Related papers: Unitary designs in nearly optimal depth

In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…

We introduce an $\varepsilon$-approximate unitary 2-design that is compatible with the structure of p- and q-quadratures in continuous-variable (CV) quantum systems. The design unitaries are defined on a finite-dimensional discretisation of…

We first show how to construct an O(n)-depth O(n)-size quantum circuit for addition of two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, which is smaller than that of any other quantum circuit ever constructed for…

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…

The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with $n$ wires, each corresponding to one…

Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…

We consider the problem of testing and learning quantum $k$-juntas: $n$-qubit unitary matrices which act non-trivially on just $k$ of the $n$ qubits and as the identity on the rest. As our main algorithmic results, we give (a) a…

We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…

Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…

Compared to general quantum states, the sparse states arise more frequently in the field of quantum computation. In this work, we consider the preparation for $n$-qubit sparse quantum states with $s$ non-zero amplitudes and propose two…

A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…

We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems. Our unified framework provides a streamlined approach for constructing…

Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly-interacting systems and black holes. The…

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…

We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be…

We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…

During the noisy intermediate-scale quantum (NISQ) era, it is important to optimize the quantum circuits in circuit depth and gate count, especially entanglement gates, including the CNOT gate. Among all the unitary operators, diagonal…

A unitary $t$-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general $t$. In this paper, we provide for the first time quantum…

One of the challenges currently facing the quantum computing community is the design of quantum circuits which can efficiently run on near-term quantum computers, known as the quantum compiling problem. Algorithms such as the Variational…

In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations…