How we equip our users to unlock the full potential of H-Series Quantum Computers
In a series of recent technical papers, Quantinuum researchers demonstrated the world-leading capabilities of the latest H-Series quantum computers, and the features and tools that make these accessible to our global customers and users.
Our teams used the H-Series quantum computers to directly measure and control non-abelian topological states of matter [1] for the first time, explore new ways to solve combinatorial optimization problems more efficiently [2], simulate molecular systems using logical qubits with error detection [3], probe critical states of matter [4], as well as exhaustively benchmark our very latest system [5].
Part of what makes such rapid technical and scientific progress possible is the effort our teams continually make to develop and improve workflow tools, helping our users to achieve successful results. In this blog post, we will explore the capabilities of three new tools in some detail, discuss their significance, and highlight their impact in recent quantum computing research.
Leakage Detection Gadget in pyTKET
“Leakage” is a quantum error process where a qubit ends up in a state outside the computational subspace and can significantly impact quantum computations. To address this issue, Quantinuum has developed a leakage detection gadget in pyTKET, a python module for interfacing with TKET, our quantum computing toolkit and optimizing compiler. This gadget, presented at the 2022 IEEE International Conference [6], acts as an error detection technique: it detects and excludes results affected by leakage, minimizing its impact on computations. It is also a valuable tool for measuring single-qubit and two-qubit spontaneous emission rates. H-Series users can access this open-source gadget through pyTKET, and an example notebook is available on the pyTKET GitHub repository.
Mid-Circuit Measurement and Qubit Reuse (MCMR) Package
The MCMR package, built as a pyTKET compiler pass, is designed to reduce the number of qubits required for executing many types of quantum algorithms, expanding the scope of what is possible on the current-generation H-Series quantum computers.
As an example, in a recent paper [4], Quantinuum researchers applied this tool to simulate the transverse-field Ising model and used only 20 qubits to simulate a much larger 128 site system (there is more detail below on this work). By measuring qubits early in the circuit, resetting them, and reusing them elsewhere, the package ingests a raw circuit and outputs an optimized circuit that requires fewer quantum resources. Previously, a scientific paper [7] and blog post on MCMR were published highlighting its benefits and applications. H-Series customers can download this package via the Quantinuum user portal.
Quantinuum H2-1 Emulator Release
To enable efficient use of Quantinuum’s 2nd generation processor, the System Model H2, Quantinuum has released the H2-1 emulator to give users greater flexibility with noise-informed state vector emulation. This emulator uses the NVIDIA's cuQuantum SDK to accelerate quantum computing simulation workflows, nearly approaching the limit of full state emulation on conventional classical hardware. The emulator is a faithful representation of the QPU it emulates. This is accomplished by not only using realistic noise models and noise parameters, but also by sharing the same software stack between the QPU and the emulator up until the job is either routed to the QPU or the classical computing processors. Most notable is that the emulator and the QPU use the same compiler allowing subtle and time-dependent errors to be appropriately represented. The H2-1 emulator was initially released as a beta product alongside the System Model H2 quantum computer at launch. It runs on a GPU backend and an upgraded global framework now offering features such as job chunking, incremental resource distribution, mid-execution job cancellation, and partial result return. Detailed information about the emulator can be found in the H2 emulator product datasheet on the Quantinuum website. H-Series customers with an H2 subscription can access the H2-1 emulator via an API or the Microsoft Azure platform.
Enabling Recent Works
Quantinuum's new enabling tools have already demonstrated their efficacy and value in recent quantum computing research, playing a vital role in advancing the field and achieving groundbreaking results. Let's expand on some notable recent examples.
All works presented here benefited from having access to our H-Series emulators; of these two significant demonstrations were the “Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor” [1] and “Demonstration of improved 1-layer QAOA with Instantaneous Quantum Polynomial” [2]. These demonstrations involved extensive testing, debugging, and experiment design, for which the versatility of the H2-1 emulator proved invaluable, providing initial performance benchmarks in a realistic noisy environment. Researchers relied on the emulator's results to gauge algorithmic performance and make necessary adjustments. By leveraging the emulator's capabilities, researchers were able to accelerate their progress.
The MCMR package was extensively used in benchmarking the System Model H2 quantum computer’s world-leading capabilities [5]. Two application-level benchmarks performed in this work, approximating the solution to a MaxCut combinatorics problem using the quantum approximate optimization algorithm (QAOA) and accurately simulating a quantum dynamics model using a holographic quantum dynamics (HoloQUADS) algorithm, would have been too large to encode on H2's 32 qubits without the MCMR package. Further illustrating the overall value of these tools, in the HoloQUADS benchmark, there is a "bond qubit" that is particularly susceptible to errors due to leakage. The leakage detection gadget was used on this "bond qubit" at the end of the circuit, and any shots with a detected leakage error were discarded. The leakage detection gadget was also used to obtain the rate of leakage error per single-qubit and two-qubit gates, two component-level benchmarks.
