Oxford researchers have made a significant leap in quantum security, which may lead to the safe deployment of quantum computing in domestic settings. The team, directed by postdoctoral research assistant Peter Drmota at Oxford University Physics, has successfully demonstrated a blind quantum computing technique on a trapped-ion quantum processora technology touted for its scalable quantum computing prospects.

This new approach marries quantum computing with quantum cryptography in a manner that hasnt been achieved before. It does so by ensuring that both the processed data and the algorithms used remain hidden from both the server and potential eavesdroppers. The concept relies on the principles of quantum mechanics, which state that attempting to observe or duplicate a quantum state will inevitably alter it.

In practical terms, the teams experiments used a standard fiber network to link a quantum computing server with a simplistic device used for detecting light particles at a separate client computer. This allowed the client to perform computations remotely on the server without the server having access to any of the data or the algorithms being used.

Drmota finds great potential in the blind aspect of this technology, particularly in verifying the correctness of computations done by a remote quantum computer. This is crucial for problems that are beyond the scope of classical computing. The relative simplicity and scalability of the Oxford approach, incorporating existing technology like fiber networks and photon detectors, herald a future where cloud-hosted quantum servers could engage with clients worldwide to process sensitive data securely.

The research is a stride towards enabling secure, confidential quantum computations by clients with minimal resources, thereby potentially bringing quantum computings formidable power to everyday users. This development was made possible thanks to collaborative efforts funded by UKs Quantum Computing and Simulation Hub and contributions from various international institutions. Insights from this study appear in the distinguished Physical Review Letters journal.

Advancements in Quantum Computing and Quantum Security

The groundbreaking research conducted by Oxford University is a notable achievement in the rapidly expanding field of quantum computing. Quantum computing is an emerging industry that boasts the potential to revolutionize various fields by performing complex computations much faster than current classical computers can. Given that quantum computing involves processing and storing information in quantum states, it brings forward not only unprecedented computational power but also unique challenges concerning data security and privacy.

Quantum security is particularly crucial as quantum computers have the potential to break current encryption methods, which would jeopardize data integrity and privacy. The blind quantum computing technique developed by Dr. Peter Drmota and his team adds an additional layer of security, allowing computations to take place without revealing the data or the algorithms to the server, thus ensuring the confidentiality of sensitive information.

Market Forecasts and Industry Growth

The global quantum computing market has been projected to grow significantly in the coming years, fueled by investments from both public and private sectors. Market analysts foresee that with continued advancements and reductions in cost, quantum computing services could become widely accessible through cloud-based models, similar to how classical computing services are offered today.

Industry Challenges and Potential Issues

Despite the optimism surrounding quantum computing, the industry is not without its challenges. One of the major hurdles lies in the current technological limitations which include error rates and quantum decoherence that can affect the stability of quantum states. Moreover, securing quantum communications to safeguard against potential quantum attacks is an ongoing area of investigation, highlighted by advancements such as the one from Oxford researchers.

Addressing the broader concerns, there is also the need to develop new standards and protocols for quantum security to ensure compatibility and protection across the various platforms and networks that may emerge. Furthermore, the issue of accessibility and education must be addressed, as the complexity of quantum computing could create a barrier for entry for many users and businesses.

As the quantum computing industry evolves, companies, governments, and educational institutions must work collaboratively to establish an ecosystem that not only fosters innovation but also ensures a secure and equitable framework for its use. Partnerships and funding, such as those from the Quantum Computing and Simulation Hub in the UK, are pivotal in supporting research that bridges the gap between theoretical quantum computing and practical, secure applications.

For readers seeking to stay updated on the latest in this transformative field or to learn more about the market and its influencers, reputable sources include the official websites for quantum technology development and research centers. One may find these sources at the main domains without any specific subpage links:

Oxford University Physics Department: physics.ox.ac.uk Quantum Computing and Simulation Hub: qcshub.org Physical Review Letters Journal: aps.org

These platforms often provide insights and updates on current research, industry trends, and market forecasts, helping individuals and businesses to navigate the complexities of quantum technologies and their implications for the future.

Roman Perkowski is a distinguished name in the field of space exploration technology, specifically known for his work on propulsion systems for interplanetary travel. His innovative research and designs have been crucial in advancing the efficiency and reliability of spacecraft engines. Perkowskis contributions are particularly significant in the development of sustainable and powerful propulsion methods, which are vital for long-duration space missions. His work not only pushes the boundaries of current space travel capabilities but also inspires future generations of scientists and engineers in the quest to explore the far reaches of our solar system and beyond.

