Related papers: Quantum Threshold is Powerful
Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling, that is beyond the practical reach of modern supercomputers. We examine the…
We show that the parity of more than three non-target input bits cannot be computed by QAC-circuits of depth-2, not even uncleanly, regardless of the number of ancilla qubits. This result is incomparable with other recent lower bounds on…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
Contemporary quantum computers encode and process quantum information in binary qubits (d = 2). However, many architectures include higher energy levels that are left as unused computational resources. We demonstrate a superconducting…
Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep…
The notion of universal quantum computation can be generalized to multi-level qudits, which offer advantages in resource usage and algorithmic efficiencies. Trapped ions, which are pristine and well-controlled quantum systems, offer an…
This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
High-dimensional quantum systems have been used to reveal interesting fundamental physics and to improve information capacity and noise resilience in quantum information processing. However, it remains a significant challenge to realize…
In dynamic quantum circuits, classical information from mid-circuit measurements is fed forward during circuit execution. This emerging capability of quantum computers confers numerous advantages that can enable more efficient and powerful…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
It is shown that a family of analytically solvable pulses can be used to obtain high fidelity quantum phase gates with surprising robustness against imperfections in the system or pulse parameters. Phase gates are important because they can…
In this work, we prove the strongest known lower bounds for QAC$^0$, allowing polynomially many gates and ancillae. Our main results show that: (1) Depth-3 QAC$^0$ circuits cannot compute PARITY, and require $\Omega(\exp(\sqrt{n}))$ gates…
We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth,…
The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine…
Quantum addition based on the quantum Fourier transform can be an integral part of a quantum circuit and proved to be more efficient than the existing classical ripple carry adder. Our study includes identifying the quantum resource…
Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
The quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum…
Quantum Fourier gates (QFG) constitute a family of quantum gates that result from an exact combination of the quantum Fourier transform (QFT) and the SWAP gate. As a direct consequence of this, the Feynman gate is a particular case of that…