Related papers: Automated Method for Building CNOT Based Quantum C…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
For years, the quantum/reversible circuit community has been convinced that: a) the addition of auxiliary qubits is instrumental in constructing a smaller quantum circuit; and, b) the introduction of quantum gates inside reversible circuits…
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…
The quantum computer has become contemporary reality, with the first two-qubit machine of mere decades ago transforming into cloud-accessible devices with tens, hundreds, or -- in a few cases -- even thousands of qubits. While such hardware…
Experimental demonstrations of quantum annealing with native implementation of Boolean logic Hamiltonians are reported. As a superconducting integrated circuit, a problem Hamiltonian whose set of ground states is consistent with a given…
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system…
We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently…
We introduce a complete transformation rule set and a minimal equation set for controlled-NOT (CNOT)-based quantum circuits. Using these rules, quantum circuits that compute the same Boolean function are reduced to the same normal form. We…
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…
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…
A quantum circuit transformation (QCT) is required when executing a quantum program in a real quantum processing unit (QPU). Through inserting auxiliary SWAP gates, a QCT algorithm transforms a quantum circuit to one that satisfies the…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…
With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of…
We present a constructive method to create quantum circuits that implement oracles $|x\rangle|y\rangle|0\rangle^k \mapsto |x\rangle|y \oplus f(x)\rangle|0\rangle^k$ for $n$-variable Boolean functions $f$ with low $T$-count. In our method…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
Shannon proved that almost all Boolean functions require a circuit of size $\Theta(2^n/n)$. We prove a quantum analog of this classical result. Unlike in the classical case the number of quantum circuits of any fixed size that we allow is…