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Quantum Encryption Advances at Oxford University Physics - yTech

On Friday April 5, I attended the ribbon-cutting for the first quantum computer installed on a university campus, an IBM Quantum System One machine at Rensselaer Polytechnic Institute. While quantum computing has the potential to solve some problems that traditional computers cant and has been advancing at a steady rate, there are still many questions and challenges around the technology. Installing the machine on a college campus will allow researchers to examine many of these issues and allow students to get hands-on experience with the technology.

RPI President Martin A. Schmidt (Credit: Michael J. Miller)

RPI President Martin A. Schmidt says that with this quantum computer, we will explore applications, develop algorithms, and in so doing help humanity solve some very large problems. He states that while it's easy to predict that quantum systems will rapidly become essential because of their computational power, we don't yet fully know how best to use them. He says we can anticipate that there will be important applications in biomedicine, in modeling climate and predicting weather, and in materials design; but there will be applications in many other fields.

With IBMs research in Yorktown Heights, manufacturing in Poughkeepsie, and partnerships with the University of Albany as well as RPI, he hopes for "an agglomeration effect," in which organizations in a region working together can create something where the whole is greater than the sum of the parts. Schmidt notes that there are already partnerships in the area for semiconductor research, and this has led to new factories being built in upstate New York: "Adding 'quantum valley' aspects to 'tech valley' is not only going to draw new businesses here and encourage startups, but also offer the region's existing businesses early insights into what it means to be quantum advantaged."

Schmidt hopes the system and its use by RPI and the University of Albany will help answer the question of how the United States educates a quantum-ready workforce for the near future. He notes RPI's history of 'hands-on' education and that students at all levels will be encouraged to use the machine.

Separately, Schmidt also tells me that he believes the quantum computer will be useful in attracting both faculty and students.

Curtis Priem, a cofounder of Nvidia and vice-chairman of RPIand the donor who arranged for the machine to come to RPInotes that he enrolled at RPI initially because of this 'hands-on' approach and remarked at how today even undergraduates can use RPI's supercomputer.

IBM CEO Arvind Krishna (Credit: Michael J. Miller)

IBM CEO Arvind Krishna says that quantum systems will solve problems that we cannot solve on today's computersproblems in materials, problems in carbon sequestration, problems around drug discovery, and problems in lightweight materials, lubricants, and EV battery materials. "When you think about it intuitively," he says "they come from a world of physical chemistry, which means that they are subject to the principles of quantum mechanics, which is why these systems, which kind of simulate nature, are the ones that are going to let us make progress on these problems." They have the potential to solve problems around stochastics and financial risk.

Krishna believes that the university could uniquely help with workforce development, saying "Students are going to imagine using these systems in ways that even the inventors of these systems can't conceive." Listing a set of potential use cases, he says, " I'll make a bet that within five years students and faculty here are going to bring up use cases that are far beyond what we are imagining."

The unveiling was preceded by a day of discussions about the opportunities and the many challenges facing quantum computing before it is ready for commercial applications. I'll talk about those in my next post.

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This University in New York Is the First With a Full-Fledged Quantum Computer - PCMag

ETH Zurichs recent foray into the realm of ion trapping has yielded promising advancements for quantum computing. A team of researchers at the esteemed institution has developed a method for trapping ions that could potentially enable the creation of quantum computers with greater numbers of qubits than currently possible. Utilizing static electric and magnetic fields, the group has taken quantum operations a step further, signaling a leap forward in computing capabilities.

**Summary:** Researchers at ETH Zurich have made a significant stride in quantum computing by devising an ion trapping technique that employs static electric and magnetic fields. This novel approach, utilizing Penning traps on a microfabricated chip, allows for arbitrary ion transport and offers a scalable solution that promises to increase the number of qubits in quantum computers considerably.

Quantum computer scientists are working tirelessly to overcome the limitations imposed by traditional oscillating field ion traps, such as the Paul trap, which restricts ions to linear motion and complicates the integration of multiple traps on a single chip. By means of steady fields, the ETH teams Penning traps have unlocked new potentials for maneuvering ions in two dimensions without the constraints of oscillating fields, offering a boon for future quantum computing applications.

The ETH researchers, led by Jonathan Home, have reimagined the ion trap architecture, traditionally used in precision experiments, to suit the demands of quantum computing. Despite encountering initial skepticism, the team constructed an advanced Penning trap that incorporated a superconducting magnet producing a field strength of 3 Tesla. They effectively implemented precise control over the ions energy states, proving their methods viability for quantum computation.

The trapped ions ability to stay put for several days within this new system has marked a remarkable achievement. This stable trapping environment, free from oscillating fields and external disturbances, allowed the researchers to maintain quantum mechanical superpositions essential for operations in quantum computers.

Looking ahead, the ETH group aims to harness these innovations for multi-qubit operations by trapping two ions in adjacent Penning traps on the same chip. This ambitious endeavor would illustrate the practicality of large-scale quantum computers using static field ion traps, potentially leading to more powerful computing technologies than any seen before.

The research at ETH Zurich represents an exciting development in the field of quantum computing, an industry that is expected to revolutionize the world of computing as we know it. With the progress made in ion trapping techniques, the scalability of quantum computers could rise precipitously, culminating in machines far exceeding the capabilities of todays supercomputers.

Industry Background: Quantum computing harnesses the phenomena of quantum mechanics to perform computation. Unlike classical bits, quantum computers use qubits, which can exist in states of 0, 1, or any quantum superposition of these states. This allows quantum computers to solve certain problemslike factoring large numbers or running simulations of quantum materialsmuch faster than classical computers.

Market Forecasts: The quantum computing market is projected to grow significantly in the coming years. According to industry analysis, the global market size, which was valued at several hundred million dollars, is expected to reach into the billions by the end of the decade, with a compound annual growth rate (CAGR) often cited in strong double digits. This growth is driven by increasing investments from both public and private sectors and advancements in quantum computing technologies.

Industry-Related Issues: There are several challenges that the quantum computing industry faces. One of the main hurdles is quantum decoherence, where the qubits lose their quantum state due to environmental interference, posing a significant issue for maintaining quantum superpositions. Another challenge involves error rates in quantum calculations that require complex error correction methods. Furthermore, the creation and maintenance of qubits are technically demanding and expensive, requiring precise control over the physical systems that host them, like ions or other particles.

The breakthrough by ETH Zurichs researchers addresses some of these challenges by using static fields, which can potentially improve the stability and coherence times of the qubits. This could lead to advancements in quantum error correction and enable the implementation of more complex quantum algorithms.

As the demand for quantum computing continues to rise, collaboration and investment in research and development are crucial. Successful implementation of quantum computers can impact various industries, including cryptography, materials science, pharmaceuticals, and finance. For those interested in the cutting-edge developments in this field, the following sources offer valuable insights:

IBM Quantum IBM is one of the companies at the forefront of quantum computing. They provide access to quantum computers through the cloud and are actively involved in advancing quantum computation technology.

D-Wave Systems Inc. D-Wave is known for developing quantum annealing-based computers, specializing in solving optimization and sampling problems.

Google Quantum AI Googles Quantum AI lab is working on developing quantum processors and novel quantum algorithms to help researchers and developers solve near-term problems across various sectors.

The innovations from the team at ETH Zurich are poised to contribute significantly to this burgeoning industry, potentially overcoming some of the critical challenges and pushing us closer to the realization of fully functional quantum computers.

Marcin Frckiewicz is a renowned author and blogger, specializing in satellite communication and artificial intelligence. His insightful articles delve into the intricacies of these fields, offering readers a deep understanding of complex technological concepts. His work is known for its clarity and thoroughness.

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Breakthrough in Quantum Computing: ETH Zurich Innovates with Static Fields in Ion Trapping - yTech

A summary of the new initiative by the South Carolina Quantum Association reveals the states forward-thinking investment in quantum computing expertise. South Carolina is funneling resources into a groundbreaking educational partnership aimed at equipping University of South Carolina students with real-world quantum computing skills. Backed by taxpayer dollars, this project is providing a platform for students to train on a cutting-edge quantum supercomputer, fostering their growth into in-demand tech professionals and invigorating local industries with innovative solutions.

In a significant development for South Carolinas aspiring quantum scientists, the states Quantum Association is collaborating with the University of South Carolina to offer an extraordinary educational experience. The venture is supported by a $20,000 research project fund and is already yielding promising outcomes.

Finance and computer science majors at the university are piloting a quantum computing project, enhancing investment strategies for a regional bank. The quantum computer, funded through a substantial $15 million state budget allocation and accessed remotely from the University of Maryland, serves as a cornerstone for the states burgeoning intellectual and industrial advancements.

The initiatives participants are already making waves on the national stage, having secured a top position at a notable MIT hackathon. With aspirations extending well into the investment sphere, these students are founding a hedge fund to apply their unique quantum computing insights.

