16 research outputs found
Partial Syndrome Measurement for Hypergraph Product Codes
Hypergraph product codes are a promising avenue to achieving fault-tolerant
quantum computation with constant overhead. When embedding these and other
constant-rate qLDPC codes into 2D, a significant number of nonlocal connections
are required, posing difficulties for some quantum computing architectures. In
this work, we introduce a fault-tolerance scheme that aims to alleviate the
effects of implementing this nonlocality by measuring generators acting on
spatially distant qubits less frequently than those which do not. We
investigate the performance of a simplified version of this scheme, where the
measured generators are randomly selected. When applied to hypergraph product
codes and a modified small-set-flip decoding algorithm, we prove that for a
sufficiently high percentage of generators being measured, a threshold still
exists. We also find numerical evidence that the logical error rate is
exponentially suppressed even when a large constant fraction of generators are
not measured.Comment: 10 pages, 4 figure
Learning crystal field parameters using convolutional neural networks
We present a deep machine learning algorithm to extract crystal field (CF)
Stevens parameters from thermodynamic data of rare-earth magnetic materials.
The algorithm employs a two-dimensional convolutional neural network (CNN) that
is trained on magnetization, magnetic susceptibility and specific heat data
that is calculated theoretically within the single-ion approximation and
further processed using a standard wavelet transformation. We apply the method
to crystal fields of cubic, hexagonal and tetragonal symmetry and for both
integer and half-integer total angular momentum values of the ground state
multiplet. We evaluate its performance on both theoretically generated
synthetic and previously published experimental data on CeAgSb, PrAgSb
and PrMgCu, and find that it can reliably and accurately extract the CF
parameters for all site symmetries and values of considered. This
demonstrates that CNNs provide an unbiased approach to extracting CF parameters
that avoids tedious multi-parameter fitting procedures.Comment: 19 pages, 9 figure
Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models
We perform a systematic study of preparing ground states of correlated
multi-orbital impurity models using variational quantum eigensolvers (VQEs). We
consider both fixed and adaptive wavefunction ans\"atze and analyze the
resulting gate depths and the performance with and without noise. For the
adaptive procedure, we develop an operator pool consisting of pairwise
commutators of Hamiltonian terms that allows for a fair comparison between the
adaptive and fixed Hamiltonian variational ansatz. Using noiseless statevector
simulations, we find that the most compact ans\"atze are obtained in an atomic
orbital representation and using parity encoding. Focusing on the adaptive
algorithms, which yield the circuits with the least number of CNOTs, we then
show that in the presence of sampling noise, high-fidelity state preparation
can still be achieved with the Hamiltonian commutator pool. By utilizing
Hamiltonian integral factorization and a noise resilient optimizer, we show
that this approach requires only a modest number of about shots per
measurement circuit. We discover a dichotomy of the operator pool complexity in
the presence of sampling noise, where a small pool size reduces the adaptive
overhead but a larger pool size accelerates convergence to the ground state.
When considering realistic gate noise in addition, we observe that the variable
optimization can still be performed as long as the two-qubit gate error lies
below , which is close but below current hardware levels. Finally, we
measure the ground state energy of the model on IBM and Quantinuum
quantum hardware using the converged adaptive ansatz. We perform a systematic
error mitigation analysis on the IBM results and obtain a relative error of
0.7\% using symmetry-based postselection and zero-noise extrapolation (ZNE).Comment: 19 pages, 9 figure
Efficient Step-Merged Quantum Imaginary Time Evolution Algorithm for Quantum Chemistry
We develop a resource-efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine the binding energy curves of a set of molecules, including H2, H4, H6, LiH, HF, H2O, and BeH2, and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional nonconvex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum devices
Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations
Development of resource-friendly quantum algorithms remains highly desirable
for noisy intermediate-scale quantum computing. Based on the variational
quantum eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate
that partitioning of the Hilbert space made possible by the point group
symmetry of the molecular systems greatly reduces the number of variational
operators by confining the variational search within a subspace. In addition,
we found that instead of including all subterms for each excitation operator, a
single-term representation suffices to reach required accuracy for various
molecules tested, resulting in an additional shortening of the quantum circuit.
With these strategies, VQE calculations on a noiseless quantum simulator
achieve energies within a few meVs of those obtained with the full UCCSD ansatz
for square, chain and hexagon
molecules; while the number of controlled-NOT (CNOT) gates, a measure of the
quantum-circuit depth, is reduced by a factor of as large as 35. Furthermore,
we introduced an efficient "score" parameter to rank the excitation operators,
so that the operators causing larger energy reduction can be applied first.
