Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with minor typos corrected.

Quantum Abacus for counting and factorizing numbers

We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base 2, base 3, or base d representation. In operating the algorithm, the number n < N = d^K is read into a K-qudit register through its interaction with a stream of n particles passing in a nearby wire; this step corresponds to a quantum Fourier transformation from the Hilbert space of particles to the Hilbert space of qudit states. An inverse quantum Fourier transformation provides the number n in the base d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semi-classical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows to find the powers of 2, 3, and other primes d in the number n. We show, that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter's performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure a voltage (analog to digital converter) and a simple procedure to entangle multi-particle states.Comment: 23 pages, 15 figure

Experimental optical phase measurement approaching the exact Heisenberg limit

The use of quantum resources can provide measurement precision beyond the shot-noise limit (SNL). The task of ab initio optical phase measurement---the estimation of a completely unknown phase---has been experimentally demonstrated with precision beyond the SNL, and even scaling like the ultimate bound, the Heisenberg limit (HL), but with an overhead factor. However, existing approaches have not been able---even in principle---to achieve the best possible precision, saturating the HL exactly. Here we demonstrate a scheme to achieve true HL phase measurement, using a combination of three techniques: entanglement, multiple samplings of the phase shift, and adaptive measurement. Our experimental demonstration of the scheme uses two photonic qubits, one double passed, so that, for a successful coincidence detection, the number of photon-passes is $N=3$. We achieve a precision that is within $4\%$ of the HL, surpassing the best precision theoretically achievable with simpler techniques with $N=3$. This work represents a fundamental achievement of the ultimate limits of metrology, and the scheme can be extended to higher $N$ and other physical systems.Comment: (12 pages, 6 figures), typos correcte

Integrated Photonic Sensing

Loss is a critical roadblock to achieving photonic quantum-enhanced technologies. We explore a modular platform for implementing integrated photonics experiments and consider the effects of loss at different stages of these experiments, including state preparation, manipulation and measurement. We frame our discussion mainly in the context of quantum sensing and focus particularly on the use of loss-tolerant Holland-Burnett states for optical phase estimation. In particular, we discuss spontaneous four-wave mixing in standard birefringent fibre as a source of pure, heralded single photons and present methods of optimising such sources. We also outline a route to programmable circuits which allow the control of photonic interactions even in the presence of fabrication imperfections and describe a ratiometric characterisation method for beam splitters which allows the characterisation of complex circuits without the need for full process tomography. Finally, we present a framework for performing state tomography on heralded states using lossy measurement devices. This is motivated by a calculation of the effects of fabrication imperfections on precision measurement using Holland-Burnett states.Comment: 19 pages, 7 figure

On Quantum Algorithms

Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle) interferometers. We show how most known quantum algorithms, including quantum algorithms for factorising and counting, may be cast in this manner. Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms.Comment: 15 pages, 8 figure

A novel haptic model and environment for maxillofacial surgical operation planning and manipulation

This paper presents a practical method and a new haptic model to support manipulations of bones and their segments during the planning of a surgical operation in a virtual environment using a haptic interface. To perform an effective dental surgery it is important to have all the operation related information of the patient available beforehand in order to plan the operation and avoid any complications. A haptic interface with a virtual and accurate patient model to support the planning of bone cuts is therefore critical, useful and necessary for the surgeons. The system proposed uses DICOM images taken from a digital tomography scanner and creates a mesh model of the filtered skull, from which the jaw bone can be isolated for further use. A novel solution for cutting the bones has been developed and it uses the haptic tool to determine and define the bone-cutting plane in the bone, and this new approach creates three new meshes of the original model. Using this approach the computational power is optimized and a real time feedback can be achieved during all bone manipulations. During the movement of the mesh cutting, a novel friction profile is predefined in the haptical system to simulate the force feedback feel of different densities in the bone

On the novelty, efficacy, and significance of weak measurements for quantum tomography

The use of weak measurements for performing quantum tomography is enjoying increased attention due to several recent proposals. The advertised merits of using weak measurements in this context are varied, but are generally represented by novelty, increased efficacy, and foundational significance. We critically evaluate two proposals that make such claims and find that weak measurements are not an essential ingredient for most of their advertised features.Comment: 12 pages, 10 figure