Related papers: Computing Majority by Constant Depth Majority Circ…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
State-of-the-art quantum computers can only reliably execute circuits with limited qubit numbers and computational depth. This severely reduces the scope of algorithms that can be run. While numerous techniques have been invented to exploit…
The depth of quantum circuits is a critical factor when running them on state-of-the-art quantum devices due to their limited coherence times. Reducing circuit depth decreases noise in near-term quantum computations and reduces overall…
We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting. We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log…
Quantum Approximate Optimization Algorithm (QAOA) is studied primarily to find approximate solutions to combinatorial optimization problems. For a graph with $n$ vertices and $m$ edges, a depth $p$ QAOA for the Max-cut problem requires…
We describe a quantum black-box network computing the majority of N bits with zero-sided error eps using only 2N/3 + O(sqrt{N (log log N + log 1/eps)}) queries: the algorithm returns the correct answer with probability at least 1 - eps, and…
We show that over the field of complex numbers, \emph{every} homogeneous polynomial of degree $d$ can be approximated (in the border complexity sense) by a depth-$3$ arithmetic circuit of top fan-in at most $d+1$. This is quite surprising…
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…
A $k$-majority digraph is a directed graph created by combining $k$ individual rankings on the same ground set to form a consensus where edges point in the direction indicated by a strict majority of the rankings. The $k$-majority digraph…
Rapid advancement in the domain of quantum technologies has opened up researchers to the real possibility of experimenting with quantum circuits and simulating small-scale quantum programs. Nevertheless, the quality of currently available…
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs.…
Algorithmic cooling is a potentially important technique for making scalable NMR quantum computation feasible in practice. Given the constraints imposed by this approach to quantum computing, the most likely cooling algorithms to be…
We examine the fundamental problem of constructing depth-optimum circuits for binary addition. More precisely, as in literature, we consider the following problem: Given auxiliary inputs $t_0, \dotsc, t_{m-1}$, so-called generate and…
Among the cost metrics characterizing a quantum circuit, the $T$-count stands out as one of the most crucial as its minimization is particularly important in various areas of quantum computation such as fault-tolerant quantum computing and…
We show that the rank of a depth-3 circuit (over any field) that is simple, minimal and zero is at most k^3\log d. The previous best rank bound known was 2^{O(k^2)}(\log d)^{k-2} by Dvir and Shpilka (STOC 2005). This almost resolves the…
Low depth measurement-based quantum computation with qudits ($d$-level systems) is investigated and a precise relationship between this powerful model and qudit quantum circuits is derived in terms of computational depth and size…
We prove a lower bound of $\Omega\left(n^{1.5}\right)$ for the number of product gates in non-commutative arithmetic circuits for an explicit $n$-variate degree-$n$ polynomial $f_{n}$ (over every field). We observe that this implies that…
The paper discusses the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The Shannon gate complexity function $L(n, q)$ for a reversible circuit, implementing a Boolean transformation $f\colon \mathbb Z_2^n…
The problem of simulatability of quantum processes using classical resources plays a cornerstone role for quantum computing. Quantum circuits can be simulated classically, e.g., using Monte Carlo sampling techniques applied to…
Predicting properties of large-scale quantum systems is crucial for the development of quantum science and technology. Shadow estimation is an efficient method for this task based on randomized measurements, where many-qubit random Clifford…