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In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
We present an efficient algorithm to reduce the number of non-Clifford gates in quantum circuits and the number of parametrized rotations in parametrized quantum circuits. The method consists in finding rotations that can be merged into a…
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…
A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…
In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$, in the single-qubit case. We report an…
As quantum computing advances toward the late-NISQ and early fault-tolerant eras, scalable and platform-independent benchmarks are essential for quantifying computational capacity in a classically verifiable manner. We introduce two…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed. To that end, we present a…
In the popular ${\cal PT}-$symmetry-based formulation of quantum mechanics of closed systems one can build unitary models using non-Hermitian Hamiltonians (i.e., $H \neq H^\dagger$) which are Hermitizable (so that one can write,…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
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…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
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…
The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range…
Quantum simulations of electronic structure with a transformed Hamiltonian that includes some electron correlation effects are demonstrated. The transcorrelated Hamiltonian used in this work is efficiently constructed classically, at…
In fault-tolerant quantum computing, the cost of calculating Hamiltonian eigenvalues using the quantum phase estimation algorithm is proportional to the constant scaling the Hamiltonian matrix block-encoded in a unitary circuit. We present…