Quantinuum’s new H2-1 quantum computer proves that trapped-ion architecture, which is well-known for achieving outstanding qubit quality and gate fidelity, is also built for scale – and Quantinuum’s benchmarking team has the data to prove it. 

The bottom line: the new System Model H2 surpasses the H1 in complexity and qubit capacity while maintaining all the capabilities and fidelities of the previous generation – an astounding accomplishment when developing successive generations of quantum systems.

The newest entry in the H-Series is starting off with 32 qubits whereas H1 started with 10. H1 underwent several upgrades, ultimately reaching a 20-qubit capacity, and H2 is poised to pick up the torch and run with it. Staying true to the ultimate goal of increasing performance, H2 does not simply increase the qubit count but has already achieved a higher Quantum Volume than any other quantum computer ever built: 2¹⁶ or 65,536. 

Most importantly for the growing number of industrials and academic research institutions using the H-Series, benchmarking data shows that none of these hardware changes reduced the high-performance levels achieved by the System Model H1. That’s a key challenge in scaling quantum computers – preserving performance while adding qubits. The error rate on the fully connected circuits is comparable to the H1, even with a significant increase in qubits. Indeed, H2 exceeds H1 in multiple performance metrics: single-qubit gate error, two-qubit gate error, measurement cross talk and SPAM. 

Key to the engineering advances made in the second-generation H-Series quantum computer are reductions in the physical resources required per qubit. To get the most out of the quantum charge-coupled device (QCCD) architecture, which the H-Series is built on, the hardware team at Quantinuum introduced a series of component innovations, to eliminate some performance limitations of the first generation in areas such as ion-loading, voltage sources, and delivering high-precision radio signals to control and manipulate ions.

The research paper, “A Race Track Trapped-Ion Quantum Processor,” details all of these engineering advances, and exactly what impacts they have on the computing performance of the machine. The paper includes results from component and system-level benchmarking tests that document the new machine’s capabilities at launch. These benchmarking metrics, combined with the company’s advances in topological qubits, represent a new phase of quantum computing.

Advancing Beyond Classical Simulation

‍In addition to the expanded capabilities, the new design provides operational efficiencies and a clear growth path.

At launch, H2’s operations can still be emulated classically. However, Quantinuum released H2 at a small percentage of its full capacity. This new machine has the ability to upgrade to more qubits and gate zones, pushing it past the level where classical computers can hope to keep up.

Increased Efficiency in New Trap Design

This new generation quantum processor represents the first major trap upgrade in the H-Series. One of the most significant changes is the new oval (or racetrack) shape of the ion trap itself, which allows for a more efficient use of space and electrical control signals. 

One key engineering challenge presented by this new design was the ability to route signals beneath the top metal layer of the trap. The hardware team addressed this by using radiofrequency (RF) tunnels. These tunnels allow inner and outer voltage electrodes to be implemented without being directly connected on the top surface of the trap, which is the key to making truly two-dimensional traps that will greatly increase the computational speed of these machines. 

The new trap also features voltage “broadcasting,” which saves control signals by tying multiple DC electrodes within the trap to the same external signal. This is accomplished in “conveyor belt” regions on each side of the trap where ions are stored, improving electrode control efficiency by requiring only three voltage signals for 20 wells on each side of the trap.

The other significant component of H2 is the Magneto Optical Trap (MOT) which replaces the effusive atomic oven that H1 used. The MOT reduces the startup time for H2 by cooling the neutral atoms before shooting them at the trap, which will be crucial for very large machines that use large numbers of qubits. 

Industry-leading Results from 15 Benchmarking Tests

Quantinuum has always valued transparency and supported its performance claims with publicly available data. 

To quantify the impact of these hardware and design improvements, Quantinuum ran 15 tests that measured component operations, overall system performance and application performance. The complete results from the tests are included in the new research paper. 

The hardware team ran four system-level benchmark tests that included more complex, multi-qubit circuits to give a broader picture of overall performance. These tests were:

• Mirror benchmarking: A scalable way to benchmark arbitrary quantum circuits.
• Quantum volume: A popular system-level test with a well-established construction that is comparable across gate-based quantum computers.
• Random circuit sampling: A computational task of sampling the output distributions of random quantum circuits.
• Entanglement certification in Greenberger-Horne-Zeilinger (GHZ) states: A demanding test of qubit coherence that is widely measured and reported across a variety of quantum hardware.

H2 showed state-of-the-art performance on each of these system-level tests, but the results of the GHZ test were particularly impressive. The verification of the globally entangled GHZ state requires a relatively high fidelity, which becomes harder and harder to achieve with larger numbers of qubits. 

With H2’s 32 qubits and precision control of the environment in the ion trap, Quantinuum researchers were able to achieve an entangled state of 32 qubits with a fidelity of 82.0(7)%, setting a new world record.

In addition to the system level tests, the Quantinuum hardware team ran these component benchmark tests:

• SPAM experiment
• Single-qubit gate randomized benchmarking
• Two-qubit gate randomized benchmarking
• Two-qubit SU gate randomized benchmarking RB
• Two-qubit parameterized gate randomized benchmarking
• Measurement/reset crosstalk benchmarking 
• Interleaved transport randomized benchmarking
  ‍

The paper includes results from those tests as well as results from these application benchmarks:

• Hamiltonian simulation
• Quantum Approximate Optimization Algorithm 
• Error correction: repetition code
• Holographic quantum dynamics simulation 

In a meaningful advance in an important area of industrial and real-world relevance, Quantinuum researchers have demonstrated a quantum algorithm capable of solving complex combinatorial optimization problems while making the most of available quantum resources. 

Results on the new H2 quantum computer evidenced a remarkable ability to solve combinatorial optimization problems with as few quantum resources as those employed by just one layer of the quantum approximate optimization algorithm (QAOA), the current and traditional workhorse of quantum heuristic algorithms. 

Optimization problems are common in industry in contexts such as route planning, scheduling, cost optimization and logistics. However, as the number of variables increases and optimization problems grow larger and more complex, finding satisfactory solutions using classical algorithms becomes increasingly difficult. 

Recent research suggests that certain quantum algorithms might be capable of solving combinatorial optimization problems better than classical algorithms. The realization of such quantum algorithms can therefore potentially increase the efficiency of industrial processes. 

However, the effectiveness of these algorithms on near-term quantum devices and even on future generations of more capable quantum computers presents a technical challenge: quantum resources will need to be reduced as much as possible in order to protect the quantum algorithm from the unavoidable effects of quantum noise.

Sebastian Leontica and Dr. David Amaro, a senior research scientist at Quantinuum, explain their advances in a new paper, “Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits” published on arXiv. This is one of several papers published at the launch of Quantinuum’s H2, that highlight the unparalleled power of the newest generation of the H-Series, Powered by Honeywell. 

“We should strive to use as few quantum resources as possible no matter how good a quantum computer we are operating on, which means using the smallest possible number of qubits that fit within the problem size and a circuit that is as shallow as possible,” Dr. Amaro said. “Our algorithm uses the fewest possible resources and still achieves good performance.”

The researchers use a parameterized instantaneous quantum polynomial (IQP) circuit of the same depth as the 1-layer QAOA to incorporate corrections that would otherwise require multiple layers. Another differentiating feature of the algorithm is that the parameters in the IQP circuit can be efficiently trained on a classical computer, avoiding some training issues of other algorithms like QAOA. Critically, the circuit takes full advantage of, and benefits from features available on Quantinuum’s devices, including parameterized two-qubit gates, all-to-all connectivity, and high-fidelity operations. 

“Our numerical simulations and experiments on the new H2 quantum computer at small scale indicate that this heuristic algorithm, compared to 1-layer QAOA, is expected to amplify the probability of sampling good or even optimal solutions of large optimization problems,” Dr. Amaro said. “We now want to understand how the solution quality and runtime of our algorithm compares to the best classical algorithms.”

This algorithm will be useful for current quantum computers as well as larger machines farther along the Quantinuum hardware roadmap. 

How the Experiment Worked

The goal of this project was to provide a quantum heuristic algorithm for combinatorial optimization that returns better solutions for optimization problems and uses fewer quantum resources than state of the art quantum heuristics. The researchers used a fully connected parameterized IQP, warm-started from 1-layer QAOA. For a problem with n binary variables the circuit contained up to n(n-1)/2 two-qubit gates and the researchers employed only 2^0.32n shots. 