South Carolinas project goes beyond mere technological enhancement. It aims to nurture top-tier talent through an expansive quantum computing curriculum and an online training platform, positioning the state to become a nexus of high-tech finance and industry professionals.

The global quantum computing industry is poised for exponential growth as this powerful technology promises to transform diverse sectors. The South Carolina initiative reflects a strategic movement to prepare for a future that demands advanced computational knowledge, amidst challenges like hardware stability and the need for specialists.

By marrying academic learning with practical application, South Carolinas initiative is setting the stage for building a proficient quantum workforce. This workforce would be adept at addressing industry challenges and leveraging the opportunities offered by this emergent technological field.

Industry and Market Forecasts

The quantum computing industry represents one of the most exciting frontiers in technology and science. As of my latest knowledge update in 2023, the industry is expected to grow substantially in the coming years. According to market research, the global quantum computing market is projected to reach billions of dollars by the end of this decade, with a compounded annual growth rate (CAGR) that underscores its dynamic potential. This growth is fueled by increased investments from both public and private sectors, along with breakthroughs in quantum algorithms and hardware.

Companies across various industries, such as finance, pharmaceuticals, automotive, and aerospace, are exploring quantum computing to gain a competitive advantage. This technology holds the promise of solving complex problems that are currently intractable by classical computers, such as optimizing enormous data sets, modeling molecular interactions for drug discovery, and improving encryption methods.

Current Issues in Quantum Computing

One of the most significant issues facing the quantum computing industry is the stabilization of qubits, the basic units of quantum information. Unlike classical bits, qubits can exist in multiple states simultaneously, through a phenomenon known as superposition. However, they are also highly susceptible to interference from their environment, which can lead to errors in computation. Overcoming this challenge, often referred to as quantum decoherence, is a key focus for researchers.

Another issue is the need for a highly specialized workforce, as quantum computing requires not just expertise in computer science but also in quantum mechanics. The intricacies of quantum algorithms and the underpinning physical principles necessitate a new breed of professionals who can bridge the gap between theory and practical application.

Moreover, the industry is also working on making quantum computing more accessible. Currently, only a handful of organizations have the resources to develop and maintain a quantum computer. However, the rise of quantum computing as a service (QCaaS) models has begun to democratize access to quantum resources, allowing more players to explore the potential of this technology.

South Carolinas Role in the Quantum Computing Ecosystem

South Carolinas initiative to invest in quantum computing education highlights the importance of building a smart workforce that can contribute to and benefit from this promising industry. With their practical projects, such as improving banking investment strategies through quantum computing, students are not only contributing to innovation but are also showcasing how these complex technologies can have real-world applications.

Such initiatives prepare a new generation to play an active role in the industry, ensuring that the U.S. remains at the forefront of technological advancements. For more information on related topics, you may consider visiting the website of professional organizations and industry leaders in quantum computing. Here are a couple of valid related links:

IBM Quantum Google Quantum AI

By promoting education and funding in quantum computing, South Carolina is positioning itself not only as a contributor to the global quantum revolution but also as a beneficiary of the quantum economy to come. It is an example of how regional initiatives can have significant outcomes in a rapidly evolving high-tech landscape.

Jerzy Lewandowski, a visionary in the realm of virtual reality and augmented reality technologies, has made significant contributions to the field with his pioneering research and innovative designs. His work primarily focuses on enhancing user experience and interaction within virtual environments, pushing the boundaries of immersive technology. Lewandowskis groundbreaking projects have gained recognition for their ability to merge the digital and physical worlds, offering new possibilities in gaming, education, and professional training. His expertise and forward-thinking approach mark him as a key influencer in shaping the future of virtual and augmented reality applications.

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Shaping the Future: South Carolina's Quantum Computing Education Initiative - yTech

Today, the paper detailing those results was published as the cover story of the scientific journal Nature.1

Last year, we demonstrated that quantum computers had entered the era of utility, where they are now capable of running quantum circuits better than classical computers can. Over the next few years, we expect to find speedups over classical computing and extract business value from these systems. But there are also algorithms with mathematically proven speedups over leading classical methods that require tuning quantum circuits with hundreds of millions, to billions, of gates. Expanding our quantum computing toolkit to include those algorithms requires us to find a way to compute that corrects the errors inherent to quantum systems what we call quantum error correction.

Read how a paper from IBM and UC Berkeley shows a path toward useful quantum computing

Quantum error correction requires that we encode quantum information into more qubits than we would otherwise need. However, achieving quantum error correction in a scalable and fault-tolerant way has, to this point, been out of reach without considering scales of one million or more physical qubits. Our new result published today greatly reduces that overhead, and shows that error correction is within reach.

