Related papers: Quantum Circuit Synthesis Using an Exact T Library

The matrices that can be exactly represented by a circuit over the Toffoli-Hadamard gate set are the orthogonal matrices of the form $M/ \sqrt{2}{}^k$, where $M$ is an integer matrix and $k$ is a nonnegative integer. The exact synthesis…

Quantum circuits consist of gates applied to qubits. Current quantum hardware platforms impose connectivity restrictions on binary CX gates. Hence, Layout Synthesis is an important step to transpile quantum circuits before they can be…

We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that…

A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…

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 recent years qubit designs such as transmons approached the fidelities of up to 0.999. However, even these devices are still insufficient for realizing quantum error correction requiring better than 0.9999 fidelity. Topologically…

We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing…

Given a quantum algorithm, it is highly nontrivial to devise an efficient sequence of physical gates implementing the algorithm on real hardware and incorporating topological quantum error correction. In this paper, we present a first step…

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…

Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…

Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…

Quantum Error Correction (QEC) codes form the foundation of Fault-Tolerant Quantum Computing (FTQC) and predominantly use the Clifford+T gate set. Recently, Clifford operations have become the key performance bottleneck in implementing QEC.…

One of the primary objectives in the field of quantum state learning is to develop algorithms that are time-efficient for learning states generated from quantum circuits. Earlier investigations have demonstrated time-efficient algorithms…

In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which…

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…

We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…

The Boolean Satisfiability (SAT) problem is a canonical NP-complete problem and a natural candidate for quantum acceleration via search-based algorithms. In Grover-based quantum SAT solvers, the dominant computational cost stems from the…

Recently, reversible circuit synthesis has been intensively studied. One of the problems that has not been solved for a long time was exact minimization of gate count (GC) in 4-bit circuits. Finally, last year a tool of practical usage for…

Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the…

Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…