Related papers: Universal Early-Time Growth in Quantum Circuit Com…
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 simulating an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ on a quantum computer. We show that this simulation has gate complexity $(nt)^{1+o(1)}$ using product formulas, a straightforward…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…
Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our…
We study the gate-based implementation of the binary reflected Gray code (BRGC) and binary code of the unitary time evolution operator due to the Laplacian discretized on a lattice with periodic boundary conditions. We find that the…
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable…
We study the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to the circuit complexity associated to a set of quantum gates. Inhomogeneous cost functions ---many examples of which have…
Quantum circuit complexity has played a central role in recent advances in holography and many-body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real-time) framework. In a departure from standard…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
We study the quantum circuit complexity of cosmological perturbations in different models of the early universe. A natural measure for the complexity of cosmological perturbations is based on the symplectic group, allowing us to identify…
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…
We investigate the problem of what evolutions an open quantum system described by a time-local Master equation can undergo with universal coherent controls. A series of conditions are given which exclude channels from being reachable by any…
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
We study the influence of conservation laws on entanglement growth. Focusing on systems with U(1) symmetry, i.e., conservation of charge or magnetization, that exhibits diffusive dynamics, we theoretically predict the growth of…
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…