In another scientific work [4], the MCMR compilation tool proved instrumental to simulating a transverse-field Ising model on 128 sites, using 20 qubits. With the MCMR package and by leveraging a state-of-the-art classical tensor-network ansatz expressed as a quantum circuit, the Quantinuum team was able to express the highly entangled ground state of the critical Ising model. The team showed that with H1-1's 20 qubits, the properties of this state could be measured on a 128-site system with very high fidelity, enabling a quantitatively accurate extraction of some critical properties of the model.
Key Takeaways
At Quantinuum, we are entirely devoted to producing a quantum hardware, middleware and software stack that leads the world on the most important benchmarks and includes features and tools that provide breakthrough benefit to our growing base of users. In today's NISQ hardware, "benefit" usually takes the form of getting the most performance out of today’s hardware, continually pushing what is considered to be possible. In this blog we describe two examples: error detection and discard using the “leakage detection gadget” and an automated method for circuit optimization for qubit reuse. “Benefit” can also take other forms, such as productivity. Our emulator brings many benefits to our users, but one that resonates the most is productivity. Being a faithful representation of our QPU performance, the emulator is an accessible tool which users have at their disposal to develop and test new, innovative algorithms. The tools and features Quantinuum releases are driven by users’ feedback; whether you are new to H-Series or a seasoned user, please reach-out and let us know how we can help bring benefit to your research and use case.
Footnotes:
[1] Mohsin Iqbal et al., Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor (2023), arXiv:2305.03766 [quant-ph]
[2] Sebastian Leontica and David Amaro, Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits (2022), arXiv:2210.05526 [quant-ph]
[3] Kentaro Yamamoto, Samuel Duffield, Yuta Kikuchi, and David Muñoz Ramo, Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection (2023), arXiv:2306.16608 [quant-ph]
[4] Reza Haghshenas, et al., Probing critical states of matter on a digital quantum computer (2023),
arXiv:2305.01650 [quant-ph]
[5] S. A. Moses, et al., A Race Track Trapped-Ion Quantum Processor (2023), arXiv:2305.03828 [quant-ph]
[6] K. Mayer, Mitigating qubit leakage errors in quantum circuits with gadgets and post-selection, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), Broomfield, CO, USA, (2022), pp. 809-809, doi: 10.1109/QCE53715.2022.00126.
[7] Matthew DeCross, Eli Chertkov, Megan Kohagen, and Michael Foss-Feig, Qubit-reuse compilation with mid-circuit measurement and reset (2022), arXiv:2210.08039 [quant-ph]
About Quantinuum
Quantinuum, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Quantinuum’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Quantinuum leads the quantum computing revolution across continents.
From September 16th – 18th, Quantum World Congress (QWC) will bring together visionaries, policymakers, researchers, investors, and students from across the globe to discuss the future of quantum computing in Tysons, Virginia.
Quantinuum is forging the path to universal, fully fault-tolerant quantum computing with our integrated full-stack. Join our quantum experts for the below sessions and at Booth #27 to discuss the latest on Quantinuum Systems, the world’s highest-performing, commercially available quantum computers, our new software stack featuring the key additions of Guppy and Selene, our path to error correction, and more.
Wednesday, September 17th
Keynote with Quantinuum's CEO, Dr. Rajeeb Hazra
9:00 – 9:20am ET | Main Stage
At QWC 2024, Quantinuum’s President & CEO, Dr. Rajeeb “Raj” Hazra, took the stage to showcase our commitment to advancing quantum technologies through the unveiling of our roadmap to universal, fully fault-tolerant quantum computing by the end of this decade. This year at QWC 2025, join Raj on the main stage to discover the progress we’ve made over the last year in advancing quantum computing on both commercial and technical fronts and be the first to hear exciting insights on what’s to come from Quantinuum.
Panel Session: Policy Priorities for Responsible Quantum and AI
1:00 – 1:30pm ET | Maplewood Hall
As part of the Track Sessions on Government & Security, Quantinuum’s Director of Government Relations, Ryan McKenney, will discuss “Policy Priorities for Responsible Quantum and AI” with Jim Cook from Actions to Impact Strategies and Paul Stimers from Quantum Industry Coalition.
