Abstract Quantum computers are getting larger and larger, but device fidelities may not be able to keep up with the increase in qubit numbers. One way to make use of a large device that has a limited gate depth is to run many small circuits simultaneously. In this paper we detail our investigations into running circuits in parallel on the Rigetti Aspen-M-1 device. We run two-qubit circuits in parallel to solve a simple instance of the Hubbard model using the variational quantum eigensolver (VQE). We present results for running up to 33 circuits in parallel (66 qubits), showing that with the use of error mitigation techniques it is possible to make use of, and gain a real-time speedup from, parallelisation on current quantum hardware. We obtain a speedup by 18× for exploring the VQE energy landscape, and by more than 8× for running VQE optimisation.
Abstract Quantum computers are getting larger and larger, but device fidelities may not be able to keep up with the increase in qubit numbers. One way to make use of a large device that has a limited gate depth is to run many small circuits simultaneously. In this paper we detail our investigations into running circuits in parallel on the Rigetti Aspen-M-1 device. We run two-qubit circuits in parallel to solve a simple instance of the Hubbard model using the variational quantum eigensolver (VQE). We present results for running up to 33 circuits in parallel (66 qubits), showing that with the use of error mitigation techniques it is possible to make use of, and gain a real-time speedup from, parallelisation on current quantum hardware. We obtain a speedup by 18× for exploring the VQE energy landscape, and by more than 8× for running VQE optimisation.
Variational quantum algorithms have promising applications in noisy intermediate-scale quantum (NISQ) devices. These algorithms rely on a classical optimization outer loop that minimizes a parameterized quantum circuit function. The optimization in variational quantum eigensolver (VQE) is NP-hard, meaning that finding the optimal solution is infeasible in the worst-case scenario. One way to address this challenge is through parallel optimization of parameters using multiple-parameterized quantum circuits. However, this approach is unsuitable for cloud-based quantum processing unit utilization due to the increased number of quantum circuit executions. Although NISQ devices have limitations in terms of gate depth, their size has been growing in recent years. Therefore, implementing multiple-parameterized quantum circuits in NISQ devices can suppress the increase in the number of executions. In this study, we propose a parallel-VQE, which leverages the parallel execution of parameterized quantum circuits to perform parallel parameter optimization in VQE, achieving convergence to solutions closer to the ground state. We validate the effectiveness of parallel-VQE in solving the random weighted max-cut problem using numerical simulations and a real quantum device. We present the results of running up to six circuits in parallel (120 qubits) and demonstrate the advantages of using multiple units to improve computational accuracy. This study provides a potential method for solving eigenvalue problems and combinatorial optimization problems for future quantum devices.
As the advances in quantum hardware bring us into the noisy intermediate-scale quantum (NISQ) era, one possible task we can perform without quantum error correction using NISQ machines is the variational quantum eigensolver (VQE) due to its shallow depth. A specific problem that we can tackle is the strongly interacting Fermi-Hubbard model, which is classically intractable and has practical implications in areas like superconductivity. In this paper, we outline the details about the gate sequence, the measurement scheme, and the relevant error-mitigation techniques for the implementation of the Hubbard VQE on a NISQ platform. We perform resource estimation for both silicon spin qubits and superconducting qubits for a 50-qubit simulation, which cannot be solved exactly via classical means, and find similar results. The number of two-qubit gates required is on the order of 20 000. Hence, to suppress the mean circuit-error count to a level such that we can obtain meaningful results with the aid of error mitigation, we need to achieve a two-qubit gate error rate of approximately ${10}^{\ensuremath{-}4}$. When searching for the ground state, we need a few days for one gradient-descent iteration, which is impractical. This can be reduced to around 10 min if we distribute our task among hundreds of quantum-processing units. Hence, implementing a 50-qubit Hubbard model VQE on a NISQ machine can be on the brink of being feasible in near term, but further optimization of our simulation scheme, improvements in the gate fidelity, improvements in the optimization scheme and advances in the error-mitigation techniques are needed to overcome the remaining obstacles. The scalability of the hardware platform is also essential to overcome the runtime issue via parallelization, which can be done on one single silicon multicore processor or across multiple superconducting processors.
