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Register a new userToward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers
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Quantum computing has recently exhibited great potentials in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum algorithms such as variational quantum eigensolver (VQE). Yet, originating from limitations of the size and the fidelity of near-term quantum hardware, how to accurately simulate large realistic molecules remains a challenge. Here, integrating an adaptive energy sorting strategy and a classical computational method, the density matrix embedding theory, which effectively finds a shallower quantum circuit and reduces the problem size, respectively, we show a means to circumvent the limitations and demonstrate the potential toward solving real chemical problems. We numerically test the method for the hydrogenation reaction of C6H8 and the equilibrium geometry of the C18 molecule, with basis sets up to cc-pVDZ (at most 144 qubits). The simulation results show accuracies comparable to those of advanced quantum chemistry methods such as coupled-cluster or even full configuration interaction, while the number of qubits required is reduced by an order of magnitude (from 144 qubits to 16 qubits for the C18 molecule) compared to conventional VQE. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices.
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Readout errors are a significant source of noise for near term quantum computers. A variety of methods have been proposed to mitigate these errors using classical post processing. For a system with $n$ qubits, the entire readout error profile is specified by a $2^ntimes 2^n$ matrix. Recent proposals to use sub-exponential approximations rely on small and/or short-ranged error correlations. In this paper, we introduce and demonstrate a methodology to categorize and quantify multiqubit readout error correlations. Two distinct types of error correlations are considered: sensitivity of the measurement of a given qubit to the state of nearby spectator qubits, and measurement operator covariances. We deploy this methodology on IBMQ quantum computers, finding that error correlations are indeed small compared to the single-qubit readout errors on IBMQ Melbourne (15 qubits) and IBMQ Manhattan (65 qubits), but that correlations on IBMQ Melbourne are long-ranged and do not decay with inter-qubit distance.
Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multi-scale entanglement renormalization ansatz (MERA) can be contracted on a small quantum computer to aid the simulation of a large quantum system. However, without the ability to selectively reset qubits, the associated spatial cost can be exorbitant. In this paper, we propose a protocol that can unitarily reset qubits when the circuit has a common convolutional form, thus dramatically reducing the spatial cost for implementing the contraction algorithm on general near-term quantum computers. This protocol generates fresh qubits from used ones by partially applying the time-reversed quantum circuit over qubits that are no longer in use. In the absence of noise, we prove that the state of a subset of these qubits becomes $|0ldots 0rangle$, up to an error exponentially small in the number of gates applied. We also provide a numerical evidence that the protocol works in the presence of noise. We also provide a numerical evidence that the protocol works in the presence of noise, and formulate a condition under which the noise-resilience follows rigorously.
With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition (PD) techniques in quantum chemistry. Specifically, we use PD techniques to decompose a target molecular system into smaller subsystems requiring fewer computational resources. In our framework, there are two levels of hybridization. At the first level, we use a classical algorithm to decompose a target molecule into subsystems, and utilize a quantum algorithm to simulate the quantum nature of the subsystems. The second level is in the quantum algorithm. We consider the quantum--classical variational algorithm that iterates between an expectation estimation using a quantum device and a parameter optimization using a classical device. We investigate three popular PD techniques for our hybrid approach: the fragment molecular-orbital (FMO) method, the divide-and-conquer (DC) technique, and the density matrix embedding theory (DMET). We examine the efficacy of these techniques in correctly differentiating conformations of simple alkane molecules. In particular, we consider the ratio between the number of qubits for PD and that of the full system; the mean absolute deviation; and the Pearson correlation coefficient and Spearmans rank correlation coefficient. Sampling error is introduced when expectation values are measured on the quantum device. Therefore, we study how this error affects the predictive performance of PD techniques. The present study is our first step to opening up the possibility of using quantum chemistry simulations at a scale close to the size of molecules relevant to industry on near-term quantum hardware.
We present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark on the 20 qubit IBM Tokyo and 16 qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH),with accuracy of the computed ground state energy serving as the primary benchmark metric. We further parameterize this benchmark suite on the trial circuit type, the level of symmetry reduction, and error mitigation strategies. Our results demonstrate the characteristically high noise level present in near-term superconducting hardware, but provide a relevant baseline for future improvement of the underlying hardware, and a means for comparison across near-term hardware types. We also demonstrate how to reduce the noise in post processing with specific error mitigation techniques. Particularly, the adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environment. Here we present a quantum embedding theory for the calculation of strongly-correlated electronic states of active regions, with the rest of the system described within density functional theory. We demonstrate the accuracy and effectiveness of the approach by investigating several defect quantum bits in semiconductors that are of great interest for quantum information technologies. We perform calculations on quantum computers and show that they yield results in agreement with those obtained with exact diagonalization on classical architectures, paving the way to simulations of realistic materials on near-term quantum computers.
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