increase the accuracy of its classical counterpart. The algorithm requires the estimation of overlaps between walker states and a trial wavefunction prepared on the quantum computer. We study the applicability of this algorithm in terms of the number of measurements required from the quantum computer and the classical costs of post-processing those measurements. We compare the classical post-processing costs of state-of-the-art measurement schemes using classical shadows to determine the overlaps and argue that the overall post-processing cost stemming from overlap estimations scales like $\mathcal{O}(N^9)$ per walker throughout the algorithm. With further numerical simulations, we compare the variance behavior of the classical shadows when randomizing over different ensembles, e.g., Cliffords and (particle-number restricted) matchgates beyond their respective bounds, and uncover the existence of covariances between overlap estimations of the AFQMC walkers at different imaginary time steps. Moreover, we include analyses of how the error in the overlap estimation propagates into the AFQMC energy and discuss its scaling when increasing the system size.

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Section: Classical Shadowsmentioning

confidence: 99%

Classical and quantum cost of measurement strategies for quantum-enhanced auxiliary field quantum Monte Carlo

Kiser,

Schroeder,

Anselmetti

et al. 2024

New J. Phys.

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“…As the method of ref 12 generates the exact TDDFT potential, one could also use real-time TDDFT to calculate excitation energies. Although in this case, it may be better to directly perform the Fourier transform on the measured densities, 66 after applying a perturbing potential, this will have the same (1/ ) evolution time requirements as QPE. One could also use the modified Sternheimer method 67 using the inverted V KS potential, but this will generally not be chemically accurate.…”

Section: Regime Of Algorithm Advantagementioning

confidence: 99%

Calculating Potential Energy Surfaces with Quantum Computers by Measuring Only the Density Along Adiabatic Transitions

Brown

2024

J. Chem. Theory Comput.

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We show that chemically accurate potential energy surfaces (PESs) can be generated from quantum computers by measuring only the density along an adiabatic transition between different molecular geometries. In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted real-space time-dependent density functional theory Kohn− Sham (KS) potential obtained from the geometry-varying densities of the full wave function. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process (which is theoretically exact but can be numerically unstable), whereas the total evolution time is the defining factor for the precision of phase estimation. We examine the method with a one-dimensional system of two electrons for both the ground and first triplet states in first quantization, as well as the ground state of three-and four-electron systems in second quantization. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve, with a shorter propagation time than may be required using phase estimation for a similar accuracy. We also show that an accurate potential energy curve can be calculated by making many imprecise density measurements (using a few shots) along the time evolution and smoothing the resulting density evolution. Finally, it is important to note that the method is able to classically provide a check of its own accuracy by comparing the density resulting from a time-independent KS calculation using the inverted potential with the measured density. This can be used to determine whether longer adiabatic evolution times are required to satisfy the adiabatic theorem.

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“…Consequently, appropriate measurement cost reduction schemes − can substantially lower the overhead due to the 3-body terms. Additionally, one can ameliorate the quantum computing measurement cost problem with approaches like informationally complete positive operator-valued measures − classical shadows or shadow spectroscopy …”

Section: Theory and Algorithmsmentioning

confidence: 99%

Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method

Dobrautz,

Sokolov,

Liao

et al. 2024

J. Chem. Theory Comput.

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Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach’s current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today’s quantum hardware.

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Algorithmic Shadow Spectroscopy

Cited by 6 publications

References 0 publications

Classical and quantum cost of measurement strategies for quantum-enhanced auxiliary field quantum Monte Carlo

Classical and quantum cost of measurement strategies for quantum-enhanced auxiliary field quantum Monte Carlo

Calculating Potential Energy Surfaces with Quantum Computers by Measuring Only the Density Along Adiabatic Transitions

Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method

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