Related papers: Topologically driven no-superposing theorem with a…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
While the no-cloning theorem forbids the perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can take…
Efficient encoding of classical data into quantum state -- currently referred to as quantum encoding -- holds crucial significance in quantum computation. For finite-size databases and qubit registers, a common strategy of the quantum…
Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in…
It is a fundamental consequence of the superposition principle for quantum states that there must exist non-orthogonal states, that is states that, although different, have a non-zero overlap. This finite overlap means that there is no way…
We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…
Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the classical Ising model. It is nonadaptive and therefore experimentally amenable.…
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
A novel no-go theorem is presented which sets a bound upon the extent to which '\Psi-epistemic' interpretations of quantum theory are able to explain the overlap between non-orthogonal quantum states in terms of an experimenter's ignorance…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a…
A new algorithm for estimating the fraction of numbers that is present in a superpositional state which satisfies a given condition,is introduced.This algorithm is conceptually simple and does not require quantum Fourier transform.Also the…
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
Quantum superposition is often phrased as the ability to add state vectors. In practice, however, the physical quantity is a ray (a rank-one projector), so each input specifies only a projector and leaves a gauge freedom in the phases of…
We study the question of what kind of a macroscopic superposition can(not) naturally exist as a ground state of some gapped local many-body Hamiltonian. We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian…
The initial state creation is a starting point of many quantum algorithms and usually is considered as a separate subroutine not included into the algorithm itself. There are many algorithms aimed on creation of special class of states. Our…
The inherent limitations of physical processes prevent the copying of arbitrary quantum states. Furthermore, even if we only aim to clone two distinct quantum states, it remains impossible unless they are mutually orthogonal. To overcome…
Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum…