11 research outputs found
Gap analysis for an adiabatic approach to the Exact Cover problem
Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2018, Tutor: José Ignacio LatorreThis paper studies the Exact Cover problem through the lens of Adiabatic Quantum Computation. It contains an introduction to the way an adiabatic computation solves a satisfiability problem, as well as further discussion on how finding and exploiting symmetries hidden in the clauses of the problem can create a speed-up over the conventional procedur
Quantum Search for Scaled Hash Function Preimages
We present the implementation of Grover's algorithm in a quantum simulator to
perform a quantum search for preimages of two scaled hash functions, whose
design only uses modular addition, word rotation, and bitwise exclusive or. Our
implementation provides the means to assess with precision the scaling of the
number of gates and depth of a full-fledged quantum circuit designed to find
the preimages of a given hash digest. The detailed construction of the quantum
oracle shows that the presence of AND gates, OR gates, shifts of bits and the
reuse of the initial state along the computation, require extra quantum
resources as compared with other hash functions based on modular additions, XOR
gates and rotations. We also track the entanglement entropy present in the
quantum register at every step along the computation, showing that it becomes
maximal at the inner core of the first action of the quantum oracle, which
implies that no classical simulation based on Tensor Networks would be of
relevance. Finally, we show that strategies that suggest a shortcut based on
sampling the quantum register after a few steps of Grover's algorithm can only
provide some marginal practical advantage in terms of error mitigation.Comment: 24 pages, 14 figure
An Optimized Quantum Implementation of ISD on Scalable Quantum Resources
The security of code based constructions is usually assessed by Information Set Decoding (ISD) algorithms. In the quantum setting, amplitude amplification yields an asymptotic square root gain over the classical analogue. However, it is still unclear whether a real quantum circuit could yield actual improvements or suffer an enormous overhead due to its implementation. This leads to different considerations of these quantum attacks in the security analysis of code based proposals. In this work we clarify this doubt by giving the first quantum circuit design of the fully-fledged ISD procedure, an implementation in the quantum simulation library Qibo as well as precise estimates of its complexities. We show that against common belief, Prange\u27s ISD algorithm can be implemented rather efficiently on a quantum computer, namely with only a logarithmic overhead in circuit depth compared to a classical implementation.
As another major contribution, we leverage the idea of classical co-processors to design hybrid classical-quantum trade-offs, that allow to tailor the necessary qubits to any available amount, while still providing quantum speedups. Interestingly, when constraining the width of the circuit instead of its depth we are able to overcome previous optimality results on constraint quantum search
Hybrid Decoding -- Classical-Quantum Trade-Offs for Information Set Decoding
The security of code-based constructions is usually assessed by Information Set Decoding (ISD) algorithms. In the quantum setting, amplitude amplification yields an asymptotic square root gain over the classical analogue. However, already the most basic ISD algorithm by Prange suffers enormous width requirements caused by the quadratic description length of the underlying problem. Even if polynomial, this need for qubits is one of the biggest challenges considering the application of real quantum circuits in the near- to mid-term.
In this work we overcome this issue by presenting the first hybrid ISD algorithms that allow to tailor the required qubits to any available amount while still providing quantum speedups of the form , , where is the running time of the purely classical procedure. Interestingly, when constraining the width of the circuit instead of its depth we are able to overcome previous optimality results on constraint quantum search.
Further we give an implementation of the fully-fledged quantum ISD procedure and the classical co-processor using the quantum simulation library Qibo and SageMath
Quantum unary approach to option pricing
We present a quantum algorithm for European option pricing in finance, where
the key idea is to work in the unary representation of the asset value. The
algorithm needs novel circuitry and is divided in three parts: first, the
amplitude distribution corresponding to the asset value at maturity is
generated using a low depth circuit; second, the computation of the expected
return is computed with simple controlled gates; and third, standard Amplitude
Estimation is used to gain quantum advantage. On the positive side, unary
representation remarkably simplifies the structure and depth of the quantum
circuit. Amplitude distributions uses quantum superposition to bypass the role
of classical Monte Carlo simulation. The unary representation also provides a
post-selection consistency check that allows for a substantial mitigation in
the error of the computation. On the negative side, unary representation
requires linearly many qubits to represent a target probability distribution,
as compared to the logarithmic scaling of binary algorithms. We compare the
performance of both unary vs. binary option pricing algorithms using error
maps, and find that unary representation may bring a relevant advantage in
practice for near-term devices.Comment: 14 (main) + 10 (appendix) pages, 22 figures. Final peer-reviewed
version, published in PRA. All suggestions from the referees have been
considered. We thank the referees and the journal for all the wor
Variational Quantum Eigensolver for SU() Fermions
Variational quantum algorithms aim at harnessing the power of noisy
intermediate-scale quantum computers, by using a classical optimizer to train a
parameterized quantum circuit to solve tractable quantum problems. The
variational quantum eigensolver is one of the aforementioned algorithms
designed to determine the ground-state of many-body Hamiltonians. Here, we
apply the variational quantum eigensolver to study the ground-state properties
of -component fermions. With such knowledge, we study the persistent current
of interacting SU() fermions, which is employed to reliably map out the
different quantum phases of the system. Our approach lays out the basis for a
current-based quantum simulator of many-body systems that can be implemented on
noisy intermediate-scale quantum computers.Comment: 9 pages, 8 figure
Qibolab: an open-source hybrid quantum operating system
We present Qibolab, an open-source software library for quantum hardware
control integrated with the Qibo quantum computing middleware framework.
Qibolab provides the software layer required to automatically execute
circuit-based algorithms on custom self-hosted quantum hardware platforms. We
introduce a set of objects designed to provide programmatic access to quantum
control through pulses-oriented drivers for instruments, transpilers and
optimization algorithms. Qibolab enables experimentalists and developers to
delegate all complex aspects of hardware implementation to the library so they
can standardize the deployment of quantum computing algorithms in a
hardware-agnostic way. We first describe the status of all components of the
library, then we show examples of control setup for superconducting qubits
platforms. Finally, we present successful application results related to
circuit-based algorithms.Comment: 18 pages, 10 figures, code available at
https://github.com/qiboteam/qibola
Efficient quantum interpolation of natural data
We present efficient methods to interpolate data with a quantum computer that
complement uploading techniques and quantum post-processing. The quantum
algorithms are supported by the efficient Quantum Fourier Transform (QFT) and
classical signal and imaging processing techniques, and open the door of
quantum advantage to relevant families of data. We showcase a QFT interpolation
method, a Quantum Cosine Transform (QCT) interpolation geared towards natural
data, and we improve upon them by utilizing a quantum circuit's capabilities of
processing data in superposition. A novel circuit for the QCT is presented. We
demonstrate the methods on probability distributions and quantum encoded
images, and discuss the precision of the resulting interpolations.Comment: Main: 6 pages, 4 figures. Appendix: 3 pages, 2 figures. Code
available onlin
Towards an open-source framework to perform quantum calibration and characterization
In this proceedings we present Qibocal, an open-source software package for calibration and characterization of quantum processing units (QPUs) based on the Qibo framework. Qibocal is specifically designed for self-hosted QPUs and provides the groundwork to easily develop, deploy and distribute characterization and calibration routines for all levels of hardware abstraction. Qibocal is based on a modular QPU platform agnostic approach and it provides a general purpose toolkit for superconducting qubits with the possibility of extensions to other quantum technologies. After motivating the need for such a module, we explain the program's flow and show examples of actual use for QPU calibration. We also showcase additional features provided by the library including automatic report generation and live plotting