Fireside Chat: Establishing a Pro-Innovation Regulatory Framework
4:00 – 4:30pm ET | Vault Theater
During the Track Session on Industry Advancement, Quantinuum’s Chief Legal Officer, Kaniah Konkoly-Thege, and Director of Government Relations, Ryan McKenney, will take the stage to discuss the importance of “Establishing a Pro-Innovation Regulatory Framework”.
In the world of physics, ideas can lie dormant for decades before revealing their true power. What begins as a quiet paper in an academic journal can eventually reshape our understanding of the universe itself.
In 1993, nestled deep in the halls of Yale University, physicist Subir Sachdev and his graduate student Jinwu Ye stumbled upon such an idea. Their work, originally aimed at unraveling the mysteries of “spin fluids”, would go on to ignite one of the most surprising and profound connections in modern physics—a bridge between the strange behavior of quantum materials and the warped spacetime of black holes.
Two decades after the paper was published, it would be pulled into the orbit of a radically different domain: quantum gravity. Thanks to work by renowned physicist Alexei Kitaev in 2015, the model found new life as a testing ground for the mind-bending theory of holography—the idea that the universe we live in might be a projection, from a lower-dimensional reality.
Holography is an exotic approach to understanding reality where scientists use holograms to describe higher dimensional systems in one less dimension. So, if our world is 3+1 dimensional (3 spatial directions plus time), there exists a 2+1, or 3-dimensional description of it. In the words of Leonard Susskind, a pioneer in quantum holography, "the three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface."
The “SYK” model, as it is known today, is now considered a quintessential framework for studying strongly correlated quantum phenomena, which occur in everything from superconductors to strange metals—and even in black holes. In fact, The SYK model has also been used to study one of physics’ true final frontiers, quantum gravity, with the authors of the paper calling it “a paradigmatic model for quantum gravity in the lab.”
The SYK model involves Majorana fermions, a type of particle that is its own antiparticle. A key feature of the model is that these fermions are all-to-all connected, leading to strong correlations. This connectivity makes the model particularly challenging to simulate on classical computers, where such correlations are difficult to capture. Our quantum computers, however, natively support all-to-all connectivity making them a natural fit for studying the SYK model.
Now, 10 years after Kitaev’s watershed lectures, we’ve made new progress in studying the SYK model. In a new paper, we’ve completed the largest ever SYK study on a quantum computer. By exploiting our system’s native high fidelity and all-to-all connectivity, as well as our scientific team’s deep expertise across many disciplines, we were able to study the SYK model at a scale three times larger than the previous best experimental attempt.
While this work does not exceed classical techniques, it is very close to the classical state-of-the-art. The biggest ever classical study was done on 64 fermions, while our recent result, run on our smallest processor (System Model H1), included 24 fermions. Modelling 24 fermions costs us only 12 qubits (plus one ancilla) making it clear that we can quickly scale these studies: our System Model H2 supports 56 qubits (or ~100 fermions), and Helios, which is coming online this year, will have over 90 qubits (or ~180 fermions).
However, working with the SYK model takes more than just qubits. The SYK model has a complex Hamiltonian that is difficult to work with when encoded on a computer—quantum or classical. Studying the real-time dynamics of the SYK model means first representing the initial state on the qubits, then evolving it properly in time according to an intricate set of rules that determine the outcome. This means deep circuits (many circuit operations), which demand very high fidelity, or else an error will occur before the computation finishes.
Our cross-disciplinary team worked to ensure that we could pull off such a large simulation on a relatively small quantum processor, laying the groundwork for quantum advantage in this field.
First, the team adopted a randomized quantum algorithm called TETRIS to run the simulation. By using random sampling, among other methods, the TETRIS algorithm allows one to compute the time evolution of a system without the pernicious discretization errors or sizable overheads that plague other approaches. TETRIS is particularly suited to simulating the SYK model because with a high level of disorder in the material, simulating the SYK Hamiltonian means averaging over many random Hamiltonians. With TETRIS, one generates random circuits to compute evolution (even with a deterministic Hamiltonian). Therefore, when applying TETRIS on SYK, for every shot one can just generate a random instance of the Hamiltonain, and generate a random circuit on TETRIS at the same time. This simple approach enables less gate counts required per shot, meaning users can run more shots, naturally mitigating noise.
In addition, the team “sparsified” the SYK model, which means “pruning” the fermion interactions to reduce the complexity while still maintaining its crucial features. By combining sparsification and the TETRIS algorithm, the team was able to significantly reduce the circuit complexity, allowing it to be run on our machine with high fidelity.
