How we equip our users to unlock the full potential of H-Series Quantum Computers
Quantinuum is proud to introduce three new tools to help enterprise and academic users to make full use of the world-leading capabilities of the System Model H1 and H2 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.
A team from Quantinuum and the University of Freiburg found that quantum computers outperform classical for a workhorse calculation often used in accelerators like the Large Hadron Collider (LHC) at CERN.
Quantinuum’s Ifan Williams worked with the University of Freiburg’s Mathieu Pellen to tackle a pernicious problem in accelerator physics: calculating “cross sections”. Together, they developed a general, scalable approach to calculating cross sections that offers a quadratic speed-up compared to its classical counterpart.
A “cross-section” relates to the probability of a certain interaction happening. Scientists who do experiments in particle accelerators compare real measurements with theoretical cross-section calculations (predictions), using the agreement (or disagreement) to reason about the nature of our universe.
Generally, scientists run Monte Carlo simulations to make their theoretical predictions. Monte Carlo simulations are currently the biggest computational bottleneck in experimental high-energy physics (HEP), costing enormous CPU resources, which will only grow larger as new experiments come online.
It’s hard to put a specific number on exactly how costly calculations like this are, but we can say that probing fundamental physics at the LHC probably uses roughly 10 billion CPUH/year for data treatment, simulations, and theory predictions. Knowing that the theory predictions represent approximately 15-25% of this total, putting even a 10% dent in this number would be a massive change.
The collaborators used Quantinuum’s Quantum Monte Carlo integration (QMCI) engine to solve the same problem. Their work is the first published general methodology for performing cross-section calculations in HEP using quantum integration.
Importantly, the team’s methodology is potentially extendable to the problem sizes needed for real-world HEP cross-section calculations (currently done classically). Overall, this work establishes a solid foundation for performing such computations on a quantum computer in the future.
The Large Hadron Collider, the world’s biggest particle accelerator, generates a billion collisions each second, far more data than can be computationally analyzed. Planned future experiments are expected to generate even more. Quantum computers are also accelerating. Quantinuum’s latest H2 System became the highest performing commercially available system in the world when it was launched. When it was upgraded in 2024, it became the first quantum computer that cannot be exactly simulated by any classical computer. Our next generation Helios, on schedule to launch in 2025, will encode at least a trillion times more information than the H2—this is the power of exponential growth.
We can’t wait to see what’s next with quantum computing and high-energy physics.
The Quantinuum team is looking forward to participating in this year’s SCAsia conference from March 10th – 13th in Singapore. Meet our team at Booth B2 to discover how Quantinuum is bridging the gap between quantum computing and high-performance compute with leading industry partners.
Our team will be participating in workshops and presenting at the keynote and plenary sessions to showcase our quantum computing technologies. Join us at the below sessions:
Monday, March 10th, 1:30 – 2:30pm
Workshop: Accelerating Quantum Supercomputing: CUDA-Q Tutorial across Multiple Quantum Platforms
Location: Room P10 – Peony Jr 4512 (Level 4)
This workshop will explore the seamless integration of classical and quantum resources for quantum-accelerated supercomputing. Join Kentaro Yamamoto and Enrico Rinaldi, Lead R&D Scientists at Quantinuum, for an Introduction to our integrated full-stack for quantum computing, Quantum Phase Estimation (QPE) for solving quantum chemistry problems, and a demonstration of a QPE algorithm with CUDA-Q on Quantinuum Systems. If you're interested in access to our quantum computers and emulator for use on the CUDA-Q platform, register here.
Tuesday, March 11th, 11:00 – 11:30pm
Keynote: Quantum Computing: A Transformative Force for Singapore's Regional Economy
Location: Melati Ballroom (Level 4)
Quantum Computing is no longer a distant promise; it has arrived and is poised to revolutionize several economies. Join our President and CEO, Dr. Rajeeb Hazra, to discover how Quantinuum’s approach to Quantum Generative AI is driving breakthroughs in applications which hold significant relevance for Singapore, in fields like chemistry, computational biology, and finance. Additionally, Raj will discuss the challenges and opportunities of adopting quantum solutions from both technical and business perspectives, emphasizing the importance of collaboration to build quantum applications that integrate the best of quantum and AI.
Tuesday, March 11th, 5:40 – 6:00pm
Industry Breakout Track: Transformative value of Quantum and AI: bringing meaningful insights for critical applications today
Location: Room L1 – Lotus Jr (Level 4)
The ability to solve classically intractable problems defines the transformative value of quantum computing, offering new tools to redefine industries and address complex humanity challenges. In this session with Dr. Elvira Shishenina, Senior Director of Strategic Initiatives, discover how Quantinuum’s hardware is leading the way in achieving early fault-tolerance, marking a significant step forward in computational capabilities. By integrating quantum technology with AI and high-performance computing, we are building systems designed to address real-world issues with efficiency, precision and scale. This approach empowers critical applications from hydrogen fuel cells and carbon capture to precision medicine, food security, and cybersecurity, providing meaningful insights at a commercial level today.
Wednesday, March 12th, 4:40 – 5:00pm
Hybrid Quantum Classical Computing Track: Quantifying Quantum Advantage with an End-to-End Quantum Algorithm for the Jones Polynomial
Location: Room O3 – Orchid Jr 4211-2 (Level 4)
Join Konstantinos Meichanetzidis, Head of Scientific Product Development, for this presentation on an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer. Specifically, they estimate the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. In their research, they demonstrate our quantum algorithm on Quantinuum’s H2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, they construct an efficiently verifiable benchmark to characterize the effect of noise present in a given quantum processor. In parallel, they implement and benchmark the state-of-the-art tensor-network-based classical algorithms.The practical tools provided in the work presented will allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.
Thursday, March 13th, 11:00 – 11:30pm
Industry Plenary: Quantum Heuristics: From Worst Case to Practice
Location: Melati Ballroom (Level 4)
Which problems allow for a quantum speedup, and which do not? This question lies at the heart of quantum information processing. Providing a definitive answer is challenging, as it connects deeply to unresolved questions in complexity theory. To make progress, complexity theory relies on conjectures such as P≠NP and the Strong Exponential Time Hypothesis, which suggest that for many computational problems, we have discovered algorithms that are asymptotically close to optimal in the worst case. In this talk, Professor Harry Buhrman, Chief Scientist for Algorithms and Innovation, will explore the landscape from both theoretical and practical perspectives. On the theoretical side, I will introduce the concept of “queasy instances”—problem instances that are quantum-easy but classically hard (classically queasy). On the practical side, I will discuss how these insights connect to advancements in quantum hardware development and co-design.
*All times in Singapore Standard Time
BY HARRY BUHRMAN
Quantum computing continues to push the boundaries of what is computationally possible. A new study by Marcello Benedetti, Harry Buhrman, and Jordi Weggemans introduces Complement Sampling, a problem that highlights a dramatic separation between quantum and classical sample complexity. This work provides a robust demonstration of quantum advantage in a way that is not only provable but also feasible on near-term quantum devices.
The Complement Sampling Problem
Imagine a universe of N = 2n elements, from which a subset S of size K is drawn uniformly at random. The challenge is to sample from the complement S̅ without explicitly knowing S, but having access to samples of S. Classically, solving this problem requires roughly K samples, as the best a classical algorithm can do is guess at random after observing only some of the elements of S.
To better understand this, consider a small example. Suppose N = 8, meaning our universe consists of the numbers {0,1,2,3,4,5,6,7}. If a subset S of size K = 4 is drawn at random—say {1,3,5,7}—the goal is to sample from the complement S̅, which consists of {0,2,4,6}. A classical algorithm would need to collect and verify enough samples from S before it could infer what S̅ might be. However, a quantum algorithm can use a single superposition state over S (a quantum sample) to instantly generate a sample from S̅, eliminating the need for iterative searching.
Why This Matters: Quantum Advantage in Sample Complexity
Quantum advantage is often discussed in terms of computational speedups, such as those achieved by Shor’s algorithm for factoring large numbers. However, quantum resources provide advantages beyond time efficiency—they also affect how data is accessed, stored, and processed.
Complement Sampling fits into the category of sample complexity problems, where the goal is to minimize the number of samples needed to solve a problem. The authors prove that their quantum approach not only outperforms classical methods but does so in a way that is:
- Provable: It provides rigorous lower bounds on classical sample complexity, demonstrating an exponential separation.
- Verifiable: The correctness of the output of the sampler can be efficiently checked classically.
- NISQable: The quantum circuit required is shallow and feasible for Noisy Intermediate-Scale Quantum (NISQ) devices.
How the Quantum Algorithm Works
At its core, the quantum approach to Complement Sampling relies on the ability to perform a perfect swap between a subset S and its complement S̅. The method draws inspiration from a construction by Aaronson, Atia, and Susskind, which links state distinguishability to state swapping. The quantum algorithm:
- Uses a unitary transformation that maps the quantum sample |S⟩ to |S̅⟩ with high probability.
- For K = N/2, the algorithm works perfectly outputting an element from S̅ with probability 1.
- For other values of K, a probabilistic zero-error approach is used, ensuring correctness while reducing success probability.
This is made possible by quantum interference and superposition, allowing a quantum computer to manipulate distributions in ways that classical systems fundamentally cannot.
Classical Hardness and Cryptographic Implications
A crucial aspect of this work is its robustness. The authors prove that even for subsets generated using strong pseudorandom permutations, the problem remains hard for classical algorithms. This means that classical computers cannot efficiently solve Complement Sampling even with structured input distributions—an important consideration for real-world applications.
This robustness suggests potential applications in cryptography, where generating samples from complements could be useful in privacy-preserving protocols and quantum-secure verification methods.
Towards an Experimental Demonstration
Unlike some quantum advantage demonstrations that are difficult to verify classically (such as the random circuit sampling experiment), Complement Sampling is designed to be verifiable. The authors propose an interactive quantum versus classical game:
- A referee provides a quantum player with quantum samples from S.
- The player must return a sample from S̅
- A classical player, given the same number of classical samples, attempts to do the same.
While the classical player must resort to random guessing, the quantum player can leverage the swap algorithm to succeed with near certainty. Running such an experiment on NISQ hardware could serve as a practical demonstration of quantum advantage in a sample complexity setting.
Future Directions
This research raises exciting new questions:
- Can Complement Sampling be extended to more general probability distributions?
- Are there cryptographic protocols that can directly leverage this advantage?
- How well does the quantum algorithm perform in real-world noisy conditions?
With its blend of theoretical depth and experimental feasibility, Complement Sampling provides a compelling new frontier for demonstrating the power of quantum computing.
Conclusion
Complement Sampling represents one of the cleanest demonstrations of quantum advantage in a practical, verifiable, and NISQ-friendly setting. By leveraging quantum information processing in ways that classical computers fundamentally cannot, this work strengthens the case for near-term quantum technologies and their impact on computational complexity, cryptography, and beyond.
For those interested in the full details, the paper provides rigorous proofs, circuit designs, and further insights into the nature of quantum sample complexity. As quantum computing continues to evolve, Complement Sampling may serve as a cornerstone for future experimental demonstrations of quantum supremacy.
We have commenced work on the experiment – watch this space!