Related papers: Any non-affine one-to-one binary gate suffices for…
Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
Any quantum computational network can be constructed with a sequence of the two-qubit diagonal quantum gates and one-qubit gates in two-state quantum systems. The universal construction of these quantum gates in the quantum systems and of…
Given a real dataset and a computation family, we wish to encode and store the dataset in a distributed system so that any computation from the family can be performed by accessing a small number of nodes. In this work, we focus on the…
We prove a general limitation in quantum information that unifies the impossibility principles such as no-cloning and no-anticloning. Further, we show that for an unknown qubit one cannot design a universal Hadamard gate for creating equal…
A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum…
It has long been known that to minimise the heat emitted by a deterministic computer during it's operation it is necessary to make the computation act in a logically reversible manner\cite{Lan61}. Such logically reversible operations…
Nonuniform families of polynomial-size finite automata, which are series of indexed finite automata having polynomially many inner states, are used in the past literature to solve nonuniform families of promise decision problems. Among such…
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
There is a large body of work studying what forms of computational hardness are needed to realize classical cryptography. In particular, one-way functions and pseudorandom generators can be built from each other, and thus require equivalent…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
We develop a multi-valued logic for quantum computing for use in multi-level quantum systems, and discuss the practical advantages of this approach for scaling up a quantum computer. Generalizing the methods of binary quantum logic, we…
We present generalized and improved constructions for simulating quantum computers with a polynomial slowdown on lattices composed of qubits on which certain global versions of one- and two-qubit operations can be performed.
We propose a non-deterministic CNOT gate based on a quantum cloner, a quantum switch based on all optical routing of single photon by single photon, a quantum-dot spin in a double-sided optical microcavity with two photonic qubits, delay…
The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two…
The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always…
A generic computation of a subset A of the natural numbers consists of a a computation that correctly computes most of the bits of A, and which never incorrectly computes any bits of A, but which does not necessarily give an answer for…
A quantum computer based on an asymmetric coupled dot system has been proposed and shown to operate as the controlled-NOT-gate. The basic idea is (1) the electron is localized in one of the asymmetric coupled dots. (2)The electron transfer…
Can a computer which runs for time $\omega^2$ compute more than one which runs for time $\omega$? No. Not, at least, for the infinite computer we describe. Our computer gets more powerful when the set of its steps gets larger. We prove that…
We propose a new physical approach for encoding and processing of quantum information in ensembles of multi-level quantum systems, where the different bits are not carried by individual particles but associated with the collective…