The algorithm showed improved performance on the Sherrington-Kirkpatrick (SK) optimization problem compared to the 1-layer QAOA. Numerical simulations showed an average speed up of 2^0.31n compared to 2^0.5n when looking for the optimal solution. 

Experimental results on our new H2 quantum computer and emulator confirmed that the new optimization algorithm outperforms 1-layer QAOA and reliably solves complex optimization problems. The optimal solution was found for 136 out of 312 instances, four of which were for the maximum size of 32 qubits. A 30-qubit instance was solved optimally on the H2 device, which means, remarkably, that at least one of the 776 shots measured after performing 432 two-qubit gates corresponds to the unique optimal solution in the huge set of 2³⁰ > 10⁹ candidate solutions. 

These results indicate that the algorithm, in combination with H2 hardware, is capable of solving hard optimization problems using minimal quantum resources in the presence of real hardware noise.

Quantinuum researchers expect that these promising results at small scale will encourage the further study of new quantum heuristic algorithms at the relevant scale for real-world optimization problems, which requires a better understanding of their performance under realistic conditions.

Speedup of IQP over QAOA

Numerical simulations of 256 SK random instances for each problem size from 4 to 29 qubits. Graph A shows the probability of sampling the optimal solution in the IQP circuit, for which the average is 2^-0.31n. Graph B shows the enhancement factor compared to 1-layer QAOA, for which the average is 2^0.23n. These results indicate that Quantinuum’s algorithm has significantly better runtime than 1-layer QAOA.

For more than two decades, there has been a general consensus among physicists pursuing the development of universal, fault-tolerant quantum computers that non-Abelian topological states would offer a promising path to success, if the states could ever be created.

These states host exotic quasi-particles—called anyons—that allow the storage of quantum information in their internal states which can only be changed by "braiding" them around each other in spacetime. Small perturbations in the trajectory of these braids would then leave the topology of the braid unchanged, making this paradigm inherently robust. It is as if they are ‘deaf’ to the noise of a system.

The problem however, is that non-Abelian anyons have never yet been detected, much less controlled. 

Until now.

Now, Quantinuum scientists, in collaboration with researchers from Harvard University and Caltech, have turned years of theory regarding topological states into reality, using the unique capabilities of the new H2 trapped-ion processor to create and control non-Abelian anyons. Using a shallow adaptive circuit on the H2, the research team prepared a non-Abelian quantum state on 27 qubits with a fidelity per site exceeding 98.4%.

This demonstration hinges on crucial advances in theory and experiment. On the theory side, Dr. Ruben Verresen, Prof. Ashvin Vishwanath (Harvard) and Dr. Nathanan Tantivasadakarn (Caltech) have shown how to use mid-circuit measurement to significantly simplify the route towards this kind of non-Abelian state. On the experimental side, the increased qubit capacity of the H2 system allows for sufficient complexity to create collective non-Abelian particles, while keeping the extremely low gate and mid-circuit measurement errors of previous generations.

The achievement has set the stage for an accelerated path to fault-tolerant quantum computing while also paving the way for new fields of research within condensed matter physics and high-energy physics.

The paper documenting the research, "Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor," is posted in Nature. This research was one of several papers published at the launch of H2, the next generation in Quantinuum's H-Series quantum computer, Powered by Honeywell.  

Advancing the Hardware Roadmap

Quantinuum has been advancing this area of research in “stealth mode” for some considerable time.  

Ilyas Khan, Quantinuum’s Chief Product Officer said "I recall vividly discussing topological quantum computing with Henrik 7 years ago during a long hot summer when devices such as our H2 processor were hard to even dream about. This research represents a milestone that benefits the industry as a whole and yet again demonstrates our ability to not only be world leaders today but also long into the future.”

"Topological order is our best shot at creating a quantum computer with very low error rates," Henrik said. "We need to be able to operate on the system while keeping it protected from the environment," he said. "Topological order can offer that protection. This research demonstrates that the more exotic kind of topological state, the non-Abelian kind, can be created with today's devices on-demand and with high fidelity. One of next steps will be to demonstrate stability by repetitive error-correction, utilizing the same ingredients used to prepare the state in the first place."

