Related papers: Almost Optimal Synthesis of Reversible Function in…
We construct $\varepsilon$-approximate unitary $k$-designs on $n$ qubits in circuit depth $O(\log k \log \log n k / \varepsilon)$. The depth is exponentially improved over all known results in all three parameters $n$, $k$, $\varepsilon$.…
Contemporary quantum computers encode and process quantum information in binary qubits (d = 2). However, many architectures include higher energy levels that are left as unused computational resources. We demonstrate a superconducting…
Many quantum algorithms make use of ancilla, additional qubits used to store temporary information during computation, to reduce the total execution time. Quantum computers will be resource-constrained for years to come so reducing ancilla…
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…
We develop a method for approximate synthesis of single--qubit rotations of the form $e^{-i f(\phi_1,\ldots,\phi_k)X}$ that is based on the Repeat-Until-Success (RUS) framework for quantum circuit synthesis. We demonstrate how smooth…
Qudits, the multi-level generalization of qubits, provide a natural extension of the binary paradigm in quantum computation and offer new opportunities to enhance algorithmic performance. Beyond their direct applicability to the simulation…
Reversible logic circuit is a necessary construction for achieving ultra low power dissipation as well as for prominent post-CMOS computing technologies such as Quantum computing. Consequently automatic synthesis of a Boolean function using…
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices,…
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in $\Theta(n \log n)$ gates, and the…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…
We exploit hyperfine interactions in a single Mn-ion confined in a quantum dot (QD) to create a qudit, i.e. a multi-level quantum-bit system, with well defined, addressable and robust set of spin states for the realization of universal…
The multisilce method is an important algorithm for electron diffraction and image simulations in transmission electron microscopy. We have proposed a quantum algorithm of the multislice method based on quantum circuit model previously. In…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
The multiplication of superpositions of numbers is a core operation in many quantum algorithms. The standard method for multiplication (both classical and quantum) has a runtime quadratic in the size of the inputs. Quantum circuits with…
When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are…
Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…