Related papers: Algebraic Characterization of CNOT-Based Quantum C…
This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable…
We study in detail the algebraic structures underlying quantum circuits generated by CNOT gates. Our results allow us to propose polynomial-time heuristics to reduce the number of gates used in a given CNOT circuit and we also give…
CNOT gates are fundamental to quantum computing, as they facilitate entanglement, a crucial resource for quantum algorithms. Certain classes of quantum circuits are constructed exclusively from CNOT gates. Given their widespread use, it is…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
We present a theoretical result, which is based on the linear algebra theory (similar operators). The obtained theoretical results optimize the experimental technique to construct quantum computer e.g., reduces the number of steps to…
We describe the construction of a conditional quantum control-not (CNOT) gate from linear optical elements following the program of Knill, Laflamme and Milburn [Nature {\bf 409}, 46 (2001)]. We show that the basic operation of this gate can…
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…
We describe the operation and tolerances of a non-deterministic, coincidence basis, quantum CNOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration.
We propose a theory of characterizing quantum circuits with qubit functional configurations. Any quantum circuit can be decomposed into alternating sequences of 1-qubit unitary gates and CNOT gates. Each CNOT sequence prepares the current…
Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…
Current proposals for quantum compilers require the synthesis and optimization of linear reversible circuits and among them CNOT circuits. Since these circuits represent a significant part of the cost of running an entire quantum circuit,…
We present an algorithm for compiling arbitrary unitaries into a sequence of gates native to a quantum processor. As accurate CNOT gates are hard for the foreseeable Noisy- Intermediate-Scale Quantum devices era, our A* inspired algorithm…
NISQ devices have inherent limitations in terms of connectivity and hardware noise. The synthesis of CNOT circuits considers the physical constraints and transforms quantum algorithms into low-level quantum circuits that can execute on…
The increasing depth of quantum circuits presents a major limitation for the execution of quantum algorithms, as the limited coherence time of physical qubits leads to noise that manifests as errors during computation. In this work, we…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
A CNOT circuit is the key gadget for entangling qubits in quantum computing systems. However, the qubit connectivity of noisy intermediate-scale quantum (NISQ) devices is constrained by their {limited connectivity architecture}. To improve…
We study the problem of CNOT-optimal quantum circuit synthesis over gate sets consisting of CNOT and Z-basis rotations of arbitrary angles. We show that the circuit-polynomial correspondence relates such circuits to Fourier expansions of…