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Quantum computing offers potential solutions for finding ground states in condensed-matter physics and chemistry. However, achieving effective ground state preparation is also computationally hard for arbitrary Hamiltonians. It is necessary…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
A cluster state cannot be a unique ground state of a two-body interacting Hamiltonian. Here, we propose the creation of a cluster state of logical qubits encoded in spin-1/2 particles by adiabatically weakening two-body interactions. The…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
How much information do we need about a process' past to faithfully simulate its future? The statistical complexity is a prominent quantifier of structure for stochastic processes. Quantum machines, however, can simulate classical…
A classical state-preparation device cannot generate states in relative superposition. We introduce classical models in which devices that are individually unable to generate states with relative superposition can be stochastically…
The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
Quantum annealers are emerging as programmable, dynamical experimental platforms for probing strongly correlated spin systems. Yet key thermal assumptions, chiefly a Gibbs-distributed output ensemble, remain unverified in the large-scale…
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the…
A quantum state is called concordant if it has zero quantum discord with respect to any part. By extension, a concordant computation is one such that the state of the computer, at each time step, is concordant. In this paper, I describe a…
We introduce a novel method of quantum emulation of a classical reversible cellular automaton. By applying this method to a chaotic cellular automaton, the obtained quantum many-body system thermalizes while all the energy eigenstates and…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum…
We develop a classical bit-flip correction method to mitigate measurement errors on quantum computers. This method can be applied to any operator, any number of qubits, and any realistic bit-flip probability. We first demonstrate the…
We develop a physics-based model for classical computation based on autonomous quantum thermal machines. These machines consist of few interacting quantum bits (qubits) connected to several environments at different temperatures. Heat flows…
We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0 quantum phase…
We investigate the correspondence between classical noise and quantum environments. Although it has been known that the classical noise can be mapped to the quantum environments only for pure dephasing and infinite-temperature dissipation…
Computation with the Ising model is central to future computing technologies like quantum annealing, adiabatic quantum computing, and thermodynamic classical computing. Traditionally, computed values have been equated with ground states.…