Universal quantum computation via quantum controlled classical operations

A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results in universal quantum computing. Motivated by the latter, we pose the following question: can one perform universal quantum computation by supplementing a set of classical gates with a quantum control, and a set of quantum gates operating solely on the latter? In this work we provide an affirmative answer to this question by considering a computational model that consists of 2n target bits together with a set of classical gates controlled by log(2n + 1) ancillary qubits. We show that this model is equivalent to a quantum computer operating on n qubits. Furthermore, we show that even a primitive computer that is capable of implementing only SWAP gates, can be lifted to universal quantum computing, if aided with an appropriate quantum control of logarithmic size. Our results thus exemplify the information processing power brought forth by the quantum control system.

On the Universal Encoding Optimality of Primes

The factorial-additive optimality of primes, i.e., that the sum of prime factors is always minimum, implies that prime numbers are a solution to an integer linear programming (ILP) encoding optimization problem. The summative optimality of primes follows from Goldbach’s conjecture, and is viewed as an upper efficiency limit for encoding any integer with the fewest possible additions. A consequence of the above is that primes optimally encode—multiplicatively and additively—all integers. Thus, the set P of primes is the unique, irreducible subset of ℤ—in cardinality and values—that optimally encodes all numbers in ℤ, in a factorial and summative sense. Based on these dual irreducibility/optimality properties of P, we conclude that primes are characterized by a universal “quantum type” encoding optimality that also extends to non-integers.

Deep reinforcement learning for universal quantum state preparation via dynamic pulse control

Accurate and efficient preparation of quantum state is a core issue in building a quantum computer. In this paper, we investigate how to prepare a certain single- or two-qubit target state from arbitrary initial states in semiconductor double quantum dots with only a few discrete control pulses by leveraging the deep reinforcement learning. Our method is based on the training of the network over numerous preparing tasks. The results show that once the network is well trained, it works for any initial states in the continuous Hilbert space. Thus repeated training for new preparation tasks is avoided. Our scheme outperforms the traditional optimization approaches based on gradient with both the higher efficiency and the preparation quality in discrete control space. Moreover, we find that the control trajectories designed by our scheme are robust against stochastic fluctuations within certain thresholds, such as the charge and nuclear noises.

Design Space Exploration of Hybrid Quantum–Classical Neural Networks

The unprecedented success of classical neural networks and the recent advances in quantum computing have motivated the research community to explore the interplay between these two technologies, leading to the so-called quantum neural networks. In fact, universal quantum computers are anticipated to both speed up and improve the accuracy of neural networks. However, whether such quantum neural networks will result in a clear advantage on noisy intermediate-scale quantum (NISQ) devices is still not clear. In this paper, we propose a systematic methodology for designing quantum layer(s) in hybrid quantum–classical neural network (HQCNN) architectures. Following our proposed methodology, we develop different variants of hybrid neural networks and compare them with pure classical architectures of equivalent size. Finally, we empirically evaluate our proposed hybrid variants and show that the addition of quantum layers does provide a noticeable computational advantage.

Machine learning of high dimensional data on a noisy quantum processor

Quantum kernel methods show promise for accelerating data analysis by efficiently learning relationships between input data points that have been encoded into an exponentially large Hilbert space. While this technique has been used successfully in small-scale experiments on synthetic datasets, the practical challenges of scaling to large circuits on noisy hardware have not been thoroughly addressed. Here, we present our findings from experimentally implementing a quantum kernel classifier on real high-dimensional data taken from the domain of cosmology using Google’s universal quantum processor, Sycamore. We construct a circuit ansatz that preserves kernel magnitudes that typically otherwise vanish due to an exponentially growing Hilbert space, and implement error mitigation specific to the task of computing quantum kernels on near-term hardware. Our experiment utilizes 17 qubits to classify uncompressed 67 dimensional data resulting in classification accuracy on a test set that is comparable to noiseless simulation.

Quantum information distance

In this paper, we give a definition for quantum information distance. In the classical setting, information distance between two classical strings is developed based on classical Kolmogorov complexity. It is defined as the length of a shortest transition program between these two strings in a universal Turing machine. We define the quantum information distance based on Berthiaume et al.’s quantum Kolmogorov complexity. The quantum information distance between qubit strings is defined as the length of the shortest quantum transition program between these two qubit strings in a universal quantum Turing machine. We show that our definition of quantum information distance is invariant under the choice of the underlying quantum Turing machine.