Related papers: Quantum Arthur-Merlin with single-qubit measuremen…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be…
We define a semantic complexity class based on the model of quantum computing with just one pure qubit (as introduced by Knill and Laflamme) and discuss its computational power in terms of the problem of estimating the trace of a large…
We explore the possibility of using "weak" measurements to carry out quantum state tomography. Given a certain fixed number of copies of identically prepared states of a qubit, we simulate state tomography using weak as well as projective…
We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an…
In this paper, we study the following question: given a black box performing some unknown quantum measurement on a multi-qudit system, how do we test whether this measurement has certain property or is far away from having this property. We…
We prove that adiabatic computation is equivalent to standard quantum computation even when the adiabatic quantum system is restricted to be a set of particles on a one-dimensional chain. We give a construction that uses a 2-local…
A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur…
Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states. However, various applications, such as integer factorization, optimization,…
We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well know that a quantum circuit over the complex numbers can be…
In the measurement of a continuous observable Q, the pure components of the reduced state do, in general, depend on the initial state. For measurements which attempt to localize the measured system in a certain region R, the localized wave…
Quantum systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately,…
In this perspective we discuss verification of quantum devices in the context of specific examples, formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input…
We prove that a quantum circuit together with measurement apparatuses and EPR sources can be fully verified without any reference to some other trusted set of quantum devices. Our main assumption is that the physical system we are working…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
We briefly review single-qubit quantum process tomography for trace-preserving and nontrace-preserving processes, and derive explicit forms of the general constraints for fitting experimental data. These new forms provide additional insight…
We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per…
Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…
QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the ``Local Hamiltonian'' problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems.…
Quantum properties of the probes used to estimate a classical parameter can be used to attain accuracies that beat the standard quantum limit. When qubits are used to construct a quantum probe, it is known that initializing $n$ qubits in an…