While quantum error correction theory dates back three decades, theoretical error correction techniques capable of running valuable quantum circuits on real hardware have been too impractical to deploy on quantum system. In our new paper, we introduce a new code, which we call the gross code, that overcomes that limitation.

This code is part of our broader strategy to bring useful quantum computing to the world.

While error correction is not a solved problem, this new code makes clear the path toward running quantum circuits with a billion gates or more on our superconducting transmon qubit hardware.

Quantum information is fragile and susceptible to noise environmental noise, noise from the control electronics, hardware imperfections, state preparation and measurement errors, and more. In order to run quantum circuits with millions to billions of gates, quantum error correction will be required.

Error correction works by building redundancy into quantum circuits. Many qubits work together to protect a piece of quantum information that a single qubit might lose to errors and noise.

On classical computers, the concept of redundancy is pretty straightforward. Classical error correction involves storing the same piece of information across multiple bits. Instead of storing a 1 as a 1 or a 0 as a 0, the computer might record 11111 or 00000. That way, if an error flips a minority of bits, the computer can treat 11001 as 1, or 10001 as 0. Its fairly easy to build in more redundancy as needed to introduce finer error correction.

Things are more complicated on quantum computers. Quantum information cannot be copied and pasted like classical information, and the information stored in quantum bits is more complicated than classical data. And of course, qubits can decohere quickly, forgetting their stored information.

Research has shown that quantum fault tolerance is possible, and there are many error correcting schemes on the books. The most popular one is called the surface code, where qubits are arranged on a two-dimensional lattice and units of information are encoded into sub-units of the lattice.

But these schemes have problems.

First, they only work if the hardwares error rates are better than some threshold determined by the specific scheme and the properties of the noise itself and beating those thresholds can be a challenge.

Second, many of those schemes scale inefficiently as you build larger quantum computers, the number of extra qubits needed for error correction far outpaces the number of qubits the code can store.

At practical code sizes where many errors can be corrected, the surface code uses hundreds of physical qubits per encoded qubit worth of quantum information, or more. So, while the surface code is useful for benchmarking and learning about error correction, its probably not the end of the story for fault-tolerant quantum computers.

The field of error correction buzzed with excitement in 2022 when Pavel Panteleev and Gleb Kalachev at Moscow State University published a landmark paper proving that there exist asymptotically good codes codes where the number of extra qubits needed levels off as the quality of the code increases.

This has spurred a lot of new work in error correction, especially in the same family of codes that the surface code hails from, called quantum low-density parity check, or qLDPC codes. These qLDPC codes are quantum error correcting codes where the operations responsible for checking whether or not an error has occurred only have to act on a few qubits, and each qubit only has to participate in a few checks.

But this work was highly theoretical, focused on proving the possibility of this kind of error correction. It didnt take into account the real constraints of building quantum computers. Most importantly, some qLDPC codes would require many qubits in a system to be physically linked to high numbers of other qubits. In practice, that would require quantum processors folded in on themselves in psychedelic hyper-dimensional origami, or entombed in wildly complex rats nests of wires.

In our paper, we looked for fault-tolerant quantum memory with a low qubit overhead, high error threshold, and a large code distance.

Bravyi, S., Cross, A., Gambetta, J., et al. High-threshold and low-overhead fault-tolerant quantum memory. Nature (2024). https://doi.org/10.1038/s41586-024-07107-7

In our Nature paper, we specifically looked for fault-tolerant quantum memory with a low qubit overhead, high error threshold, and a large code distance.

Lets break that down:

Fault-tolerant: The circuits used to detect errors won't spread those errors around too badly in the process, and they can be corrected faster than they occur

Quantum memory: In this paper, we are only encoding and storing quantum information. We are not yet doing calculations on the encoded quantum information.

High error threshold: The higher the threshold, the higher amount of hardware errors the code will allow while still being fault tolerant. We were looking for a code that allowed us to operate the memory reliably at physical error rates as high as 0.001, so we wanted a threshold close to 1 percent.

Large code distance: Distance is the measure of how robust the code is how many errors it takes to completely flip the value from 0 to 1 and vice versa. In the case of 00000 and 11111, the distance is 5. We wanted one with a large code distance that corrects more than just a couple errors. Large-distance codes can suppress noise by orders of magnitude even if the hardware quality is only marginally better than the code threshold. In contrast, codes with a small distance become useful only if the hardware quality is significantly better than the code threshold.

