Related papers: A log-depth in-place quantum Fourier transform tha…
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to…
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not…
Routing is the task of permuting qubits in such a way that quantum operations can be parallelized maximally, given constraints on the hardware geometry. When simulating fermions in the Jordan-Wigner encoding with qubits, a one-dimensional…
Simulation of fermionic systems is one of the most promising applications of quantum computers. It spans problems in quantum chemistry, high-energy physics and condensed matter. Underpinning the core steps of any quantum simulation…
Quantum computing is one of the most promising technology advances of the latest years. Once only a conceptual idea to solve physics simulations, quantum computation is today a reality, with numerous machines able to execute quantum…
Dynamic quantum circuits combine mid-circuit measurement with classical feed-forward, enabling circuit constructions with reduced entangling-gate depth. Here, we investigate their use in Quantum Imaginary Time Evolution (QITE), where…
While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can…
Discrete-time quantum walks with position-dependent coin operators have numerous applications. For a position dependence that is sufficiently smooth, it has been provided in Ref. [1] an approximate quantum-circuit implementation of the coin…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
Advanced simulations and calculations on quantum computers require high-fidelity implementations of quantum operations. The universal gateset approach builds complex unitaries from a small set of primitive gates, often resulting in a long…
Noise in existing quantum processors only enables an approximation to ideal quantum computation. However, these approximations can be vastly improved by error mitigation, for the computation of expectation values, as shown by small-scale…
A pure state of fixed Hamming weight is a superposition of computational basis states such that each bitstring in the superposition has the same number of ones. Given a Hilbert space of the form $\mathcal{H} = (\mathbb{C}_2)^{\otimes n}$,…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant…
Quantum circuits for mathematical functions such as division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to…
Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate scale quantum simulators relying on variational hybrid quantum-classical algorithms. To…
We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits…
The ability to perform quantum error correction (QEC) and robust gate operations on encoded qubits opens the door to demonstrations of quantum algorithms. Contemporary QEC schemes typically require mid-circuit measurements with feed-forward…
Current quantum devices have unutilized high-level quantum resources. More and more attention has been paid to the qudit quantum systems with larger than two dimensions to maximize the potential computing power of quantum computation. Then,…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…