Related papers: No-iteration of unknown quantum gates
One of the essential building blocks of classical computer programs is the "if" clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
We show that a unitary operation (quantum circuit) secretely chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or…
Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
We propose a new quantum circuit for the quantum search problem. The quantum circuit is superior to Grover's algorithm in some realistic cases. The reasons for the superiority are in short as follows: In the quantum circuit proposed in this…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…
From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…
So far, only the results on 3 qubit spaces (both on superconducting and ion-trap realisations of quantum processors) have beaten the classical unstructured search in the expected number of oracle calls using optimal protocols in both…
The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm. Given the name of a special ENTRANCE vertex, a quantum walk can find…
Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can…
As the field of quantum computing grows, novel algorithms which take advantage of quantum phenomena need to be developed. As we are currently in the NISQ (noisy intermediate scale quantum) era, quantum algorithm researchers cannot reliably…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…
Given a quantum gate implementing a $d$-dimensional unitary operation $U_d$, without any specific description but $d$, and permitted to use $k$ times, we present a universal probabilistic heralded quantum circuit that implements the exact…
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…