scholarly journals Efficient verification of Boson Sampling

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 578
Author(s):  
Ulysse Chabaud ◽  
Frédéric Grosshans ◽  
Elham Kashefi ◽  
Damian Markham
Keyword(s):  
Large Class ◽  
Single Mode ◽  
Continuous Variable ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Classical Simulation ◽  
Efficient Verification ◽  
Quantum Speedup ◽  
Important Milestone ◽  
Boson Sampling

The demonstration of quantum speedup, also known as quantum computational supremacy, that is the ability of quantum computers to outperform dramatically their classical counterparts, is an important milestone in the field of quantum computing. While quantum speedup experiments are gradually escaping the regime of classical simulation, they still lack efficient verification protocols and rely on partial validation. Here we derive an efficient protocol for verifying with single-mode Gaussian measurements the output states of a large class of continuous-variable quantum circuits demonstrating quantum speedup, including Boson Sampling experiments, thus enabling a convincing demonstration of quantum speedup with photonic computing. Beyond the quantum speedup milestone, our results also enable the efficient and reliable certification of a large class of intractable continuous-variable multimode quantum states.

Towards Compact Modeling of Noisy Quantum Computers: A Molecular-Spin-Qubit Case of Study

2022 ◽  
Vol 18 (1) ◽  
pp. 1-26
Author(s):  
Mario Simoni ◽  
Giovanni Amedeo Cirillo ◽  
Giovanna Turvani ◽  
Mariagrazia Graziano ◽  
Maurizio Zamboni
Keyword(s):  
Physical Simulation ◽  
Quantum Circuits ◽  
Compact Modeling ◽  
Quantum Computers ◽  
Expected Performance ◽  
Classical Simulation ◽  
Spin Qubit ◽  
Compact Models ◽  
Standard Formalism ◽  
Definition Of

Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.

scholarly journals Unsupervised event classification with graphs on classical and photonic quantum computers

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Andrew Blance ◽  
Michael Spannowsky
Keyword(s):  
Anomaly Detection ◽  
Clustering Algorithm ◽  
High Energy ◽  
New Physics ◽  
Continuous Variable ◽  
Quantum Computers ◽  
Detection Model ◽  
Novel Method ◽  
Formula Complexity ◽  
Boson Sampling

Abstract Photonic Quantum Computers provide several benefits over the discrete qubit-based paradigm of quantum computing. By using the power of continuous-variable computing we build an anomaly detection model to use on searches for New Physics. Our model uses Gaussian Boson Sampling, a #P-hard problem and thus not efficiently accessible to classical devices. This is used to create feature vectors from graph data, a natural format for representing data of high-energy collision events. A simple K-means clustering algorithm is used to provide a baseline method of classification. We then present a novel method of anomaly detection, combining the use of Gaussian Boson Sampling and a quantum extension to K-means known as Q-means. This is found to give equivalent results compared to the classical clustering version while also reducing the $$ \mathcal{O} $$ O complexity, with respect to the sample’s feature-vector length, from $$ \mathcal{O}(N) $$ O N to $$ \mathcal{O}\left(\log (N)\right) $$ O log N .

scholarly journals Simulating quantum computers with probabilistic methods

2011 ◽  
Vol 11 (9&10) ◽  
pp. 784-812 ◽  
Author(s):  
Maarten Van den Nest
Keyword(s):  
Fourier Spectrum ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Probabilistic Methods ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Partition Functions ◽  
Classical Simulation ◽  
Last Stage ◽  
Standard Techniques

We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate new classes of classically simulatable quantum circuits where standard techniques relying on the exact computation of measurement probabilities fail to provide efficient simulations. For example, we show how various concatenations of matchgate, Toffoli, Clifford, bounded-depth, Fourier transform and other circuits are classically simulatable. We also prove that sparse quantum circuits as well as circuits composed of CNOT and $\exp[{i\theta X}]$ gates can be simulated classically. In a second part, we apply our results to the simulation of quantum algorithms. It is shown that a recent quantum algorithm, concerned with the estimation of Potts model partition functions, can be simulated efficiently classically. Finally, we show that the exponential speed-ups of Simon's and Shor's algorithms crucially depend on the very last stage in these algorithms, dealing with the classical postprocessing of the measurement outcomes. Specifically, we prove that both algorithms would be classically simulatable if the function classically computed in this step had a sufficiently peaked Fourier spectrum.

scholarly journals Coreset Clustering on Small Quantum Computers

Electronics ◽  
2021 ◽  
Vol 10 (14) ◽  
pp. 1690
Author(s):  
Teague Tomesh ◽  
Pranav Gokhale ◽  
Eric R. Anschuetz ◽  
Frederic T. Chong
Keyword(s):  
Quantum Algorithms ◽  
Quantum Computers ◽  
Data Sets ◽  
New Paradigm ◽  
Data Set ◽  
Small Quantum ◽  
Natural Data ◽  
Near Term ◽  
Classical Computing ◽  
Quantum Speedup

Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare the performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.

scholarly journals Decoherence dynamics estimation for superconducting gate-model quantum computers

2020 ◽  
Vol 19 (10) ◽  
Author(s):  
Laszlo Gyongyosi
Keyword(s):  
Gaussian Noise ◽  
Quantum Computer ◽  
Computer Architectures ◽  
Quantum Circuits ◽  
Optimal Placement ◽  
Quantum Computers ◽  
Intermediate Scale ◽  
Layout Generation ◽  
Quantum Technology ◽  
Physical Layout

Abstract Superconducting gate-model quantum computer architectures provide an implementable model for practical quantum computations in the NISQ (noisy intermediate scale quantum) technology era. Due to hardware restrictions and decoherence, generating the physical layout of the quantum circuits of a gate-model quantum computer is a challenge. Here, we define a method for layout generation with a decoherence dynamics estimation in superconducting gate-model quantum computers. We propose an algorithm for the optimal placement of the quantum computational blocks of gate-model quantum circuits. We study the effects of capacitance interference on the distribution of the Gaussian noise in the Josephson energy.

scholarly journals Option Pricing using Quantum Computers

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 291 ◽  
Author(s):  
Nikitas Stamatopoulos ◽  
Daniel J. Egger ◽  
Yue Sun ◽  
Christa Zoufal ◽  
Raban Iten ◽  
...  
Keyword(s):  
Option Pricing ◽  
Quantum Computer ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Barrier Options ◽  
Error Mitigation ◽  
Quantum Device ◽  
Amplitude Estimation ◽  
Simulation Results ◽  
Path Dependent

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

A FRAMEWORK FOR REPRESENTING AND PRODUCING MOVIES ON QUANTUM COMPUTERS

2011 ◽  
Vol 09 (06) ◽  
pp. 1459-1497 ◽  
Author(s):  
ABDULLAH M. ILIYASU ◽  
PHUC Q. LE ◽  
FANGYAN DONG ◽  
KAORU HIROTA
Keyword(s):  
Quantum Circuits ◽  
Quantum Computers ◽  
Transition Rates ◽  
Projective Measurement ◽  
Physical Realization ◽  
Quantum Devices ◽  
Frame Transition ◽  
Key Frames ◽  
Movie Script ◽  
The Physical Realization

Adopting a generalization of the DiVincenzo criteria for the physical realization of quantum devices, a standalone component each, is proposed to prepare, manipulate, and measure the various content required to represent and produce movies on quantum computers. The quantum CD encodes, prepares, and initializes the broad content or key frames conveying the movie script. The quantum player uses the simple motion operations to manipulate the contents of the key frames in order to interpolate the missing viewing frames required to effectively depict the shots and scenes of the movie. The movie reader combines the projective measurement technique and the ancilla-driven quantum computation to retrieve the classical movie sequence comprising of both the key and viewing frames for each shot. At appropriate frame transition rates, this sequence creates the impression of continuity in order to depict the various movements and actions in the movie. Two well-thought-out examples demonstrate the feasibility of the proposed framework. Concatenated, these components together facilitate the proposed framework for quantum movie representation and production, thus, opening the door towards manipulating quantum circuits aimed at applications for information representation and processing.

scholarly journals Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Agung Budiyono ◽  
Hermawan K. Dipojono
Keyword(s):  
Phase Space ◽  
Continuous Variable ◽  
Complex Hilbert Space ◽  
Quantum Circuits ◽  
Space Distribution ◽  
Space Representation ◽  
Specific Class ◽  
Expectation Values ◽  
Conceptual Tool ◽  
Quantum Uncertainty

Abstract We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable—after the Heisenberg evolution associated with the circuits—is at most second order in momentum. The classical computational algorithm exploits a specific epistemic restriction in classical phase space which directly captures the quantum uncertainty relation, to transform the quantum circuits in the complex Hilbert space into classical albeit unconventional stochastic processes in the phase space. The resulting multidimensional integral is then evaluated using the Monte Carlo sampling method. The convergence rate of the classical sampling algorithm is determined by the variance of the classical physical quantity over the epistemically restricted phase space distribution. The work shows that for the specific class of computational schemes, Wigner negativity is not a sufficient resource for quantum speedup. It highlights the potential role of the epistemic restriction as an intuitive conceptual tool which may be used to study the boundary between quantum and classical computations.

scholarly journals Quantum arithmetic operations based on quantum fourier transform on signed integers

2020 ◽  
Vol 18 (06) ◽  
pp. 2050035
Author(s):  
Engin Şahin
Keyword(s):  
Fourier Transform ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Arithmetic Operations ◽  
Absolute Value ◽  
Addition And Subtraction ◽  
Quantum Arithmetic

The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction, division and exponentiation operations are presented. The proposed arithmetic operations can perform nonmodular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two’s complement, absolute value and comparison operations are also presented by using the proposed QFT-based addition and subtraction operations.

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