55 research outputs found
Quantum computation and simulation in silicon donors: from optically-controlled entangling gates to the Hubbard model
Quantum computing holds the promise to solve classically intractable problems. While some beyond-classical computations have been demonstrated, a useful application has yet to be shown. The biggest challenge is to scale up the number of quantum bits and simultaneously increase the accuracy of elementary operations in order to enable correction of errors. Silicon-based implementations promise to enable compatibility with complementary metal–oxide–semiconductor technology and hence a rapid scaling up. For the main part, this thesis is focussed on one particular quantum computing implementation in which the qubit is represented by the spin of the electron of a phosphorous atom in a silicon lattice. This implementation holds the record for the longest coherence times, of the order of days. So far, scalability with such donor-based computers is challenging because of the requirement to precisely position donors in the silicon lattice in architectures currently proposed. In this thesis, two architectures which do not require precise placement of donors are presented: an implementation of a quantum computer in a completely randomly doped sample and a scheme based on the electric dipolar long-range interactions between donors using a translation of ideas from implementations with laser-cooled atoms. Furthermore, we discuss the simulation of quantum materials with dopant atom arrays, in particular making precise predictions for feasible small-scale proof of principle experiments. Lastly, a condensed matter model which is known to be a symmetry protected topological state is implemented into a quantum software library originally written for qubits which is being expanded for use in continuous-variable systems. Our results work towards enabling the implementation of large-scale quantum computation in silicon
Probing finite-temperature observables in quantum simulators with short-time dynamics
Preparing low temperature states in quantum simulators is challenging due to
their almost perfect isolation from the environment. Here, we show how
finite-temperature observables can be obtained with an algorithm that consists
of classical importance sampling of initial states and a measurement of the
Loschmidt echo with a quantum simulator. We use the method as a
quantum-inspired classical algorithm and simulate the protocol with matrix
product states to analyze the requirements on a quantum simulator. This way, we
show that a finite temperature phase transition in the long-range transverse
field Ising model can be characterized in trapped ion quantum simulators. We
propose a concrete measurement protocol for the Loschmidt echo and discuss the
influence of measurement noise, dephasing, as well as state preparation and
measurement errors. We argue that the algorithm is robust against those
imperfections under realistic conditions. The algorithm can be readily applied
to study low-temperature properties in various quantum simulation platforms.Comment: 4+3 pages, 4+1 figure
Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements
The ground state of the spin-1 Affleck, Kennedy, Lieb and Tasaki (AKLT) model
is a paradigmatic example of both a matrix product state and a
symmetry-protected topological phase, and additionally holds promise as a
resource state for measurement-based quantum computation. Having a nonzero
correlation length, the AKLT state cannot be exactly prepared by a
constant-depth unitary circuit composed of local gates. In this work, we
demonstrate that this no-go limit can be evaded by augmenting a constant-depth
circuit with fusion measurements, such that the total preparation time is
independent of system size and entirely deterministic. We elucidate our
preparation scheme using the language of tensor networks, and furthermore show
that the symmetry of the AKLT state directly
affords this speed-up over previously known preparation methods. To demonstrate
the practical advantage of measurement-assisted preparation on noisy
intermediate-scale quantum (NISQ) devices, we carry out our protocol on an IBM
Quantum processor. We measure both the string order and entanglement spectrum
of prepared AKLT chains and, employing these as metrics, find improved results
over the known (purely unitary) sequential preparation approach. We conclude
with a demonstration of quantum teleportation using the AKLT state prepared by
our measurement-assisted scheme. This work thus serves to provide an efficient
strategy to prepare a specific resource in the form of the AKLT state and, more
broadly, experimentally demonstrates the possibility for realizable improvement
in state preparation afforded by measurement-based circuit depth reduction
strategies on NISQ-era devices.Comment: 17 pages, 8 figures. Supplemental Material: 13 pages, 11 figure
Leveraging Hamiltonian Simulation Techniques to Compile Operations on Bosonic Devices
Circuit QED enables the combined use of qubits and oscillator modes. Despite
a variety of available gate sets, many hybrid qubit-boson (i.e., oscillator)
operations are realizable only through optimal control theory (OCT) which is
oftentimes intractable and uninterpretable. We introduce an analytic approach
with rigorously proven error bounds for realizing specific classes of
operations via two matrix product formulas commonly used in Hamiltonian
simulation, the Lie--Trotter and Baker--Campbell--Hausdorff product formulas.
