Related papers: Complexity Classification of Conjugated Clifford C…
The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for…
Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available…
Clifford group lies at the core of quantum computation -- it underlies quantum error correction, its elements can be used to perform magic state distillation and they form randomized benchmarking protocols, Clifford group is used to study…
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…
Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…
We consider quantum circuits composed of single-qubit operations and global entangling gates generated by Ising-type Hamiltonians. It is shown that such circuits can implement a large class of unitary operators commonly used in quantum…
Determining the quantum-classical boundary between quantum circuits which can be efficiently simulated classically and those which cannot remains a fundamental question. One approach to classical simulation is to represent the output of a…
A major challenge in developing quantum computing technologies is to accomplish high precision tasks by utilizing multiplex optimization approaches, on both the physical system and algorithm levels. Loss functions assessing the overall…
Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have…
In this paper we study single qutrit circuits consisting of words over the Clifford$+D$ cyclotomic gate set, where $D=\text{diag}(\pm\xi^{a},\pm\xi^{b},\pm\xi^{c})$, $\xi$ is a primitive $9$-th root of unity and $a,b,c$ are integers. We…
We report the characterization of a universal set of logic gates for one-way quantum computing using a four-photon `star' cluster state generated by fusing photons from two independent photonic crystal fibre sources. We obtain a fidelity…
Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes…
We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford…
Significant advances have been made in the study of quantum advantage both in theory and experiment, although these have mostly been limited to artificial setups. In this work, we extend the scope to address quantum advantage in tasks…
We show that all quantum gates which could be implemented by braiding of Ising anyons in the Ising topological quantum computer preserve the n-qubit Pauli group. Analyzing the structure of the Pauli group's centralizer, also known as the…
Equational reasoning is central to quantum circuit optimisation and verification: one replaces subcircuits by provably equivalent ones using a fixed set of rewrite rules viewed as equations. A finite rule set is most informative when it…
We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each…
Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…
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…
Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of non-iterative energy corrections, based on the method of…