They didn’t stop there. The team also proposed two new noise mitigation techniques, ensuring that they could run circuits deep enough without devolving entirely into noise. The two techniques both worked quite well, and the team was able to show that their algorithm, combined with the noise mitigation, performed significantly better and delivered more accurate results. The perfect agreement between the circuit results and the true theoretical results is a remarkable feat coming from a co-design effort between algorithms and hardware.
As we scale to larger systems, we come closer than ever to realizing quantum gravity in the lab, and thus, answering some of science’s biggest questions.
At Quantinuum, we pay attention to every detail. From quantum gates to teleportation, we work hard every day to ensure our quantum computers operate as effectively as possible. This means not only building the most advanced hardware and software, but that we constantly innovate new ways to make the most of our systems.
A key step in any computation is preparing the initial state of the qubits. Like lining up dominoes, you first need a special setup to get meaningful results. This process, known as state preparation or “state prep,” is an open field of research that can mean the difference between realizing the next breakthrough or falling short. Done ineffectively, state prep can carry steep computational costs, scaling exponentially with the qubit number.
Recently, our algorithm teams have been tackling this challenge from all angles. We’ve published three new papers on state prep, covering state prep for chemistry, materials, and fault tolerance.
In the first paper, our team tackled the issue of preparing states for quantum chemistry. Representing chemical systems on gate-based quantum computers is a tricky task; partly because you often want to prepare multiconfigurational states, which are very complex. Preparing states like this can cost a lot of resources, so our team worked to ensure we can do it without breaking the (quantum) bank.
To do this, our team investigated two different state prep methods. The first method uses Givens rotations, implemented to save computational costs. The second method exploits the sparsity of the molecular wavefunction to maximize efficiency.
Once the team perfected the two methods, they implemented them in InQuanto to explore the benefits across a range of applications, including calculating the ground and excited states of a strongly correlated molecule (twisted C_2 H_4). The results showed that the “sparse state preparation” scheme performed especially well, requiring fewer gates and shorter runtimes than alternative methods.
In the second paper, our team focused on state prep for materials simulation. Generally, it’s much easier for computers to simulate materials that are at zero temperature, which is, obviously, unrealistic. Much more relevant to most scientists is what happens when a material is not at zero temperature. In this case, you have two options: when the material is steadily at a given temperature, which scientists call thermal equilibrium, or when the material is going through some change, also known as out of equilibrium. Both are much harder for classical computers to work with.
In this paper, our team looked to solve an outstanding problem: there is no standard protocol for preparing thermal states. In this work, our team only targeted equilibrium states but, interestingly, they used an out of equilibrium protocol to do the work. By slowly and gently evolving from a simple state that we know how to prepare, they were able to prepare the desired thermal states in a way that was remarkably insensitive to noise.
Ultimately, this work could prove crucial for studying materials like superconductors. After all, no practical superconductor will ever be used at zero temperature. In fact, we want to use them at room temperature – and approaches like this are what will allow us to perform the necessary studies to one day get us there.
Finally, as we advance toward the fault-tolerant era, we encounter a new set of challenges: making computations fault-tolerant at every step can be an expensive venture, eating up qubits and gates. In the third paper, our team made fault-tolerant state preparation—the critical first step in any fault-tolerant algorithm—roughly twice as efficient. With our new “flag at origin” technique, gate counts are significantly reduced, bringing fault-tolerant computation closer to an everyday reality.
The method our researchers developed is highly modular: in the past, to perform optimized state prep like this, developers needed to solve one big expensive optimization problem. In this new work, we’ve figured out how to break the problem up into smaller pieces, in the sense that one now needs to solve a set of much smaller problems. This means that now, for the first time, developers can prepare fault-tolerant states for much larger error correction codes, a crucial step forward in the early-fault-tolerant era.
On top of this, our new method is highly general: it applies to almost any QEC code one can imagine. Normally, fault-tolerant state prep techniques must be anchored to a single code (or a family of codes), making it so that when you want to use a different code, you need a new state prep method. Now, thanks to our team’s work, developers have a single, general-purpose, fault-tolerant state prep method that can be widely applied and ported between different error correction codes. Like the modularity, this is a huge advance for the whole ecosystem—and is quite timely given our recent advances into true fault-tolerance.
This generality isn’t just applicable to different codes, it’s also applicable to the states that you are preparing: while other methods are optimized for preparing only the |0> state, this method is useful for a wide variety of states that are needed to set up a fault tolerant computation. This “state diversity” is especially valuable when working with the best codes – codes that give you many logical qubits per physical qubit. This new approach to fault-tolerant state prep will likely be the method used for fault-tolerant computations across the industry, and if not, it will inform new approaches moving forward.
From the initial state preparation to the final readout, we are ensuring that not only is our hardware the best, but that every single operation is as close to perfect as we can get it.