Quantum computers are the next evolution of computing hardware. Quantum devices are being exposed through the same familiar cloud platforms used for classical computers, and enabling seamless execution of hybrid applications that combine quantum and classical components. Quantum devices vary in features, e.g., number of qubits, quantum volume, CLOPS, noise profile, queuing delays and resource cost. So, it may be useful to split hybrid workloads with either large quantum circuits or a large number of quantum circuits, into smaller units. In this paper, we profile two workload splitting techniques on IBM's Quantum Cloud: (1) Circuit parallelization, to split one large circuit into multiple smaller ones, and (2) Data parallelization to split a large number of circuits that run on one device to smaller batches of circuits that run on concurrently on multiple devices. These can improve the utilization of heterogeneous quantum hardware, but involve trade-offs. We evaluate these techniques on two key algorithmic classes: Variational Quantum Eigensolver (VQE) and Quantum Support Vector Machine (QSVM), and measure the impact on quality of the result, circuit execution times, quantum resource usage, and processing overheads, relative to a baseline without such parallelization. The results are obtained on real hardware and complemented by simulations. We see that (1) VQE with circuit cutting is ~ 39% better in ground state estimation than the uncut version, and (2) QSVM that combines data parallelization with a reduced feature set yields upto 3 ×improvement in quantum workload execution time and reduces quantum resource use by 3 ×, while providing comparable accuracy. Error mitigation can improve the accuracy by ≈ 7% and reduce resource footprint by ≈4% compared to the best case among the considered scenarios.
The state-of-the-art quantum computing hardware has entered the noisy intermediate-scale quantum (NISQ) era. Having been constrained by the limited number of qubits and shallow circuit depth, NISQ devices have nevertheless demonstrated the potential of applications on various subjects. One example is the variational quantum eigensolver (VQE) that was first introduced for computing ground states. Although VQE has now been extended to the study of excited states, the algorithms previously proposed involve a recursive optimization scheme which requires many extra operations with significantly deeper quantum circuits to ensure the orthogonality of different trial states. Here we propose a new algorithm to determine many low energy eigenstates simultaneously. By introducing ancillary qubits to purify the trial states so that they keep orthogonal to each other throughout the whole optimization process, our algorithm allows these states to be efficiently computed in one quantum circuit. Our algorithm reduces significantly the complexity of circuits and the readout errors, and enables flexible post-processing on the eigen-subspace from which the eigenpairs can be accurately determined. We demonstrate this algorithm by applying it to the transverse Ising model. By comparing the results obtained using this variational algorithm with the exact ones, we find that the eigenvalues of the Hamiltonian converge quickly with the increase of the circuit depth. The accuracies of the converged eigenvalues are of the same order, which implies that the difference between any two eigenvalues can be more accurately determined than the eigenvalues themselves.
Quantum spin systems may offer the first opportunities for beyond-classical quantum computations of scientific interest. While general quantum simulation algorithms likely require error-corrected qubits, there may be applications of scientific interest prior to the practical implementation of quantum error correction. The variational quantum eigensolver (VQE) is a promising approach to finding energy eigenvalues on noisy quantum computers. Lattice models are of broad interest for use on near-term quantum hardware due to the sparsity of the number of Hamiltonian terms and the possibility of matching the lattice geometry to the hardware geometry. Here, we consider the Kitaev spin model on a hardware-native square-octagon qubit connectivity map, and examine the possibility of efficiently probing its rich phase diagram with VQE approaches. By benchmarking different choices of variational Ansatz states and classical optimizers, we illustrate the advantage of a mixed optimization approach using the Hamiltonian variational Ansatz (HVA) and the potential of probing the system's phase diagram using VQE. We further demonstrate the implementation of HVA circuits on Rigetti's Aspen-9 chip with error mitigation.
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for ground-state energies of molecular systems. We compute the potential energy surface of the hydrogen molecule (H2) at 100 bond lengths with PennyLane on the ERAU Vega cluster (AMD EPYC 9654 CPUs, 4 NVIDIA H100 GPUs) and compare a serial baseline, an Optax and Catalyst JIT version, a lightning.gpu version, and an MPI version. Early stopping, a larger learning rate, and warm starts reduce the iteration count from 30,000 to 7,033 and the runtime from 593.95 s to 143.80 s, while the time per iteration stays between 0.0198 s and 0.0204 s. At 4 qubits, lightning.gpu lowers the time per iteration to 0.0145 s. MPI runs with 2 to 32 ranks finish in 8.45 s to 5.04 s; the serial and MPI jobs ran under different core allocations, so we do not report their ratio as a parallel speedup. In a 4 to 26 qubit study with different CPU and GPU software stacks, the CPU/GPU time ratio ranges from 3.5 to 81.5. One H100 runs up to 29 qubits.