We show how this technique can be used to realize a number of operations of
interest, including polynomials of annihilation and creation operators, i.e.,
for integer . We show examples of this paradigm
including: obtaining universal control within a subspace of the entire Fock
space of an oscillator, state preparation of a fixed photon number in the
cavity, simulation of the Jaynes--Cummings Hamiltonian, simulation of the
Hong-Ou-Mandel effect and more. This work demonstrates how techniques from
Hamiltonian simulation can be applied to better control hybrid boson-qubit
devices.Comment: 48 pages, 5 figure
Bosonic Qiskit
The practical benefits of hybrid quantum information processing hardware that
contains continuous-variable objects (bosonic modes such as mechanical or
electromagnetic oscillators) in addition to traditional (discrete-variable)
qubits have recently been demonstrated by experiments with bosonic codes that
reach the break-even point for quantum error correction and by efficient
Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic
molecules that is well beyond the capabilities of current qubit-only hardware.
The goal of this Co-design Center for Quantum Advantage (C2QA) project is to
develop an instruction set architecture (ISA) for hybrid qubit/bosonic mode
systems that contains an inventory of the fundamental operations and
measurements that are possible in such hardware. The corresponding abstract
machine model (AMM) would also contain a description of the appropriate error
models associated with the gates, measurements and time evolution of the
hardware. This information has been implemented as an extension of Qiskit.
Qiskit is an opensource software development toolkit (SDK) for simulating the
quantum state of a quantum circuit on a system with Python 3.7+ and for running
the same circuits on prototype hardware within the IBM Quantum Lab. We
introduce the Bosonic Qiskit software to enable the simulation of hybrid
qubit/bosonic systems using the existing Qiskit software development kit. This
implementation can be used for simulating new hybrid systems, verifying
proposed physical systems, and modeling systems larger than can currently be
constructed. We also cover tutorials and example use cases included within the
software to study Jaynes- Cummings models, bosonic Hubbard models, plotting
Wigner functions and animations, and calculating maximum likelihood estimations
using Wigner functions
Observation of a finite-energy phase transition in a one-dimensional quantum simulator
One of the most striking many-body phenomena in nature is the sudden change
of macroscopic properties as the temperature or energy reaches a critical
value. Such equilibrium transitions have been predicted and observed in two and
three spatial dimensions, but have long been thought not to exist in
one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out
that a phase transition in 1D can occur in the presence of long-range
interactions, but an experimental realization has so far not been achieved due
to the requirement to both prepare equilibrium states and realize sufficiently
long-range interactions. Here we report on the first experimental demonstration
of a finite-energy phase transition in 1D. We use the simple observation that
finite-energy states can be prepared by time-evolving product initial states
and letting them thermalize under the dynamics of a many-body Hamiltonian. By
preparing initial states with different energies in a 1D trapped-ion quantum
simulator, we study the finite-energy phase diagram of a long-range interacting
quantum system. We observe a ferromagnetic equilibrium phase transition as well
as a crossover from a low-energy polarized paramagnet to a high-energy
unpolarized paramagnet in a system of up to spins, in excellent agreement
with numerical simulations. Our work demonstrates the ability of quantum
simulators to realize and study previously inaccessible phases at finite energy
density.Comment: 5+9 pages, 4+14 figure
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Atomic-Scale Patterning of Arsenic in Silicon by Scanning Tunneling Microscopy
Over the past two decades, prototype devices for future classical and quantum computing technologies have been fabricated by using scanning tunneling microscopy and hydrogen resist lithography to position phosphorus atoms in silicon with atomic-scale precision. Despite these successes, phosphine remains the only donor precursor molecule to have been demonstrated as compatible with the hydrogen resist lithography technique. The potential benefits of atomic-scale placement of alternative dopant species have, until now, remained unexplored. In this work, we demonstrate the successful fabrication of atomic-scale structures of arsenic-in-silicon. Using a scanning tunneling microscope tip, we pattern a monolayer hydrogen mask to selectively place arsenic atoms on the Si(001) surface using arsine as the precursor molecule. We fully elucidate the surface chemistry and reaction pathways of arsine on Si(001), revealing significant differences to phosphine. We explain how these differences result in enhanced surface immobilization and in-plane confinement of arsenic compared to phosphorus, and a dose-rate independent arsenic saturation density of 0.24 ± 0.04 monolayers. We demonstrate the successful encapsulation of arsenic delta-layers using silicon molecular beam epitaxy, and find electrical characteristics that are competitive with equivalent structures fabricated with phosphorus. Arsenic delta-layers are also found to offer confinement as good as similarly prepared phosphorus layers, while still retaining >80% carrier activation and sheet resistances of <2 kω/square. These excellent characteristics of arsenic represent opportunities to enhance existing capabilities of atomic-scale fabrication of dopant structures in silicon, and may be important for three-dimensional devices, where vertical control of the position of device components is critical. Copyright © 2020 American Chemical Society
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