Approaching the theoretical limit in quantum gate decomposition

Abstract

In this work we propose a novel numerical approach to decompose general quantum programs in terms of single- and two-qubit quantum gates with a CNOT gate count very close to the current theoretical lower bounds. In particular, it turns out that 15 and 63CNOT gates are sufficient to decompose a general 3- and 4-qubit unitary, respectively, with high numerical accuracy. Our approach is based on a sequential optimization of parameters related to the single-qubit rotation gates involved in a pre-designed quantum circuit used for the decomposition. In addition, the algorithm can be adopted to sparse inter-qubit connectivity architectures provided by current mid-scale quantum computers, needing only a few additional CNOT gates to be implemented in the resulting quantum circuits.

Modularized and Scalable Compilation for Double Quantum Dot Quatum Computing

“…Compared to schemes such as [32][33][34] where ansatz's parameters are updated in a closed-loop style, the application of random states reduces the susceptibility of the optimization to local optima akin to the usage of random samples in the training landscape of classical neural networks [26]. In addition, this utilization of quantum states is more resource efficient than commonly used approaches based on matrices in loss calculation, such as the Hilbert-Schmidt distance or other customized metrics between the associated unitaries [32][33][34]. It is worth noting that this training approach is scalable and applicable generally to the construction or decomposition of unitary transformations with any number of qubits.…”

“…In this paper, we enlist another emerging and powerful technique to compile a desired unitary into a native gate sequence without changed length -the variational quantum algorithm (VQA) [31], which has recently been used for decomposing complex unitary transformations into ordered universal gates [32,33] or Schmidt decomposition [34], etc.…”

“…Additionally, we suggest training the Ansatz, a circuit of parametric native gates, with random quantum states. Compared to the widely used matrix-based approaches [32][33][34], this training scheme offers reduced overhead in loss calculation and smaller possibility of being stucked in local optimums during optimization. Considering singlequbit rotations and entangling two-qubit gates are crucial ingredients for universal quantum computation, a series of them are compiled and high fidelities are reached, underling the foundations for accurately implementing quantum programs in DQDs.…”

Non-local Andreev reflection through Andreev molecular states in graphene Josephson junctions

“…Using hard wall boundary conditions [37,38], the transverse wavenumber q parallel to the y direction is a good quantum number, see the SI for further details. The numerical calculations discussed below were performed using the tight-binding framework implemented in the EQuUs [39] package.…”

Parallel Driving for Fast Quantum Computing Under Speed Limits

“…2). Simple techniques for gate decomposition use this interleaving template and via an exact analytical solution [23], [24], or an approximate numerical optimizer [25]- [27], find a solution to the 1Q gates for a variable number of repetitions. We refer to a basis template, as a quantum circuit that interleaves the basis gate K times.…”