Related papers: A Criterion for Post-Selected Quantum Advantage

Molecular simulations are widely regarded as leading candidates to demonstrate quantum advantage--defined as the point at which quantum methods surpass classical approaches in either accuracy or scale. Yet the qubit counts and error rates…

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…

The Clifford group plays a central role in quantum randomized benchmarking, quantum tomography, and error correction protocols. Here we study the structural properties of this group. We show that any Clifford operator can be uniquely…

We show that families of Instantaneous Quantum Polynomial (IQP) circuits corresponding to nontrivial Bell tests exhibit nonlocality. However, we also prove that this nonlocality can only be demonstrated using post-selection or nonlinear…

Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…

Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time…

Non-Hermitian (NH) quantum systems demonstrate striking differences from their Hermitian counterparts, leading to claims of NH advantage in areas ranging from metrology to entanglement generation. We show that in the context of quantum…

Suppose we want to implement a unitary $U$, for instance a circuit for some quantum algorithm. Suppose our actual implementation is a unitary $\tilde{U}$, which we can only apply as a black-box. In general it is an exponentially-hard task…

We introduce a measure for evaluating the efficiency of finite universal quantum gate sets $\mathcal{S}$, called the Quantum Circuit Overhead (QCO), and the related notion of $T$-Quantum Circuit Overhead ($T$-QCO). QCO compares the circuit…

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…

We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…

We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical…

Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show…

The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and 'nearly diagonal' semi-Clifford gates are particularly important:…

The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The groups of Pauli and Clifford gates constitute the…

Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…

In continuous-variable quantum computation, identifying key elements that enable a quantum computational advantage is a long-standing issue. Starting from the standard results on the necessity of Wigner negativity, we develop a…

Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…

Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…

Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still…