Related papers: Quantified Derandomization of Linear Threshold Cir…
The relevance of shallow-depth quantum circuits has recently increased, mainly due to their applicability to near-term devices. In this context, one of the main goals of quantum circuit complexity is to find problems that can be solved by…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
$\mathsf{QAC}^0$ is the class of constant-depth polynomial-size quantum circuits constructed from arbitrary single-qubit gates and generalized Toffoli gates. It is arguably the smallest natural class of constant-depth quantum computation…
Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…
It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results…
We design a deterministic subexponential time algorithm that takes as input a multivariate polynomial $f$ computed by a constant-depth circuit over rational numbers, and outputs a list $L$ of circuits (of unbounded depth and possibly with…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…
Quantum circuit depth minimization is critical for practical applications of circuit-based quantum computation. In this work, we present a systematic procedure to decompose multiqubit controlled unitary gates, which is essential in many…
We study the class $\textrm{AC}^0$ of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates. No model-theoretic characterization for arithmetic circuit classes is…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic,…
Classical simulation of quantum circuits is a critical tool for validating quantum hardware and probing the boundary between classical and quantum computational power. Existing state-of-the-art methods, notably tensor network approaches,…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
We introduce a classical algorithm for sampling the output of shallow, noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently-proposed "space-evolving block decimation" (SEBD) and extends it to the case…
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…
Towards better understanding of gate elimination, the only method known that can prove complexity lower bounds for explicit functions against unrestricted Boolean circuits, this work contributes: (1) formalizing circuit simplifications as a…
In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms,…
We show that sharp thresholds for Boolean functions directly imply average-case circuit lower bounds. More formally we show that any Boolean function exhibiting a sharp enough threshold at \emph{arbitrary} critical density cannot be…
QAC circuits are quantum circuits with one-qubit gates and Toffoli gates of arbitrary arity. QAC$^0$ circuits are QAC circuits of constant depth, and are quantum analogues of AC$^0$ circuits. We prove the following: $\bullet$ For all $d \ge…