Related papers: Quantified Derandomization of Linear Threshold Cir…
The efficient decomposition of multi-controlled gates is a significant factor in quantum compiling, both in circuit depth and T-gate count. Recent work has demonstrated that qudits have the potential to reduce resource requirements from…
Parallelization is a major challenge in quantum algorithms due to physical constraints like no-cloning. This is vividly illustrated by the conjecture of Moore and Nilsson from their seminal work on quantum circuit complexity [MN01,…
Squared tensor networks (TNs) and their generalization as parameterized computational graphs -- squared circuits -- have been recently used as expressive distribution estimators in high dimensions. However, the squaring operation introduces…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
We investigate the problem of synthesizing T-depth optimal quantum circuits over the Clifford+T gate set. First we construct a special subset of T-depth 1 unitaries, such that it is possible to express the T-depth-optimal decomposition of…
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…
We present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade off in terms of depth and space complexity. As a result we…
Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC$^0$) can solve with near certainty (probability $1 - o(1)$), but that any bounded fan-in constant-depth classical circuit (NC$^0$)…
We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 is…
The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
Recently, Bravyi, Gosset, and K\"{o}nig (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth quantum circuit using bounded fan-in gates (or QNC^0…
We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical ${\rm AC}^0$. Among others, we derive such a lower bound for all fpt-approximations of the parameterized clique problem and…
Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting…
We study the problem of constructing explicit families of matrices which cannot be expressed as a product of a few sparse matrices. In addition to being a natural mathematical question on its own, this problem appears in various…
Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However, our understanding of the…
In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…
We investigate the complexity of uniform OR circuits and AND circuits of polynomial-size and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant (0/1) gates.…
Let $S_d(n)$ denote the minimum number of wires of a depth-$d$ (unbounded fan-in) circuit encoding an error-correcting code $C:\{0, 1\}^n \to \{0, 1\}^{32n}$ with distance at least $4n$. G\'{a}l, Hansen, Kouck\'{y}, Pudl\'{a}k, and Viola…
Optimizing quantum circuits by reducing circuit depth is essential for improving the efficiency and scalability of quantum algorithms, particularly as quantum hardware continues to evolve. This can be achieved by restructuring quantum…