According to Tony Uttley, President and COO of Quantinuum, this advance represents a breakaway moment for Quantinuum.  

"We've reached a point with our technology that we can build a quantum computer on top of a quantum computer," Tony said. "These non-Abelian topological qubits can layer on top of physical qubits without changing how our quantum computer operates. That accomplishment will accelerate our work on the path to fault-tolerant quantum computing."

When thinking about changes in phases of matter, the first images that come to mind might be ice melting or water boiling. The critical point in these processes is located at the boundary between the two phases – the transition from solid to liquid or from liquid to gas. 

Phase transitions like these get right to the heart of how large material systems behave and are at the frontier of research in condensed matter physics for their ability to provide insights into emergent phenomena like magnetism and topological order. In classical systems, phase transitions are generally driven by thermal fluctuations and occur at finite temperature. On the contrary, quantum systems can exhibit phase transitions even at zero temperatures; the residual fluctuations that control such phase transitions at zero temperature are due to entanglement and are entirely quantum in origin.  

Quantinuum researchers recently used the H1-1 quantum computer to computationally model a group of highly correlated quantum particles at a quantum critical point — on the border of a transition between a paramagnetic state (a state of magnetism characterized by a weak attraction) to a ferromagnetic one (characterized by a strong attraction).

Simulating such a transition on a classical computer is possible using tensor network methods, though it is difficult. However, generalizations of such physics to more complicated systems can pose serious problems to classical tensor network techniques, even when deployed on the most powerful supercomputers.  On a quantum computer, on the other hand, such generalizations will likely only require modest increases in the number and quality of available qubits.

In a technical paper submitted to the arXiv, Probing critical states of matter on a digital quantum computer, the Quantinuum team demonstrated how the powerful components and high fidelity of the H-Series digital quantum computers could be harnessed to tackle a 128-site condensed matter physics problem, combining a quantum tensor network method with qubit reuse to make highly productive use of the 20-qubit H1-1 quantum computer.

Reza Haghshenas, Senior Advanced Physicist, and the lead author the paper said, “This is the kind of problem that appeals to condensed-matter physicists working with quantum computers, who are looking forward to revealing exotic aspects of strongly correlated systems that are still unknown to the classical realm. Digital quantum computers have the potential to become a versatile tool for working scientists, particularly in fields like condensed matter and particle physics, and may open entirely new directions in fundamental research.”

The role of quantum tensor networks

Tensor networks are mathematical frameworks whose structure enables them to represent and manipulate quantum states in an efficient manner. Originally associated with the mathematics of quantum mechanics, tensor network methods now crop up in many places, from machine learning to natural language processing, or indeed any model with a large number of interacting, high-dimensional mathematical objects. 

The Quantinuum team described using a tensor network method--the multi-scale entanglement renormalization ansatz (MERA)--to produce accurate estimates for the decay of ferromagnetic correlations and the ground state energy of the system. MERA is particularly well-suited to studying scale invariant quantum states, such as ground states at continuous quantum phase transitions, where each layer in the mathematical model captures entanglement at different scales of distance. 

“By calculating the critical state properties with MERA on a digital quantum computer like the H-Series, we have shown that research teams can program the connectivity and system interactions into the problem,” said Dave Hayes, Lead of the U.S. quantum theory team at Quantinuum and one of the paper’s authors. “So, it can, in principle, go out and simulate any system that you can dream of.”

Simulating a highly entangled quantum spin model

In this experiment, the researchers wanted to accurately calculate the ground state of the quantum system in its critical state. This quantum system is composed of many tiny quantum magnets interacting with one another and pointing in different directions, known as a quantum spin model. In the paramagnetic phase, tiny, individual magnets in the material are randomly oriented, and only correlated with each other over small length-scales. In the ferromagnetic phase, these individual atomic magnetic moments align spontaneously over macroscopic length scales due to strong magnetic interactions. 

In the computational model, the quantum magnets were initially arranged in one dimension, along a line. To describe the critical point in this quantum magnetism problem, particles in the line needed to be entangled with one another in a complex way, making this as a very challenging problem for a classical computer to solve in high dimensional and non-equilibrium systems. 

“That's as hard as it gets for these systems,” Dave explained. “So that's where we want to look for quantum advantage – because we want the problem to be as hard as possible on the classical computer, and then have a quantum computer solve it.”

To improve the results, the team used two error mitigation techniques, symmetry-based error heralding, which is made possible by the MERA structure, and zero-noise extrapolation, a method originally developed by researchers at IBM. The first involved enforcing local symmetry in the model so that errors affecting the symmetry of the state could be detected. The second strategy, zero-noise extrapolation, involves adding noise to the qubits to measure the impact it has, and then using those results to extrapolate the results that would be expected under conditions with less noise than was present in the experiment.

Future applications

The Quantinuum team describes this sort of problem as a stepping-stone, which allows the researchers to explore quantum tensor network methods on today’s devices and compare them either to simulations or analytical results produced using classical computers. It is a chance to learn how to tackle a problem really well before quantum computers scale up in the future and begin to offer solutions that are not possible to achieve on classical computers. 

“Potentially, our biggest applications over the next couple of years will include studying solid-state systems, physics systems, many-body systems, and modeling them,” said Jenni Strabley, Senior Director of Offering Management at Quantinuum.

The team now looks forward to future work, exploring more complex MERA generalizations to compute the states of 2D and 3D many-body and condensed matter systems on a digital quantum computer – quantum states that are much more difficult to calculate classically. 

The H-Series allows researchers to simulate a much broader range of systems than analog devices as well as to incorporate quantum error mitigation strategies, as demonstrated in the experiment. Plus, Quantinuum’s System Model H2 quantum computer, which was launched earlier this year, should scale this type of simulation beyond what is possible using classical computers.

Quantum computing is set to have a huge impact on cybersecurity. Much of the discussion today is around the threat that it could pose to the foundation of security systems, but there is also enormous potential for quantum computing to transform the security of communications and data.

Quantinuum is hosting an exclusive RSA Conference session titled “Cyber Secrets: What best-in-class cyber experts know about quantum” on Tuesday, April 25^th, from 7:30-8:15am PST in the Moscone Center South Hall at Booth #2100. 

During the session, you can expect to learn more about:

• The impact of quantum computing on cybersecurity
• Separating hype from reality with quantum security technologies
• What leading organizations are doing to build resilience with quantum technologies

With our expert panelists, direct from the world of quantum computing and cybersecurity:

• Kaniah Konkoly-Thege, Chief Legal Counsel and SVP Government Relations for Quantinuum
• Jeff Miller, Chief Information Officer for Quantinuum
• Matt Bohne, Vice President & Chief Product Security Officer for Honeywell Corporation
• Todd Moore, Head of the Data Security Products Portfolio for Thales
• John Davis, Vice President, Public Sector for Palo Alto Networks

Breakfast and refreshments will be provided for all attendees. Come early and stick around after to talk with our panelists. We hope to see you at the session and invite you to Quantinuum’s Booth #5176 in the North Hall.

In 1952, facing opposition from scientists who disbelieved her thesis that computer programming could be made more useful by using English words, the mathematician and computer scientist Grace Hopper published her first paper on compilers and wrote a precursor to the modern compiler, the A-0, while working at Remington Rand.

Over subsequent decades, the principles of compilers, whose task it is to translate between high level programming languages and machine code, took shape and new methods were introduced to support their optimization. One such innovation was the intermediate representation (IR), which was introduced to manage the complexity of the compilation process, enabling compilers to represent the program without loss of information, and to be broken up into modular phases and components.

This developmental path spawned the modern computer industry, with languages that work across hardware systems, middleware, firmware, operating systems, and software applications. It has also supported the emergence of the huge numbers of small businesses and professionals who make a living collaborating to solve problems using code that depends on compilers to control the underlying computing hardware.

Now, a similar story is unfolding in quantum computing. There are efforts around the world to make it simpler for engineers and developers across many sectors to take advantage of quantum computers by translating between high level coding languages and tools, and quantum circuits — the combinations of gates that run on quantum computers to generate solutions. Many of these efforts focus on hybrid quantum-classical workflows, which allow a problem to be solved by taking advantage of the strengths of different modes of computation, accessing central processing units (CPUs), graphical processing units (GPUs) and quantum processing units (QPUs) as needed.

