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As quantum computing evolves, a new era unfolds, promising breakthroughs that span industries, sciences, and the very fabric of our technological future.

In the realm of modern technology, where the pursuit of computational power knows no bounds, quantum computing has emerged as a groundbreaking paradigm shift. This article explores the significance of quantum computing and traces its evolution, providing insights into its transformative potential for the future.

Quantum development frameworks and simulation tools play a pivotal role in quantum computing, providing essential resources for researchers and developers to explore and harness the unprecedented capabilities of quantum systems. These tools are the backbone of quantum programming, offering platforms for designing, simulating, and optimising quantum algorithms before deployment on actual quantum processors. These frameworks and tools, which include IBMs Qiskit and Googles Cirq, not only propel quantum algorithm development but also contribute to the collaborative and dynamic landscape of quantum research and innovation.

Qiskit stands at the forefront of quantum development frameworks, spearheaded by IBM as an open source initiative. It provides a robust and comprehensive toolkit for quantum computing, offering a wide array of features that cater to both novices and seasoned quantum developers.

Key components

Qiskit Terra: At the heart of Qiskit is Terra, the foundational component for quantum circuit design and optimisation. Terra allows users to define and manipulate quantum circuits with ease, enabling the creation of complex algorithms through a straightforward and intuitive interface.

Qiskit Aer: Qiskit Aer is a high-performance simulator designed for accurate quantum circuit simulations. This component is instrumental during the development phase, allowing developers to test and debug quantum algorithms before deploying them on actual quantum hardware. Aer supports a variety of noise models, enhancing the fidelity of simulations.

Qiskit Ignis: Addressing the challenges of noisy quantum processors, Qiskit Ignis provides tools for characterising and mitigating errors in quantum systems. Ignis enables developers to optimise the performance of quantum algorithms in the presence of noise, contributing to the advancement of practical quantum computing.

Qiskit Aqua: Qiskit Aqua extends Qiskits capabilities into domain-specific libraries for quantum applications. It includes functionalities tailored for chemistry, finance, and optimisation, opening doors to innovative solutions in fields that stand to benefit from quantum computing advancements.

Integration with quantum hardware

Qiskit seamlessly integrates with IBMs cloud-based quantum processors, allowing developers to execute their quantum algorithms on real quantum hardware. This integration facilitates a bridge between simulation and practical implementation, providing valuable insights into the behaviour and performance of algorithms in a quantum environment.

The future of Qiskit

As quantum computing continues to evolve, Qiskit remains at the forefront, adapting to technological advancements and expanding its capabilities. With its modular architecture, rich documentation, and constant updates, Qiskit continues to be a cornerstone for those navigating the quantum landscape, empowering them to explore, experiment, and innovate in the realm of quantum computing.

Cirq, developed by Google, is purpose-built for crafting and optimising quantum circuits. This powerful tool in the quantum programmers arsenal offers specialised features tailored to the unique challenges posed by quantum computing.

Key components

Qubits and circuits: Cirq provides an intuitive approach to defining qubits and constructing quantum circuits. Developers can seamlessly express quantum algorithms in a language that reflects the intricacies of quantum mechanics, enhancing the clarity and expressiveness of quantum programming.

Noise models and quantum virtual machines: Understanding and mitigating the impact of noise on quantum algorithms is critical. Cirq allows developers to simulate and analyse noise models, providing insights into the behaviour of algorithms in real-world, imperfect quantum processors. Quantum virtual machines in Cirq enable simulations on classical hardware, facilitating robust testing and debugging.

Integration with Google quantum processors: Cirq seamlessly integrates with Googles quantum processors, offering a direct path for developers to implement and execute their quantum algorithms on cutting-edge hardware. This integration aligns Cirq with Googles quantum computing efforts, providing users with the opportunity to harness the capabilities of actual quantum processors.

Future endeavours

Googles commitment to pushing the boundaries of quantum research ensures that Cirq remains a dynamic and adaptable framework, offering a platform that bridges the gap between theoretical quantum algorithms and practical implementations on emerging quantum processors.

The Microsoft Quantum Development Kit represents a comprehensive and integrated set of tools, designed to empower developers in the realm of quantum computing. Anchored by the Q# programming language, this kit combines a versatile programming language, a robust development environment, and powerful simulators to facilitate quantum algorithm development.