Using square and chain as examples, We
demonstrated on noisy quantum simulators that the first few variational
operators can bring the energy within the chemical accuracy, while additional
operators do not improve the energy since the accumulative noise outweighs the
gain from the expansion of the variational ansatz
Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
We demonstrate a post-quench dynamics simulation of a Heisenberg model on present-day IBM quantum hardware that extends beyond the coherence time of the device. This is achieved using a hybrid quantum-classical algorithm that propagates a state using Trotter evolution and then performs a classical optimization that effectively compresses the time-evolved state into a variational form. When iterated, this procedure enables simulations to arbitrary times with an error controlled by the compression fidelity and a fixed Trotter step size. We show how to measure the required cost function, the overlap between the time-evolved and variational states, on present-day hardware, making use of several error mitigation methods. In addition to carrying out simulations on real hardware, we investigate the performance and scaling behavior of the algorithm with noiseless and noisy classical simulations. We find the main bottleneck in going to larger system sizes to be the difficulty of carrying out the optimization of the noisy cost function.This is a pre-print of the article Berthusen, Noah F., Thaís V. Trevisan, Thomas Iadecola, and Peter P. Orth. "Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression." arXiv preprint arXiv:2112.12654 (2021).
DOI: 10.48550/arXiv.2112.12654.
Copyright 2022 The Authors.
Posted with permission
Learning crystal field parameters using convolutional neural networks
We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is trained on magnetization, magnetic susceptibility and specific heat data that is calculated theoretically within the single-ion approximation and further processed using a standard wavelet transformation. We apply the method to crystal fields of cubic, hexagonal and tetragonal symmetry and for both integer and half-integer total angular momentum values J of the ground state multiplet. We evaluate its performance on both theoretically generated synthetic and previously published experimental data on CeAgSb 2 , PrAgSb 2 and PrMg 2 Cu 9 , and find that it can reliably and accurately extract the CF parameters for all site symmetries and values of J considered. This demonstrates that CNNs provide an unbiased approach to extracting CF parameters that avoids tedious multi-parameter fitting procedures.</p
Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
We demonstrate a post-quench dynamics simulation of a Heisenberg model on
present-day IBM quantum hardware that extends beyond the coherence time of the
device. This is achieved using a hybrid quantum-classical algorithm that
propagates a state using Trotter evolution and then performs a classical
optimization that effectively compresses the time-evolved state into a
variational form. When iterated, this procedure enables simulations to
arbitrary times with an error controlled by the compression fidelity and a
fixed Trotter step size. We show how to measure the required cost function, the
overlap between the time-evolved and variational states, on present-day
hardware, making use of several error mitigation methods. In addition to
carrying out simulations on real hardware, we investigate the performance and
scaling behavior of the algorithm with noiseless and noisy classical
simulations. We find the main bottleneck in going to larger system sizes to be
the difficulty of carrying out the optimization of the noisy cost function.Comment: 11 pages, 9 figure
Differentiation of Myositis-Induced Models of Bacterial Infection and Inflammation with T2-Weighted, CEST, and DCE-MRI
We used T2 relaxation, chemical exchange saturation transfer (CEST), and dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) to assess whether bacterial infection can be differentiated from inflammation in a myositis-induced mouse model. We measured the T2 relaxation time constants, %CEST at 5 saturation frequencies, and area under the curve (AUC) from DCE-MRI after maltose injection from infected, inflamed, and normal muscle tissue models. We applied principal component analysis (PCA) to reduce dimensionality of entire CEST spectra and DCE signal evolutions, which were analyzed using standard classification methods. We extracted features from dimensional reduction as predictors for machine learning classifier algorithms. Normal, inflamed, and infected tissues were evaluated with H&E and gram-staining histological studies, and bacterial-burden studies. The T2 relaxation time constants and AUC of DCE-MRI after injection of maltose differentiated infected, inflamed, and normal tissues. %CEST amplitudes at −1.6 and −3.5 ppm differentiated infected tissues from other tissues, but these did not differentiate inflamed tissue from normal tissue. %CEST amplitudes at 3.5, 3.0, and 2.5 ppm, AUC of DCE-MRI for shorter time periods, and relative Ktrans and kep values from DCE-MRI could not differentiate tissues. PCA and machine learning of CEST-MRI and DCE-MRI did not improve tissue classifications relative to traditional analysis methods. Similarly, PCA and machine learning did not further improve tissue classifications relative to T2 MRI. Therefore, future MRI studies of infection models should focus on T2-weighted MRI and analysis of T2 relaxation times
Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models
Hybrid quantum-classical embedding methods for correlated materials simulations provide a path towards potential quantum advantage. However, the required quantum resources arising from the multi-band nature of d and f electron materials remain largely unexplored. Here we compare the performance of different variational quantum eigensolvers in ground state preparation for interacting multi-orbital embedding impurity models, which is the computationally most demanding step in quantum embedding theories. Focusing on adaptive algorithms and models with 8 spin-orbitals, we show that state preparation with fidelities better than 99.9% can be achieved using about 214 shots per measurement circuit. When including gate noise, we observe that parameter optimizations can still be performed if the two-qubit gate error lies below 10−3, which is slightly smaller than current hardware levels. Finally, we measure the ground state energy on IBM and Quantinuum hardware using a converged adaptive ansatz and obtain a relative error of 0.7%.This article is published as Mukherjee, Anirban, Noah F. Berthusen, João C. Getelina, Peter P. Orth, and Yong-Xin Yao. "Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models." Communications Physics 6, no. 1 (2023): 4.
DOI: 10.1038/s42005-022-01089-6.
Copyright 2023 The Author(s).
Attribution 4.0 International (CC BY 4.0).
Posted with permission.
DOE Contract Number(s): AC02-07CH11358; AC05-00OR2272