Related papers: Finding Quantum Codes via Riemannian Optimization
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
Quantum noise is known to strongly affect quantum computation, thus potentially limiting the performance of currently available quantum processing units. Even learning models based on variational quantum algorithms, which were designed to…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…
We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual…
Recent years have witnessed the fast development of quantum computing. Researchers around the world are eager to run larger and larger quantum algorithms that promise speedups impossible to any classical algorithm. However, the available…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…