Key components

Q# programming language: Central to the quantum development kit is Q#, a domain-specific programming language tailored for expressing quantum algorithms. Q# seamlessly integrates with classical languages like C# and F#, allowing developers to create hybrid quantum-classical applications with ease. Its high-level abstractions simplify quantum circuit design.

Quantum simulators: The Quantum Development Kit comes equipped with quantum simulators that enable efficient testing and debugging of quantum code. These simulators provide an essential environment for developers to simulate the behaviour of quantum algorithms on classical hardware, aiding in the refinement of quantum solutions before deploying them on actual quantum processors.

Quantum libraries and samples: The kit includes a rich set of quantum libraries and code samples, accelerating the learning curve for developers venturing into the quantum landscape. These resources provide practical insights into the implementation of quantum algorithms and applications across various domains.

Outlook and evolution

As quantum computing advances, Microsofts Quantum Development Kit continues to evolve. With ongoing updates and enhancements, it remains at the forefront of quantum development frameworks. The commitment to combining theoretical advances with practical tools positions it as a key player in shaping the future of quantum computing and its integration into mainstream application development.

Quipper is a distinctive player in the quantum computing landscape, offering a functional, scalable programming language designed for expressing quantum algorithms. Developed through a collaboration between Microsoft Research and the University of Oxford, Quipper embraces the principles of functional programming to provide a structured and versatile approach to quantum circuit design.

Key features

Functional quantum programming: Quippers primary strength lies in its functional programming paradigm, allowing developers to express quantum algorithms in a modular and composable manner. This functional approach enhances code readability and maintainability, offering a unique perspective in the world of quantum programming.

Modularity and scalability: Quipper excels in handling complex quantum algorithms by providing a modular and scalable architecture. Quantum circuits can be designed in a hierarchical fashion, facilitating the construction of intricate algorithms while maintaining code clarity. This modularity enables quantum programmers to build on existing libraries and efficiently manage the complexity of large-scale quantum computations.

Quantum gate library: Quipper comes equipped with an extensive library of quantum gates and operations. This library simplifies the process of designing quantum circuits, allowing developers to leverage a broad range of quantum gates seamlessly. The library is an essential resource for quantum information scientists and researchers working on diverse quantum algorithms.

Future prospects

As the field of quantum computing evolves, Quipper stands poised to play a pivotal role in advancing functional quantum programming. Its focus on modularity, scalability, and integration with classical languages positions it as a tool that could significantly impact the development of intricate quantum algorithms and contribute to the broader landscape of quantum software development.

QuTiP, short for Quantum Toolbox in Python, is a powerful open source software suite designed for quantum computing research. Leveraging the versatility and ease of use of the Python programming language, QuTiP provides a comprehensive set of tools for simulating and analysing quantum systems, making it an invaluable resource for researchers and developers in the quantum information science community.

Key features

Python-based quantum simulation: At its core, QuTiP is built on Python, making it accessible to a wide range of researchers and developers familiar with this popular programming language. Its Pythonic syntax and integration with other scientific computing libraries contribute to a seamless and user-friendly experience.

Quantum operator library: QuTiP offers a rich library of quantum operators and functions, allowing researchers to model and simulate a diverse array of quantum systems. This includes the ability to represent Hamiltonians, Lindblad operators for open quantum systems, and other essential quantum operators, providing a flexible foundation for quantum dynamics simulations.

Quantum states and dynamics: Researchers benefit from QuTiPs capabilities in simulating quantum states and the dynamics of open quantum systems. This is crucial for studying the behaviour of quantum systems over time, making QuTiP an ideal tool for investigations in quantum information theory, quantum optics, and related fields.

Visualisation tools: QuTiP includes visualisation tools that aid researchers in gaining insights into quantum systems. The ability to plot and visualise quantum states, probabilities, and expectation values provides an intuitive means of interpreting simulation results, enhancing the understanding of complex quantum phenomena.

Application areas

Quantum optics: QuTiP is extensively used in the simulation of quantum optics experiments, including the study of cavity quantum electrodynamics, quantum optics phenomena, and quantum information processing with optical systems.

Quantum information processing: Researchers utilise QuTiP for simulating quantum algorithms, quantum error correction, and other aspects of quantum information processing. Its flexibility makes it suitable for a wide range of quantum computing applications.

Quantum control: QuTiP supports the simulation of quantum control scenarios, allowing researchers to explore optimal control strategies for manipulating quantum systems.

