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Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…
Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and…
This paper presents novel methods for optimizing multi-controlled quantum gates, which naturally arise in high-level quantum programming. Our primary approach involves rewriting $U(2)$ gates as $SU(2)$ gates, utilizing one auxiliary qubit…
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…
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently…
Quantum optimization has gained increasing attention as advances in quantum hardware enable the exploration of problem instances approaching real-world scale. Among existing approaches, variational quantum algorithms and quantum annealing…
A quantum circuit may be strongly classically simulated with the aid of ZX-calculus by decomposing its $t$ T-gates into a sum of $2^{\alpha t}$ classically computable stabiliser terms. In this paper, we introduce a general procedure to find…
This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…
Quantum circuits are time dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable and heuristic methods must…
In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
We introduce an approach for estimating the expectation values of arbitrary $n$-qubit matrices $M \in \mathbb{C}^{2^n\times 2^n}$ on a quantum computer. In contrast to conventional methods like the Pauli decomposition that utilize $4^n$…
We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected…
Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…