Related papers: Multi-qubit circuit synthesis and Hermitian lattic…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…
Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…
We describe a new method for the decomposition of an arbitrary $n$ qubit operator with entries in $\mathbb{Z}[i,\frac{1}{\sqrt{2}}]$, i.e., of the form $(a+b\sqrt{2}+i(c+d\sqrt{2}))/{\sqrt{2}^{k}}$, into Clifford+$T$ operators where $n\le…
Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum…
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…
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…
CNOT optimization plays a significant role in noise reduction for Quantum Circuits. Several heuristic and exact approaches exist for CNOT optimization. In this paper, we investigate more complicated variations of optimal synthesis by…
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…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
We provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of…
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…
Quantum computing is a promising paradigm that may overcome the current computational power bottlenecks. The increasing maturity of quantum processors provides more possibilities for the development and implementation of quantum algorithms.…
Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As…
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 computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a…
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…