Low qubit overhead: Overhead is the number of extra qubits required for correcting errors. We want the number of qubits required to do error correction to be far less than we need for a surface code of the same quality, or distance.

Were excited to report that our teams mathematical analysis found concrete examples of qLDPC codes that met all of these required conditions. These fall into a family of codes called Bivariate Bicycle (BB) codes. And they are going to shape not only our research going forward, but how we architect physical quantum systems.

While many qLDPC code families show great promise for advancing error correction theory, most arent necessarily pragmatic for real-world application. Our new codes lend themselves better to practical implementation because each qubit needs only to connect to six others, and the connections can be routed on just two layers.

To get an idea of how the qubits are connected, imagine they are put onto a square grid, like a piece of graph paper. Curl up this piece of graph paper so that it forms a tube, and connect the ends of the tube to make a donut. On this donut, each qubit is connected to its four neighbors and two qubits that are farther away on the surface of the donut. No more connections needed.

The good news is we dont actually have to embed our qubits onto a donut to make these codes work we can accomplish this by folding the surface differently and adding a few other long-range connectors to satisfy mathematical requirements of the code. Its an engineering challenge, but much more feasible than a hyper-dimensional shape.

We explored some codes that have this architecture and focused on a particular [[144,12,12]] code. We call this code the gross code because 144 is a gross (or a dozen dozen). It requires 144 qubits to store data but in our specific implementation, it also uses another 144 qubits to check for errors, so this instance of the code uses 288 qubits. It stores 12 logical qubits well enough that fewer than 12 errors can be detected. Thus: [[144,12,12]].

Using the gross code, you can protect 12 logical qubits for roughly a million cycles of error checks using 288 qubits. Doing roughly the same task with the surface code would require nearly 3,000 qubits.

This is a milestone. We are still looking for qLDPC codes with even more efficient architectures, and our research on performing error-corrected calculations using these codes is ongoing. But with this publication, the future of error correction looks bright.

Fig. 1 | Tanner graphs of surface and BB codes.

Fig. 1 | Tanner graphs of surface and BB codes. a, Tanner graph of a surface code, for comparison. b, Tanner graph of a BB code with parameters [[144, 12, 12]] embedded into a torus. Any edge of the Tanner graph connects a data and a check vertex. Data qubits associated with the registers q(L) and q(R) are shown by blue and orange circles. Each vertex has six incident edges including four short-range edges (pointing north, south, east and west) and two long-range edges. We only show a few long-range edges to avoid clutter. Dashed and solid edges indicate two planar subgraphs spanning the Tanner graph, see the Methods. c, Sketch of a Tanner graph extension for measuring Z ={Z} and X ={X} following ref. 50, attaching to a surface code. The ancilla corresponding to the X ={X} measurement can be connected to a surface code, enabling load-store operations for all logical qubits by means of quantum teleportation and some logical unitaries. This extended Tanner graph also has an implementation in a thickness-2 architecture through the A and B edges (Methods).

Fig. 2 | Syndrome measurement circuit.

Fig. 2 | Syndrome measurement circuit. Full cycle of syndrome measurements relying on seven layers of CNOTs. We provide a local view of the circuit that only includes one data qubit from each register q(L) and q(R). The circuit is symmetric under horizontal and vertical shifts of the Tanner graph. Each data qubit is coupled by CNOTs with three X-check and three Z-check qubits: see the Methods for more details.

This code is part of our broader strategy to bring useful quantum computing to the world.

Today, our users benefit from novel error mitigation techniques methods for reducing or eliminating the effect of noise when calculating observables, alongside our work suppressing errors at the hardware level. This work brought us into the era of quantum utility. IBM researchers and partners all over the world are exploring practical applications of quantum computing today with existing quantum systems. Error mitigation lets users begin looking for quantum advantage on real quantum hardware.

But error mitigation comes with its own overhead, requiring running the same executions repeatedly so that classical computers can use statistical methods to extract an accurate result. This limits the scale of the programs you can run, and increasing that scale requires tools beyond error mitigation like error correction.

Last year, we debuted a new roadmap laying out our plan to continuously improve quantum computers over the next decade. This new paper is an important example of how we plan to continuously increasing the complexity (number of gates) of the quantum circuits that can be run on our hardware. It will allow us to transition from running circuits with 15,000 gates to 100 million, or even 1 billion gates.

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IBM Quantum Computing Blog | Landmark IBM error correction paper on Nature cover - IBM