Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy (i.e., how
to sample sequences to be run in the protocol). The sampling strategy is determined by a set of configurable parameters (an RB configuration) that includes Clifford lengths (a list of the number of independent Clifford gates in a sequence) and the number of sequences for each Clifford length. The RB configuration is often chosen heuristically and there has been little research on its best configuration. Therefore, we propose a method for fully optimizing an RB configuration so that the confidence interval of the estimated fidelity is minimized while not increasing the total execution time of sequences. By experiments on real devices, we demonstrate the efficacy of the optimization method against heuristic selection in reducing the variance of the estimated fidelity.
Variational quantum algorithms (VQAs) are promising methods that leverage noisy quantum computers and classical computing techniques for practical applications. In VQAs, the classical optimizers such as gradient-based optimizers are utilized to adjus
t the parameters of the quantum circuit so that the objective function is minimized. However, they often suffer from the so-called vanishing gradient or barren plateau issue. On the other hand, the normalized gradient descent (NGD) method, which employs the normalized gradient vector to update the parameters, has been successfully utilized in several optimization problems. Here, we study the performance of the NGD methods in the optimization of VQAs for the first time. Our goal is two-fold. The first is to examine the effectiveness of NGD and its variants for overcoming the vanishing gradient problems. The second is to propose a new NGD that can attain the faster convergence than the ordinary NGD. We performed numerical simulations of these gradient-based optimizers in the context of quantum chemistry where VQAs are used to find the ground state of a given Hamiltonian. The results show the effective convergence property of the NGD methods in VQAs, compared to the relevant optimizers without normalization. Moreover, we make use of some normalized gradient vectors at the past iteration steps to propose the novel historical NGD that has a theoretical guarantee to accelerate the convergence speed, which is observed in the numerical experiments as well.
Parameterized quantum circuits (PQCs), which are essential for variational quantum algorithms, have conventionally been optimized by parameterized rotational angles of single-qubit gates around predetermined set of axes. We propose a new method to op
timize a PQC by continuous parameterization of both the angles and the axes of its single-qubit rotations. The method is based on the observation that when rotational angles are fixed, optimal axes of rotations can be computed by solving a system of linear equations whose coefficients can be determined from the PQC with small computational overhead. The method can be further simplified to select axes freely from continuous parameters with rotational angles fixed to $pi$. We show the simplified free-axis selection method has better expressibility against other structural optimization methods when measured with Kullback-Leibler (KL) divergence. We also demonstrate PQCs with free-axis selection are more effective to search the ground states of Heisenberg models and molecular Hamiltonians. Because free-axis selection allows designing PQCs without specifying their single-qubit rotational axes, it may significantly improve the handiness of PQCs.
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to the best o
f our knowledge there is no existing graph kernel that considers all subgraphs to measure similarity. We propose a novel graph kernel that applies a quantum computer to measure the graph similarity taking all subgraphs into account by fully exploiting the power of quantum superposition to encode every subgraph into a feature. For the construction of the quantum kernel, we develop an efficient protocol that removes the index information of subgraphs encoded in the quantum state. We also prove that the quantum computer requires less query complexity to construct the feature vector than the classical sampler used to approximate the same vector. A detailed numerical simulation of a bioinformatics problem is presented to demonstrate that, in many cases, the proposed quantum kernel achieves better classification accuracy than existing graph kernels.
Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer. We propose
a novel estimator for this task, which is locally optimised with knowledge of the Hamiltonian and a classical approximation to the underlying quantum state. Our estimator is based on the concept of classical shadows of a quantum state, and has the important property of not adding to the circuit depth for the state preparation. We test its performance numerically for molecular Hamiltonians of increasing size, finding a sizable reduction in variance with respect to current measurement protocols that do not increase circuit depths.
This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output circuit obey
ing the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. Based upon a previous work of quantum circuit mapping that leverages gate commutation rules, this paper shows algorithms that utilize both transformation and commutation rules. Experiments on a standard benchmark dataset confirm the algorithms with more rules can find even better circuit mappings compared with the previously-known best algorithms.
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists
of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.
