Related papers: Space-Efficient Circuit Evaluation
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…
Some physical implementation schemes of quantum computing can apply two-qubit gates only on certain pairs of qubits. These connectivity constraints are commonly viewed as a significant disadvantage. For example, compiling an unrestricted…
Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of…
Given a simple polygon $P$ consisting of $n$ vertices, we study the problem of designing space-efficient algorithms for computing (i) the visibility polygon of a point inside $P$, (ii) the weak visibility polygon of a line segment inside…
Conventional vector-based simulators for quantum computers are quite limited in the size of the quantum circuits they can handle, due to the worst-case exponential growth of even sparse representations of the full quantum state vector as a…
We study algorithms for computing stable models of propositional logic programs and derive estimates on their worst-case performance that are asymptotically better than the trivial bound of O(m 2^n), where m is the size of an input program…
It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at $\omega(\log n)$ depth, where $n$ is the number of qubits, making them classically simulable. We show…
We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…
A random access memory, or RAM, is a device that, when interrogated, returns the content of a memory location in a memory array. A quantum RAM, or qRAM, allows one to access superpositions of memory sites, which may contain either quantum…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk…
Let $G$ be an unlabeled planar and simple $n$-vertex graph. Unlabeled graphs are graphs where the label-information is either not given or lost during the construction of data-structures. We present a succinct encoding of $G$ that provides…
Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size $n^{O(1)}$ and treewidth $O(\log^i n)$ can be simulated by a…
We consider unidirectional data streams with restricted access, such as read-only and write-only streams. For read-write streams, we also introduce a new complexity measure called expansion, the ratio between the space used on the stream…
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…
We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically…
The paper presents the first nontrivial upper and lower bounds for (non-oblivious) quantum read-once branching programs. It is shown that the computational power of quantum and classical read-once branching programs is incomparable in the…
Parallel computation enables multiple processors to execute different parts of a task simultaneously, improving processing speed and efficiency. In quantum computing, parallel gate implementation involves executing gates independently in…
We study the problem of designing a data structure that reports the positions of the distinct $\tau$-majorities within any range of an array $A[1,n]$, without storing $A$. A $\tau$-majority in a range $A[i,j]$, for $0<\tau< 1$, is an…