scholarly journals Hartree-Fock on a superconducting qubit quantum computer

Science ◽  
2020 ◽  
Vol 369 (6507) ◽  
pp. 1084-1089 ◽  
Author(s):  
◽  
Frank Arute ◽  
Kunal Arya ◽  
Ryan Babbush ◽  
Dave Bacon ◽  
...  
Keyword(s):  
Quantum Computer ◽  
Scaling Up ◽  
Mitigation Strategies ◽  
Superconducting Qubit ◽  
Hartree Fock ◽  
Givens Rotation ◽  
Error Mitigation ◽  
Fermionic Systems ◽  
Isomerization Mechanism ◽  
Computational Basis

The simulation of fermionic systems is among the most anticipated applications of quantum computing. We performed several quantum simulations of chemistry with up to one dozen qubits, including modeling the isomerization mechanism of diazene. We also demonstrated error-mitigation strategies based on N-representability that dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realized the Givens rotation approach to noninteracting fermion evolution, which we variationally optimized to prepare the Hartree-Fock wave function. This ubiquitous algorithmic primitive is classically tractable to simulate yet still generates highly entangled states over the computational basis, which allowed us to assess the performance of our hardware and establish a foundation for scaling up correlated quantum chemistry simulations.

scholarly journals Error mitigation with Clifford quantum-circuit data

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 592
Author(s):  
Piotr Czarnik ◽  
Andrew Arrasmith ◽  
Patrick J. Coles ◽  
Lukasz Cincio
Keyword(s):  
State Energy ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Training Data ◽  
Quantum Circuits ◽  
Accurate Estimation ◽  
Error Mitigation ◽  
Order Of Magnitude ◽  
Quantum Observables ◽  
Near Term

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

scholarly journals Sexual production of corals for reef restoration in the Anthropocene

2020 ◽  
Vol 635 ◽  
pp. 203-232 ◽  
Author(s):  
CJ Randall ◽  
AP Negri ◽  
KM Quigley ◽  
T Foster ◽  
GF Ricardo ◽  
...  
Keyword(s):  
Scaling Up ◽  
Mitigation Strategies ◽  
Broadcast Spawning ◽  
Reef Restoration ◽  
Coral Abundance ◽  
Coral Communities ◽  
Coral Reef Ecosystems ◽  
Sexual Production ◽  
Coral Recovery ◽  
Severe Disturbance

Coral-reef ecosystems are experiencing frequent and severe disturbance events that are reducing global coral abundance and potentially overwhelming the natural capacity for reefs to recover. While mitigation strategies for climate warming and other anthropogenic disturbances are implemented, coral restoration programmes are being established worldwide as an additional conservation measure to minimise coral loss and enhance coral recovery. Current restoration efforts predominantly rely on asexually produced coral fragments—a process with inherent practical constraints on the genetic diversity conserved and the spatial scale achieved. Because the resilience of coral communities has hitherto relied on regular renewal with natural recruits, the scaling-up of restoration programmes would benefit from greater use of sexually produced corals, which is an approach that is gaining momentum. Here we review the present state of knowledge of scleractinian coral sexual reproduction in the context of reef restoration, with a focus on broadcast-spawning corals. We identify key knowledge gaps and bottlenecks that currently constrain the sexual production of corals and consider the feasibility of using sexually produced corals for scaling-up restoration to the reef- and reef-system scales.

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.

Fundamentals of Quantum Computing, Quantum Supremacy, and Quantum Machine Learning

2021 ◽  
pp. 21-46
Author(s):  
Kamaljit I. Lakhtaria ◽  
Vrunda Gadesha
Keyword(s):  
Machine Learning ◽  
Quantum Computing ◽  
Quantum Computer ◽  
Error Mitigation ◽  
Fundamental Goal ◽  
Quantum Device ◽  
Quantum Machine Learning ◽  
Simulation Error ◽  
The Difference ◽  
Quantum Optimization

When we aim to demonstrate that a programmable quantum device can solve complex problems which cannot be addressed by classic computers, this fundamental goal is known as quantum supremacy. This concept has changed every fundamental rule of computation. In this chapter, the detailed concept of quantum computing and quantum supremacy is explained along with various open source tools and real-time applications of this technology. The major base concepts, quantum computing, the difference between classical and quantum computer on physical level, programing quantum device, and the experiment-quantum supremacy are explained conceptually. This chapter also includes an introduction of the tools Cirq and OpenFermion plus the applications like quantum simulation, error mitigation technique, quantum machine learning, and quantum optimization, which are explained with illustrations.

