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Related papers: A Framework for Approximating Qubit Unitaries

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We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…

Quantum Physics · Physics 2014-11-17 Edward Farhi , Jeffrey Goldstone , Sam Gutmann

We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…

Quantum Physics · Physics 2025-05-27 Ragesh Jaiswal

Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…

This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more…

Quantum Physics · Physics 2021-11-24 Michele Mosca , Priyanka Mukhopadhyay

Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…

Quantum Physics · Physics 2026-03-16 Daisuke Sakamoto , Soshun Naito , Yusei Mori , Kosuke Mitarai

Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…

Quantum Physics · Physics 2025-12-16 Sarah Schneider , Lukas Burgholzer , Robert Wille

This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate…

We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…

Quantum Physics · Physics 2021-08-18 Ewout van den Berg

We investigate the problem of synthesizing T-depth optimal quantum circuits over the Clifford+T gate set. First we construct a special subset of T-depth 1 unitaries, such that it is possible to express the T-depth-optimal decomposition of…

Quantum Physics · Physics 2022-09-14 Vlad Gheorghiu , Michele Mosca , Priyanka Mukhopadhyay

This thesis contains contributions to the theory of quantum computation. We first define a new method to efficiently approximate special unitary operators. Specifically, given a special unitary U and a precision {\epsilon} > 0, we show how…

Quantum Physics · Physics 2017-02-17 Neil J. Ross

Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…

Quantum Physics · Physics 2024-05-24 Igor Ermakov , Oleg Lychkovskiy , Tim Byrnes

This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…

Quantum Physics · Physics 2024-10-01 Zhong-Yi Ni , Yu-Sheng Zhao , Jin-Guo Liu

Block-encodings have become one of the most common oracle assumptions in the circuit model. I present an algorithm that uses von Neumann's measurement procedure to measure a phase, using time evolution on a block-encoded Hamiltonian as a…

Quantum Physics · Physics 2025-09-05 S. E. Skelton

We present an algorithm for compiling arbitrary unitaries into a sequence of gates native to a quantum processor. As accurate CNOT gates are hard for the foreseeable Noisy- Intermediate-Scale Quantum devices era, our A* inspired algorithm…

Emerging Technologies · Computer Science 2019-12-09 Marc Grau Davis , Ethan Smith , Ana Tudor , Koushik Sen , Irfan Siddiqi , Costin Iancu

In this work, we report on a novel quantum gate approximation algorithm based on the application of parametric two-qubit gates in the synthesis process. The utilization of these parametric two-qubit gates in the circuit design allows us to…

Quantum Physics · Physics 2022-11-16 Péter Rakyta , Zoltán Zimborás

Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…

Quantum Physics · Physics 2026-03-20 Priyanka Mukhopadhyay , Alexandru Gheorghiu , Hari Krovi

There is currently a significant need for robust and efficient methods for characterizing quantum devices. While there has been significant progress in this direction, there remains a crucial need to precisely determine the strength and…

Quantum Physics · Physics 2019-09-04 Arnaud Carignan-Dugas , Joel J. Wallman , Joseph Emerson

We use quantum process tomography to characterize a full universal set of all-microwave gates on two superconducting single-frequency single-junction transmon qubits. All extracted gate fidelities, including those for Clifford group…

Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate $R=|0\rangle \langle 0| + |1\rangle \langle 1| - |2\rangle \langle 2|$. It is arguably, a ternary basis…

Quantum Physics · Physics 2018-01-22 Alex Bocharov

We present an algorithm for performing quantum process tomography on an unknown $n$-qubit unitary $C$ from the Clifford group. Our algorithm uses Bell basis measurements to deterministically learn $C$ with $4n + 3$ queries, which is the…

Quantum Physics · Physics 2026-01-21 Timothy Skaras , Paul Ginsparg