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Register a new userGenerating 3 qubit quantum circuits with neural networks
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A new method for compiling quantum algorithms is proposed and tested for a three qubit system. The proposed method is to decompose a a unitary matrix U, into a product of simpler U j via a neural network. These U j can then be decomposed into product of known quantum gates. Key to the effectiveness of this approach is the restriction of the set of training data generated to paths which approximate minimal normal subRiemannian geodesics, as this removes unnecessary redundancy and ensures the products are unique. The two neural networks are shown to work effectively, each individually returning low loss values on validation data after relatively short training periods. The two networks are able to return coefficients that are sufficiently close to the true coefficient values to validate this method as an approach for generating quantum circuits. There is scope for more work in scaling this approach to larger quantum systems.
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We propose quantum neural networks that include multi-qubit interactions in the neural potential leading to a reduction of the network depth without losing approximative power. We show that the presence of multi-qubit potentials in the quantum perceptrons enables more efficient information processing tasks such as XOR gate implementation and prime numbers search, while it also provides a depth reduction to construct distinct entangling quantum gates like CNOT, Toffoli, and Fredkin. This simplification in the network architecture paves the way to address the connectivity challenge to scale up a quantum neural network while facilitates its training.
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct errors without destroying coherence by using quantum error correcting codes [1]. The simplest of these are the three-qubit codes, which map a one-qubit state to an entangled three-qubit state and can correct any single phase-flip or bit-flip error of one of the three qubits, depending on the code used [2]. Here we demonstrate both codes in a superconducting circuit by encoding a quantum state as previously shown [3,4], inducing errors on all three qubits with some probability, and decoding the error syndrome by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate which corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate, known as a conditional-conditional NOT (CCNot) or Toffoli gate, using an interaction with the third excited state of a single qubit, in 63 ns. We find 85pm1% fidelity to the expected classical action of this gate and 78pm1% fidelity to the ideal quantum process matrix. Using it, we perform a single pass of both quantum bit- and phase-flip error correction with 76pm0.5% process fidelity and demonstrate the predicted first-order insensitivity to errors. Concatenating these two codes and performing them on a nine-qubit device would correct arbitrary single-qubit errors. When combined with recent advances in superconducting qubit coherence times [5,6], this may lead to scalable quantum technology.
Despite the pursuit of quantum advantages in various applications, the power of quantum computers in neural network computations has mostly remained unknown, primarily due to a missing link that effectively designs a neural network model suitable for quantum circuit implementation. In this article, we present the co-design framework, namely QuantumFlow, to provide such a missing link. QuantumFlow consists of novel quantum-friendly neural networks (QF-Nets), a mapping tool (QF-Map) to generate the quantum circuit (QF-Circ) for QF-Nets, and an execution engine (QF-FB). We discover that, in order to make full use of the strength of quantum representation, it is best to represent data in a neural network as either random variables or numbers in unitary matrices, such that they can be directly operated by the basic quantum logical gates. Based on these data representations, we propose two quantum friendly neural networks, QF-pNet and QF-hNet in QuantumFlow. QF-pNet using random variables has better flexibility, and can seamlessly connect two layers without measurement with more qbits and logical gates than QF-hNet. On the other hand, QF-hNet with unitary matrices can encode 2^k data into k qbits, and a novel algorithm can guarantee the cost complexity to be O(k^2). Compared to the cost of O(2^k)in classical computing, QF-hNet demonstrates the quantum advantages. Evaluation results show that QF-pNet and QF-hNet can achieve 97.10% and 98.27% accuracy, respectively. Results further show that for input sizes of neural computation grow from 16 to 2,048, the cost reduction of QuantumFlow increased from 2.4x to 64x. Furthermore, on MNIST dataset, QF-hNet can achieve accuracy of 94.09%, while the cost reduction against the classical computer reaches 10.85x. To the best of our knowledge, QuantumFlow is the first work to demonstrate the potential quantum advantage on neural network computation.
We present novel algorithms to estimate outcomes for qubit quantum circuits. Notably, these methods can simulate a Clifford circuit in linear time without ever writing down stabilizer states explicitly. These algorithms outperform previous noisy near-Clifford techniques for most circuits. We identify a large class of input states that can be efficiently simulated despite not being stabilizer states. The algorithms leverage probability distributions constructed from Bloch vectors, paralleling previously known algorithms that use the discrete Wigner function for qutrits.
Qubits strongly coupled to a photonic crystal give rise to many exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Here, we present experimental results from a device with two qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and inter-bound state interactions. We observe a fourth-order two photon virtual process between bound states indicating strong coupling between the photonic crystal and qubits. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits spatial organization, a key criterion for realization of certain quantum many-body models. The widely tunable, strong and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems of bound states.
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