scholarly journals How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 433
Author(s):  
Craig Gidney ◽  
Martin Ekerå
Keyword(s):  
Finite Fields ◽  
Large Scale ◽  
Nearest Neighbor ◽  
Quantum Computer ◽  
Superconducting Qubit ◽  
Logical Qubits ◽  
Surface Code ◽  
Neighbor Connectivity ◽  
Approximate Cost ◽  
The Cost

We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Niu 1996, Zalka 2006, Fowler 2012, Ekerå-Håstad 2017, Ekerå 2017, Ekerå 2018, Gidney-Fowler 2019, Gidney 2019. We estimate the approximate cost of our construction using plausible physical assumptions for large-scale superconducting qubit platforms: a planar grid of qubits with nearest-neighbor connectivity, a characteristic physical gate error rate of 10−3, a surface code cycle time of 1 microsecond, and a reaction time of 10 microseconds. We account for factors that are normally ignored such as noise, the need to make repeated attempts, and the spacetime layout of the computation. When factoring 2048 bit RSA integers, our construction's spacetime volume is a hundredfold less than comparable estimates from earlier works (Van Meter et al. 2009, Jones et al. 2010, Fowler et al. 2012, Gheorghiu et al. 2019). In the abstract circuit model (which ignores overheads from distillation, routing, and error correction) our construction uses 3n+0.002nlg⁡n logical qubits, 0.3n3+0.0005n3lg⁡n Toffolis, and 500n2+n2lg⁡n measurement depth to factor n-bit RSA integers. We quantify the cryptographic implications of our work, both for RSA and for schemes based on the DLP in finite fields.

scholarly journals Simulating quench dynamics on a digital quantum computer with data-driven error mitigation

2021 ◽  
Author(s):  
Alejandro Sopena ◽  
Max Hunter Gordon ◽  
German Sierra ◽  
Esperanza López
Keyword(s):  
Quantum Computer ◽  
Data Driven ◽  
Error Mitigation ◽  
Quench Dynamics

scholarly journals Variational Quantum Computation of Excited States

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 156 ◽  
Author(s):  
Oscar Higgott ◽  
Daochen Wang ◽  
Stephen Brierley
Keyword(s):  
Excited State ◽  
Excited States ◽  
Quantum Algorithms ◽  
Reaction Rates ◽  
Mitigation Strategies ◽  
Quantum Computers ◽  
Error Mitigation ◽  
Near Term ◽  
Ground State Energies ◽  
High Depth

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.

IMPLEMENTING DEUTSCH–JOZSA ALGORITHM USING SUPERCONDUCTING QUBIT NETWORK

2008 ◽  
Vol 22 (31) ◽  
pp. 3035-3042 ◽  
Author(s):  
XIAO-HU ZHENG ◽  
MING YANG ◽  
PING DONG ◽  
ZHUO-LIANG CAO
Keyword(s):  
Josephson Junction ◽  
Quantum Computer ◽  
Superconducting Qubit ◽  
Charge Qubit ◽  
Current Technology

An improved architecture, which performs a universal set of gates by current biasing of coupling Josephson junction, has been proposed. This improvement is necessary to the realization of a functional and scalable quantum computer. The proposed architecture is in line with current technology. Secondly, we investigate a scheme for implementing the Deutsch–Jozsa algorithm via the improved architecture. It is a simple, scalable and feasible scheme for the implementation of the Deutsch–Jozsa algorithm based on the current-controlled superconducting charge qubit network.

CLUSTER STATE QUANTUM COMPUTATION AND THE REPEAT-UNTIL-SUCCESS SCHEME

2008 ◽  
Vol 22 (01n02) ◽  
pp. 33-43 ◽  
Author(s):  
L. C. KWEK
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Cluster State ◽  
Entangled State ◽  
Single Qubit ◽  
Computation Process ◽  
Measurement Results ◽  
Basic Ideas ◽  
The One ◽  
Computational Basis

Cluster state computation or the one way quantum computation (1WQC) relies on an initially highly entangled state (called a cluster state) and an appropriate sequence of single qubit measurements along different directions, together with feed-forward based on the measurement results, to realize a quantum computation process. The final result of the computation is obtained by measuring the last remaining qubits in the computational basis. In this short tutorial on cluster state quantum computation, we will also describe the basic ideas of a cluster state and proceed to describe how a single qubit operation can be done on a cluster state. Recently, we proposed a repeat-until-success (RUS) scheme that could effectively be used to realize one-way quantum computer on a hybrid system of photons and atoms. We will briefly describe this RUS scheme and show how it can be used to entangled two distant stationary qubits.

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