Related papers: Interactive shallow Clifford circuits: quantum adv…
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…
Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output…
For random quantum circuits on $n$ qubits of depth $\Theta(\log n)$ with depolarizing noise, the task of sampling from the output state can be efficiently performed classically using a Pauli path method [Aharonov et al. Proceedings of the…
We study quantum-classical separations between classical and quantum supervised learning models based on constant depth (i.e., shallow) circuits, in scenarios with and without noises. We construct a classification problem defined by a…
We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…
Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible…
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates,…
We present a robust shadow estimation protocol for wide classes of low-depth measurement circuits that mitigates noise as long as the effective measurement map including noise is locally unitarily invariant. This is in practice an excellent…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
We consider quantum circuits composed of single-qubit operations and global entangling gates generated by Ising-type Hamiltonians. It is shown that such circuits can implement a large class of unitary operators commonly used in quantum…
We introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-efficient way to realize approximate…
Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have…
We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a…
Quantum advantage schemes probe the boundary between classically simulatable and classically intractable quantum dynamics. We explore the impact of mid-circuit measurements on the computational power of quantum circuits. To this effect, we…
The design and optimization of a large-scale fault-tolerant quantum computer architecture relies extensively on numerical simulations to assess the performance of each component of the architecture. The simulation of fault-tolerant gadgets,…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and…
We introduce a new family of quantum circuits for which the scrambling of a subspace of non-local operators is classically simulable. We call these circuits `super-Clifford circuits', since the Heisenberg time evolution of these operators…