Future development

As the field of quantum computing continues to advance, QuTiP remains actively developed, adapting to emerging research trends and technological advancements. Its open source nature ensures that the community-driven efforts behind QuTiP contribute to its relevance in the rapidly evolving landscape of quantum research and computation.

Quantum Tic-Tac-Toe: Quantum Tic-Tac-Toe is a fascinating adaptation of the traditional game, injecting quantum mechanics into the classic grid-based strategy. In this quantum variant, players are introduced to the concept of superposition, allowing a quantum piece to exist in multiple states simultaneously. Unlike classical Tic-Tac-Toe, where each cell can either be X or O or empty, quantum superposition introduces the possibility for a cell to contain both X and O states simultaneously until observed.

Quantum Chess: Quantum Chess fuses classic chess strategy with the principles of quantum mechanics. In this variant, developed by physicist Chris Cantwell, each piece on the board is assigned a quantum state, allowing it to exist in a superposition of multiple classical states simultaneously. This introduces an entirely new layer of complexity and strategy, as players can leverage the principles of superposition and entanglement to create intricate moves and surprise their opponents. The game introduces the concept of quantum moves, where a player can move a piece in a superposition of multiple ways until the move is observed. Additionally, entanglement enables the connection of pieces states across the board, causing the state of one piece to instantaneously affect another. Quantum Chess challenges players to think beyond the classical constraints of traditional chess, encouraging a deeper understanding of quantum concepts while delivering an intellectually stimulating and entertaining gameplay experience.

Quantum optimisation: Quantum optimisation represents a revolutionary paradigm in problem-solving, leveraging the computational capabilities of quantum computers to address complex optimisation challenges. Traditional optimisation problems, which arise in fields such as logistics, finance, and artificial intelligence, often become exponentially more challenging as the scale of the problem increases. Quantum optimisation algorithms, like the Quantum Approximate Optimisation Algorithm (QAOA), harness quantum parallelism and interference to explore vast solution spaces efficiently. Quantum optimisation algorithms excel at finding optimal solutions by leveraging the inherent properties of superposition and entanglement. These algorithms can potentially outperform classical optimisation approaches for certain problem instances, offering a promising avenue for industries seeking to enhance efficiency and streamline decision-making processes.

Quantum computing holds immense promise in transforming both cybersecurity and Artificial Intelligence (AI) landscapes. The advent of quantum computers poses a potential threat to classical cryptographic methods, particularly those relying on factorisation and discrete logarithm problems. Conversely, quantum-safe cryptographic algorithms, such as those based on lattice cryptography or hash-based techniques, are being developed to fortify digital security in anticipation of quantum threats. The race to quantum-proof encryption methods is crucial for ensuring the resilience of sensitive data against the exponentially enhanced computational power of quantum adversaries.

On the AI front, quantum computing offers exciting prospects for accelerating machine learning algorithms. Quantum Machine Learning (QML) algorithms leverage quantum principles to enhance the efficiency of tasks such as pattern recognition, optimisation, and data analysis. Quantum computers, with their ability to process vast data sets and explore complex solution spaces simultaneously, have the potential to outperform classical computers in certain machine learning applications. The synergy between quantum computing, cybersecurity, and AI opens new frontiers for technological advancement, calling for interdisciplinary research to harness quantum capabilities for both securing digital landscapes and enhancing the efficiency of intelligent systems.

It is evident that we stand at the precipice of a transformative era in computational science. The interplay between quantum hardware and software tools, exemplified by platforms like Qiskit, Cirq, and Q# along with cloud services, not only fosters innovation in quantum research but also beckons researchers, developers, and enthusiasts to collectively push the boundaries of our computational capabilities. Quantum technologies hold immense promise for addressing complex problems, from optimisation and cryptography to machine learning and drug discovery.

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Much like the artificial intelligence stock boom, we could see a similar rally with some of the topquantum computing stocksto buy. Quantum computing allows us to solve problems far too complex for your average computer, within minutes, or even seconds.

In fact, it may be able to help speed up solutions for machine learning, cybersecurity, medical treatments, the law, and education. Most exciting is its potential use in drug discovery.According to Medriva.com, The pharmaceutical industrys quest for new drugs is both vital and incredibly challenging, involving the screening of millions of compounds and rigorous testing.

However, with quantum computing, the industry could accelerate the identification and development of new pharmaceuticals by efficiently simulating molecular interactions on a quantum level,they added.

Can you imagine if quantum computing helped cure cancers?

No wonder governments all over the world are pledging billions to get quantum computing up and running in the next decade, according to the State of Quantum 2024 report.

With that, here are just a few top quantum computing stocks to buy and hold today.

Source: T. Schneider / Shutterstock

The last time I mentionedD-Wave Quantum(NYSE:QBTS), it traded at about 90 cents. At the time, I noted, Most recently, itinked a dealwithDeloitteto speed up quantum computing adoption for governments and companies all over Canada. Its even been working with Deloitte on transportation and national security issues in the U.S., too. Even better, the company isseeing quarter-over-quarter, and year-over-year growthin revenue, and customer bookings.

By Feb. 20, it was up to $2.17. Now at $1.43, I still like it long-term.

Fueling the upside, the company also just announced theavailability of its 1,200+ Qubit Advantage2prototype. According to the companys site, the new tool demonstrates significant performance gains on hard optimization problems and is expected to be particularly powerful for new use cases such as machine learning.

Helping, as noted in thecompanys investor deck, 80% of companies plan to increase their use of quantum computing over the next two to three years. Also, nearly 31% of companies have already abandoned complex problems they face because of the time to solve them.

Source: Bartlomiej K. Wroblewski / Shutterstock.com

Another one of the top quantum computing stocks to buy isRigetti Computing (NASDAQ:RGTI).

Over the last few weeks, the RGTI stock popped from about 95 cents to a high of $2.20. While its starting to pull back on profit-taking, RGTI is another hot quantum computing stock to buy and hold for the long haul.

Helping, analysts atAlliance Global Partnersjust initiated coverage of the RGTI stock with a buy rating, with a price target of $3.50.

There is a race to achieve quantum advantage and as the only company to publicly report multiple sales of a quantum computer at 99% fidelity, the firm said,as quoted by TheFly.com. The firm estimates revenue of $14.3M in 2024 and $21M in 2025, adding that it expects the inflection points to be in 2026 and 2027.

Well get a better idea of how RGTI is doing when it posts fourth quarter and full year 2023 results on March 14.

In addition, the company and Riverlane, a leader in quantum error correction technology just announced their participation in a project led by the US Department of Energys Oak Ridge National Laboratory to explore the challenges of integrating a quantum computer with a large-scale, supercomputing center,as noted in a recent press release.

Source: Shutterstock

Or, if you just want to make life easier for yourself, you can just invest in the Defiance Quantum ETF(NYSEARCA:QTUM). With this ETF, you can diversify with 71 quantum computing and machine learning-related stocks for less than $62 a share.

Better, since bottoming out in late October around $44.25, the QTUM ETF is now up to $61.42. From here, Id like to see it closer to $70, even $80 given the strong appeal of quantum computing and machine learning stocks.

With anexpense ratio of 0.40%, the Defiance Quantum fund provides exposure to quantum computing, artificial intelligence, and machine learning stocks, with holdings inIntel(NASDAQ:INTC),Nvidia(NASDAQ:NVDA),MicroStrategy(NASDAQ:MSTR), Rigetti Computing,Advanced Micro Devices(NASDAQ:AMD), andApplied Materials(NASDAQ:AMAT) to name a few. Again, as we note with exchange-traded funds, its always better to be well diversified, especially with strong up-and-coming markets like quantum computing.

On the date of publication, Ian Cooper did not hold (either directly or indirectly) any positions in the securities mentioned. The opinions expressed in this article are those of the writer, subject to the InvestorPlace.comPublishing Guidelines.

Ian Cooper, a contributor to InvestorPlace.com, has been analyzing stocks and options for web-based advisories since 1999.

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This post was contributed by Eyal Leviatan, Barak Katzir, Eyal Bairey, Omri Golan, and Netanel Lindner from Qedma, Joshua Goings from IonQ, and Daniela Becker from AWS.

Quantum computing is an exciting, fast-paced field. And especially in these early days, unfettered access to the right set of resources is critical in order to accelerate experimentation and innovation. Amazon Braket provides customers access to a choice of quantum hardware and the tooling they need to experiment, while also enabling them to engage directly with experts across the field from scientists to device manufacturers.

In this post, the team from Qedma, a quantum software company, dives into how they used Braket Direct to accomplish a milestone demonstration of their error mitigation software on IonQs Aria device. Leveraging dedicated access to quantum hardware capacity using reservations and collaborating with IonQ scientists for expert guidance directly via AWS, Qedma was able to successfully execute some of the most challenging Variational Quantum Eigensolver (VQE) circuits on a quantum processor to date.

In todays quantum processing units (QPUs), the susceptibility to various forms of noise results in errors that corrupt the quantum program and eventually render the results useless. The accumulation of errors over time, limits the duration and therefore the performance of quantum algorithms. Thus, achieving quantum advantage the ability to perform computations on quantum computers significantly faster than with classical supercomputers, needs a solution to mitigate the detrimental impact of these errors and enable algorithms to scale.

Error mitigation aims to reduce the effect of errors on the outputs of circuits executed on noisy quantum devices. However, these improvements come at the cost of runtime overhead that increases with the number of two-qubit gates (circuit volume) in the circuit. To overcome this, Qedmas novel approach to error mitigation, and the Qedma Error Suppression and Error Mitigation (QESEM) product, requires exponentially less overhead compared to other methods and suppresses errors at the hardware level to run longer programs while maintaining reasonable runtimes, potentially accelerating the path to quantum advantage.

Below we detail how QESEM was used in conjunction with IonQs Aria device via Braket Direct to produce high-accuracy results for a variety of quantum chemistry and quantum materials applications. We also show how Braket Direct provided us with dedicated QPU access, ideally suited for QESEMs interactive workflow, as well as the ability to connect directly with IonQs hardware experts. Scientific guidance from IonQ was important for tailoring QESEM to make the best use of Aria, and for constructing novel quantum chemistry circuits for the demonstration. These included VQE and Hamiltonian simulation circuits on 12 qubits, leveraging the high connectivity of IonQs devices. The results presented in this blog post demonstrate how users can push the boundaries of quantum chemistry and materials applications accessible on IonQs devices with Qedmas error mitigation, powered by Braket Direct.

QESEM can be used with any quantum program. When applied, QESEM first carries out a hardware-specific characterization protocol. According to the deduced error model, QESEM recompiles the input quantum circuit to a set of circuits that are sent to the device; the measurement outcomes are then classically post-processed, returning high-accuracy outputs, as we demonstrate below. The characterization process underlying QESEM ensures that its results are unbiased for any circuit. This means that QESEM provides results whose accuracy is only limited by the QPU time allocated for execution. In contrast, many error mitigation methods are algorithm-specific or heuristic. Algorithm-specific methods are not designed to mitigate generic errors across any quantum circuit, whereas heuristic methods generically converge to an incorrect (biased) output [1]. Relative to the leading unbiased and algorithm-agnostic methods, QESEMs QPU time is exponentially shorter as a function of circuit volume, as shown below.

We applied QESEM to three circuits from various applications and with a range of structural circuit properties (see Table 1). Specifically, we created a reservation via Braket Direct to get dedicated device access to IonQs Aria device. The reservation enabled the entire QESEM workflow to execute within a single working session where exclusive QPU access avoided the need to wait in line, and optimized throughput resulted in the shortest possible runtime. Along with the inherent stability of the physical properties of IonQs Aria, the reduced runtime ensured minimal drift of the system parameters during our experiments. This allowed QESEM to obtain an efficient description of the noise model during the execution.

Table 1: Properties of the circuits we demonstrated QESEM on.

Compared to the number of qubits they employ, all three circuits are comprised of a relatively high number of unique two-qubit gates between different pairs of qubits. This is made possible by the all-to-all qubit connectivity of IonQs hardware, which can calibrate an entangling gate between any pair of qubits; each of those gates is uniquely facilitated through the vibrational modes of the ion chain encoding the qubits. On the one hand, high qubit connectivity allows the compilation of complex circuits without incurring significant depth overhead. In contrast, on devices with lower connectivity, e.g., square lattice, applying a two-qubit gate to qubits that are not connected requires additional SWAP gates. On the other hand, the ability to run a large number of two-qubit gates poses a challenge for any characterization-based error mitigation method, since the noise model becomes very complicated. To address this challenge, QESEM used a characterization model specifically tailored to trapped ions, efficiently describing the errors of trapped-ion devices using a tractable noise model.