Microsoft is a significant contributor to this burgeoning quantum ecosystem, providing access to multiple quantum computing systems through Azure Quantum, and a founding member of the QIR Alliance, a cross-industry effort to make quantum computing source code portable across different hardware systems and modalities and to make quantum computing more useful to engineers and developers. QIR offers an interoperable specification for quantum programs, including a hardware profile designed for Quantinuum’s H-Series quantum computers, and has the capacity to support cross-compiling quantum and classical workflows, encouraging hybrid use-cases.

As one of the largest integrated quantum computing companies in the world, Quantinuum was excited to become a QIR steering member alongside partners including Nvidia, Oak Ridge National Laboratory, Quantum Circuits Inc., and Rigetti Computing. Quantinuum supports multiple open-source eco-system tools including its own family of open-source software development kits and compilers, such as TKET for general purpose quantum computation and lambeq for quantum natural language processing.

Rapid progress with KPMG and Microsoft

As founding members of QIR, Quantinuum recently worked with Microsoft Azure Quantum alongside KPMG on a project that involved Microsoft’s Q#, a stand-alone language offering a high level of abstraction and Quantinuum’s System Model H1, Powered by Honeywell. The Q# language has been designed for the specific needs of quantum computing and provides a high-level of abstraction enabling developers to seamlessly blend classical and quantum operations, significantly simplifying the design of hybrid algorithms. 

KPMG’s quantum team wanted to translate an existing algorithm into Q#, and to take advantage of the unique and differentiating capabilities of Quantinuum’s H-Series, particularly qubit reuse, mid-circuit measurement and all-to-all connectivity. System Model H1 is the first generation trapped-ion based quantum computer built using the quantum charge-coupled device (QCCD) architecture. KPMG accessed the H1-1 QPU with 20 fully connected qubits. H1-1 recently achieved a Quantum Volume of 32,768, demonstrating a new high-water mark for the industry in terms of computation power as measured by quantum volume.

Q# and QIR offered an abstraction from hardware specific instructions, allowing the KPMG team, led by Michael Egan, to make best use of the H-Series and take advantage of runtime support for measurement-conditioned program flow control, and classical calculations within runtime.

Nathan Rhodes of the KPMG team wrote a tutorial about the project to demonstrate how an algorithm writer would use the KPMG code step-by-step as well as the particular features of QIR, Q# and the H-Series. It is the first time that code from a third party will be available for end users on Microsoft’s Azure portal.

Microsoft recently announced the roll-out of integrated quantum computing on Azure Quantum, an important milestone in Microsoft’s Hybrid Quantum Computing Architecture, which provides tighter integration between quantum and classical processing. 

Fabrice Frachon, Principal PM Lead, Azure Quantum, described this new Azure Quantum capability as a key milestone to unlock a new generation of hybrid algorithms on the path to scaled quantum computing.

The demonstration

The team ran an algorithm designed to solve an estimation problem, a promising use case for quantum computing, with potential application in fields including traffic flow, network optimization, energy generation, storage, and distribution, and to solve other infrastructure challenges. The iterative phase estimation algorithm¹ was compiled into quantum circuits from code written in a Q# environment with the QIR toolset, producing a circuit with approximately 500 gates, including 111 2-Qubit gates, running across three qubits with one reused three times, and achieving a fidelity of 0.92. This is possible because of the high gate fidelity and the low SPAM error which enables qubit reuse.

The results compare favorably with the more standard Quantum Phase Estimation version described in “Quantum computation and quantum information,” by Michael A. Nielsen and Isaac Chuang.

Quantinuum’s H1 had five capabilities that were crucial to this project:

1. Qubit reuse
2. Mid-circuit measurement
3. Bound loop (a restriction on how many times the system will do the iterative circuit)
4. Classical computation
5. Nested functions

The project emphasized the importance of companies experimenting with quantum computing, so they can identify any possible IT issues early on, understanding the development environment and how quantum computing integrates with current workflows and processes.

As the global quantum ecosystem continues to advance, collaborative efforts like QIR will play a crucial role in bringing together industrial partners seeking novel solutions to challenging problems, talented developers, engineers, and researchers, and quantum hardware and software companies, which will continue to add deep scientific and engineering knowledge and expertise.

1. Phys. Rev. A 76, 030306(R) (2007) - Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark (aps.org)