The first two circuits are examples of the VQE algorithm, which aims to find the ground state energy of a quantum many-body system, e.g., a molecule [1]. The specific examples we ran were designed to find the ground states of the NaH and O2 molecules. The third circuit realized a Hamiltonian simulation algorithm, implementing the time evolution of a quantum spin-lattice. We first describe the VQE circuits and focus on the oxygen molecule O2. Our efforts concentrated there due to its relevance to industrial and biological processes, while striking a balance between complexity and tractability making it a robust test for todays quantum devices. Moreover, the O2 experiment used a circuit volume of 99 two-qubit gates, larger than all VQE circuits featured in a recent experimental survey [3].

Typically, the presence of errors severely limits the size of VQE circuits because of the need for particularly accurate results. The ability to leverage the all-to-all connectivity of trapped-ion devices to reduce gate overhead is therefore well suited to this type of algorithm. With Braket Direct, we were able to incorporate expert guidance from IonQ on how to maximize the benefit of using their high connectivity and compile directly to their native gates to optimize the VQE circuits for the Aria device and produce the best results.

IonQ brought their quantum chemistry expertise to the table, equipping Qedma with circuits precisely crafted for the O2 molecule. Designed to mirror full configuration interaction results [4], these circuits included a chemistry-inspired Ansatz [5] supplemented by particle-conserving unitaries, which reflects the underlying molecular electronic structure. Additionally, IonQ undertook the classical optimization of the circuit parameters, setting the ground work for Qedma to apply QESEM effectively during the final energy assessment.

QESEM significantly enhanced the accuracy of the ground-state energy of the O2 molecule. Running this VQE circuit on Aria without error mitigation and measuring the ground state energy yields the result shown in red in Figure 1. This unmitigated result, i.e. executed without error mitigation, misses its mark by roughly 30%. In black, we show the exact energy, as it would have been obtained from the VQE circuit had it been run on a noise-free, i.e., ideal device. Using QESEM, the error mitigated energy (blue) closely matches the exact result up to the statistical error bar corresponding to the finite mitigation time. Moreover, the error bar accompanying the mitigated result is small enough to indicate a very clear statistical separation from the unmitigated result.

Figure 1: The ground state energy of the O2 molecule as obtained from running the VQE circuit on IonQ Aria without error mitigation (red) and with QESEM (blue) compared to the exact result that would be obtained on an ideal, i.e., noise-free, device.

Aside from the ground state energy, this VQE circuit also allows us to learn about the electronic structure of the O2 molecule. The states of individual qubits encode the electronic occupations of the molecules orbitals. A qubit in the 0 state signifies an empty orbital whereas the 1 state corresponds to occupation by a single electron. Moreover, from the correlations between pairs of qubits, we can extract the correlations between occupations. Some examples of occupations and their correlations can be seen in Figure 2. Again, all mitigated values match the ideal values up to the statistical error bars while the noisy results are, in most cases, far off.

Figure 2. Ideal, noisy and mitigated values for example orbitals occupations and their correlations.

Similar results for the NaH VQE circuit are shown in Figure 3. While the NaH circuit is narrower, i.e., involves fewer qubits, it requires a full qubit-connectivity graph and is of a comparable depth. Since this circuit only makes use of 6 qubits, the number of all possible outcomes is not very large, allowing the depiction of the full probability distribution of measurement outcomes (see Figure 3). Excellent agreement of the mitigated results with the ideal outcome can be seen for all bitstrings, demonstrating QESEMs capability to provide an unbiased estimate for any output observable of interest.

Figure 3: Results for the NaH VQE circuit. Left: The probability distribution of all possible measurement outcomes. Right: Observables of interest, e.g., the ground state energy. QESEM results (blue) reproduce the ideal values (black) up to statistical accuracy while the unmitigated results (red) are off.

In the study of quantum materials, there are two fundamental questions of interest: energetics and dynamics. The VQE algorithm presented above addresses the question of energetics. In contrast, the Hamiltonian simulation algorithm computes the time evolution of the quantum state of the material, i.e., its dynamics. The quantum circuit approximates the continuous dynamics by small discrete time evolution steps [6].

Spin Hamiltonians are widely used as models for quantum materials where the electrons are in fixed positions but interact magnetically. For this demonstration, we chose a canonical Hamiltonian, the so-called XY model with a perpendicular magnetic field [7]. The 12 spins, encoded by 12 qubits, reside on the sites of a three-by-four triangular lattice with periodic boundary conditions (see Figure 4). Under these conditions, the Hamiltonian simulation circuit requires high connectivity between the qubits to be compiled compactly. Beyond being a highly demanding benchmark, the Hamiltonian we simulated also illustrates rich quantum physical phenomena. The XY model is a model of strongly interacting bosons, as in a Josephson junction array. On a triangular lattice, this type of system can form an exotic phase of matter called a Supersolid [8].

Figure 4: Hamiltonian simulation. Left: the simulated triangular spin lattice. Colors represent different observables of interest the magnetization of individual spins (gray), and correlations between magnetizations of different spin patterns. Right: ideal, noisy and mitigated values for the different observables

Figure 4 shows the values of various observables of physical interest after one time-step (consisting of 72 two-qubit gates) is performed to an initial state where all spins, i.e., qubits, are oriented along the X direction. From left to right, these observables are the projections onto the X direction of the magnetization of single spins, and correlations of spin magnetizations along interaction bonds, lattice plaquettes, and strings of spins that envelop the lattice in one of its directions. Examples of each appear on the top panel in matching colors. These observables indicate the strength of various magnetic properties of the model. For each observable, we present the exact expectation values in black, the noisy unmitigated values in red, and the error mitigated results using QESEM in blue. Again, QESEM results reproduce the ideal values up to statistical accuracy, while the unmitigated results are statistically well-separated from both.

While we presented only a few specific examples, QESEM can be applied to any quantum circuit for which error-free results are desired. It is meticulously designed to optimize the accuracy-to-runtime tradeoff inherent to error mitigation methods. In particular, QESEMs QPU time, at a given statistical accuracy, scales exponentially better as a function of the volume of the target circuit compared to competing unbiased error mitigation protocols. For instance, a circuit with 120 two-qubit gates, run on a trapped-ion device with 99% two-qubit gate fidelity, would take 90 minutes to execute to 90% accuracy using QESEM, which can be easily completed within a two-hour device reservation using Braket Direct. The same circuit, executed with the leading competing unbiased and algorithm-generic error mitigation technique, Probabilistic Error Cancellation [9, 10], would take over a month.

Error mitigation is essential for executing cutting-edge applications on near-term quantum devices [1]. While the problems discussed in this blog can be simulated classically, QESEM enables accurate, error-free execution of large circuits increasing the number of two-qubit gates that can be utilized by more than an order of magnitude compared to unmitigated execution at the same level of accuracy.

Figure 5 shows the circuit volumes accessible with QESEM on trapped-ion devices. With expected near-future improvements in hardware fidelities and qubit counts, QESEM could enable executing generic quantum circuits faster than a supercomputer performing a state-vector simulation of the same circuit. Achieving this milestone will spur further exploration of applications requiring simulations of quantum systems, such as the design of novel materials.

Figure 5: accessible circuit volumes with QESEM on ion traps, assuming a desired accuracy of 90%. Active volume denotes the number of two-qubit gates within the circuit that affect the observable of interest. Here it is measured in terms of IonQs MlmerSrensen (MS) entangling gates. The black line estimates the time it would take a supercomputer to perform a state-vector simulation for a square circuit with the corresponding circuit volume. A square circuit consists of a sequence of layers in which each qubit participates in an MS gate, and the number of layers equals to the number of qubits (width=depth).

To learn more about Qedma and QESEM, visit Qedmas website. To further accelerate your research with dedicated access to quantum hardware including IonQs latest Forte QPU, check out the Braket Direct documentation or navigate to the AWS Management Console.

The content and opinions in this blog are those of the third-party authors and AWS is not responsible for the content or accuracy of this blog.

[1] Quantum Error Mitigation, https://arxiv.org/abs/2210.00921 (2022) [2] A variational eigenvalue solver on a photonic quantum processor, https://www.nature.com/articles/ncomms5213 (2014) [3] Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers https://www.nature.com/articles/s41534-023-00730-8 (2023) [4] Molecular Electronic-Structure Theory; John Wiley & Sons (2014) [5] Universal quantum circuits for quantum chemistry, https://doi.org/10.22331/q-2022-06-20-742 (2022) [6] Universal Quantum Simulators, https://www.science.org/doi/10.1126/science.273.5278.1073 (1996) [7] Boson localization and the superfluid-insulator transition, https://journals.aps.org/prb/abstract/10.1103/PhysRevB.40.546 (1989) [8] Superfluids and supersolids on frustrated two-dimensional lattices, https://journals.aps.org/prb/abstract/10.1103/PhysRevB.55.3104 (1997) [9] Probabilistic error cancellation with sparse PauliLindblad models on noisy quantum processors, https://www.nature.com/articles/s41567-023-02042-2 (2023) [10] Efficiently improving the performance of noisy quantum computers, https://arxiv.org/abs/2201.10672 (2022)

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Today Rolls-Royce, Riverlane and Xanadu secured more than 400,000 grant funding from Innovate UK to accelerate the development of applications that will allow quantum computers to model the flow of air through jet engines.

An additional CAD $500,000 has been awarded from the National Research Council of Canada Industrial Research Assistance Program (NRC IRAP) as part of a growing relationship between the UK and Canada on quantum computing technology and expertise.

The project, called CATALYST, will deliver a hybrid quantum-classical framework combination, where computers of the type we use now are programmed to instruct quantum computers.

It draws on the unique expertise of each partner: industrial applications (Rolls-Royce); UK-based quantum error correction company, Riverlane, and Canadian quantum computing company, Xanadu.

This will give Rolls-Royce the means to rapidly evaluate and implement new quantum algorithms, accelerating the time to do this from several hours to just a few minutes. This will bring huge efficiencies to future product design processes and also contributes to the first of the UK Governments recently announced National Quantum Strategy Missions.

Leigh Lapworth, Rolls-Royce Fellow in Computational Science, said:

"This is the first quantum computing R&D collaboration to be led by a large industry partner, instead of smaller startups.

Our shared vision and approach will make us one of the first companies to benefit from fault-tolerant computers.

The techniques we develop in this project will be those that enable us to benefit from the UKs quantum pathway of a million error-corrected quantum operations in 2028; a billion in 2032; and a trillion in 2035."

Steve Brierley, CEO and founder from Riverlane, said:

"The CATALYST project brings together leading quantum computing companies and industry experts from the UK and Canada to help improve the quality of the quantum algorithms.

By developing better quantum algorithms, we can reduce the number of quantum operations required to unlock world-changing applications, sooner.

Such work across the quantum computing stack is vital to help us unlock millions and then trillions of reliable quantum operations."

Josh Izaac, Director of Product at Xanadu, said:

"As quantum hardware continues to grow in both scale and capabilities, we need to re-think the quantum software technical stack to enable the design and execution of larger and more complex quantum algorithms."

This will unlock the ability to explore bigger, more complex, and more dynamic quantum algorithms with PennyLane and our world-class simulators."

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Ethereum is already well-positioned to mitigate the impact of a massive quantum computing attack on the network, according to Ethereum co-founder Vitalik Buterin.

In a March 9 post to Ethereum Research, Buterin discussed what would happen if a quantum emergency happened as early as tomorrow.

Suppose that it is announced tomorrow that quantum computers are available, and bad actors already have access to them and are able to use them to steal users funds, Buterin postulated.

The blockchain would have to hard fork and users would have to download new wallet software, but few users would lose their funds, he added.

Buterin explained that the process of such a hard fork would involve rolling back the Ethereum network to the point where it is clear that large-scale theft was occurring and disabling all traditional transactions from that point.

Ethereum developers would then add a new transaction type which forms part of the Ethereum Improvement Proposal (EIP) 7560 to allow transactions from smart contract wallets.

When a user makes a transaction from their Ethereum wallet, the signature of that transaction reveals the public key, and in a post-quantum world, this would see the users private key revealed as well.

The new transaction type that forms the core part of the quantum-resist EIP would leverage Winternitz signatures and zero-knowledge proof technologies known as STARKs to ensure that existing wallets are switched to new validation code, he added.

This validation code leverages ERC-4337 account abstraction the underlying technology of smart contract wallets to prevent private keys from being displayed while signing transactions in the future, rendering these accounts immune from a quantum attack.

Related:Ethereum leans into rollup-centric future as Dencun hard fork looms

According to Buterin, users who have never approved a transaction from an Ethereum wallet are already safe from any potential quantum-related exploit, as only the wallet address has ever been made publicly available.

He also added that the infrastructure needed to implement such as hard fork could in principle start to be built tomorrow.

The advent of quantum computing has been a long-feared inflection point for the crypto industry, as a computer capable of breaking blockchain encryption could see once-untouchable user funds stolen in large volumes and at rapid rates.

However, most computer scientists and developers believe that quantum computing is still a ways off, with Google and IBM engineers estimating that quantum computing wont be sufficiently developed until 2029 at the earliest.

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A 'simple' hard fork could subvert a quantum attack on Ethereum: Vitalik Buterin - Cointelegraph

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