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In a series of recent technical papers, ҹɫֱ�� 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 [1] for the first time, [2], [3], [4], as well as exhaustively [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, ҹɫֱ�� 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 [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 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 [4], ҹɫֱ�� 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 [7] and on MCMR were published highlighting its benefits and applications. H-Series customers can download this package via the ҹɫֱ�� user portal.

ҹɫֱ�� H2-1 Emulator Release

To enable efficient use of ҹɫֱ��’s 2^nd generation processor, the System Model H2, ҹɫֱ�� 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 ҹɫֱ�� 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

ҹɫֱ��'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 “” [1] and “” [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 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 ҹɫֱ�� 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 ҹɫֱ��, 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 ҹɫֱ�� 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.

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Footnotes:

[1] Mohsin Iqbal et al., Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor (2023),

[2] Sebastian Leontica and David Amaro, Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits (2022),

[3] Kentaro Yamamoto, Samuel Duffield, Yuta Kikuchi, and David Muñoz Ramo, Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection (2023),

[4] Reza Haghshenas, et al., Probing critical states of matter on a digital quantum computer (2023),

[5] S. A. Moses, et al., A Race Track Trapped-Ion Quantum Processor (2023),

[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: .

[7] Matthew DeCross, Eli Chertkov, Megan Kohagen, and Michael Foss-Feig, Qubit-reuse compilation with mid-circuit measurement and reset (2022),

In the last 6 months, ҹɫֱ�� H-Series hardware has demonstrated explosive performance improvement. ҹɫֱ��’s System Model H1-1, Powered by Honeywell, has demonstrated going from 2¹⁴ = 16,384 quantum volume (QV) announced in February 2023 to now 2¹⁹ = 524,288, with all the details and data released on for full transparency. At a quantum volume of 524,288, H1-1 is 1000x higher than the next best reported quantum volume.

We set a big goal back in 2020 when we launched our first quantum computer, HØ. HØ was launched with six qubits and a quantum volume of 2⁶ = 64, and at that time we made the bold and audacious commitment to increasing the quantum volume of our commercial machines 10x per year for 5 years, equating to a quantum volume of 8,388,608 or 2²³ by the end of 2025. In an industry that is often accused of being over-hyped, a commitment like this was easy to forget. But we did not forget. Diligently, our scientists and engineers continued to achieve world-record after world-record in a tireless and determined pursuit to systematically improve the overall performance of our quantum computers. As seen in Figure 1, from 2020 to early 2023, we have steadily been increasing the quantum volume to demonstrate that increased qubit count while reducing errors directly translates to more computational power. Just within 2023 we’ve had multiple announcements of quantum volume improvements.  In February we announced that H1-1 had leapfrogged 2¹⁴ and achieved a quantum volume of 2¹⁵. In May 2023, we launched H2-1 with 32 qubits at a quantum volume of 2¹⁶. Now we are thrilled to announce the sequential improvements of 2¹⁷, 2¹⁸, and 2¹⁹, all on H1-1.

Importantly, none of these results were “hero results”, meaning there are no special calibrations made just to try to make the system look better. Our quantum volume data is taken on our commercial systems interwoven with customer jobs. What we experience is what our customers experience. Instead of improving at 10x per year as we committed back in 2020, the pace of improvement over the past 6 months has been 30x, accelerating at least one year from our 5-year commitment. While these demonstrations were made using H1-1, the similarities in the designs of H1-2 (now upgraded with 20 qubits) and H2-1, our recently released second generation system, make it straightforward to share the improvements from one machine to another and achieve the same results.

In this young and rapidly evolving industry, there are and will be disagreements about which benchmarks are best to use. Quantum volume, developed by IBM, is undeniably rigorous. Quantum volume can be measured on any gate-based machine. Quantum volume has been peer-reviewed and has well defined . Improvements in QV require consistent reductions in errors, making it likely that no matter the application, QV improvements translate to better performance. In fact, to realize the exponential increase in power that quantum computers promise, it is required to continue to reduce these error rates. The average two-qubit gate error with these three new QV demonstrations was 0.13%, the best in the industry. We measure many benchmarks, but it is for these reasons that we have adopted quantum volume as our primary system-wide benchmark to report our performance.

Putting aside the argument of which benchmark is better, year-over-year improvements in a rigorous benchmark do not happen accidentally. It can only happen because the dedicated, talented scientists and engineers that work on H-Series hardware have a deep understanding of its error model and a deep understanding of how to reduce the errors to make overall performance improvements. Equally important the talented scientists and engineers have mastery of their domain expertise and can dream-up and then implement the improvements. These validated error models become the bedrock of future systems’ design, instilling confidence that those systems will have well understood error models, and the performance of those systems can also be systematically improved and ultimate performance goals achieved. Taking nothing away from those talented scientists and engineers, but having perfect, identical qubits and employing our quantum charge coupled device (QCCD) architecture does give us an advantage that all the other architectures and other modalities do not have.

What should potential users of H-Series quantum computers take away from this write-up (and what do current users already know)?

1. ҹɫֱ�� is committed to systematically improving the core performance of our quantum computing hardware. The better the fundamental performance, the lower the overhead will be when doing error mitigation, error detection, and ultimately error correction. This provides confidence in our ability to deliver fault-tolerant compute capabilities.
2. Progress on your research, use-case, or application can be accelerated by getting access to H-series technology because our quantum computers can do circuits that other technologies cannot. “It actually works!” exclaim excited first-time users.
3. ҹɫֱ�� intends to continue to be the quantum computing company that quietly over-delivers, even on big goals.

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ҹɫֱ��’s recent announcement about its breakthrough on topological qubits garnered headlines across both the specialist scientific media as well as those more broadly interested in the advances that will make quantum computing useful more quickly than anticipated. However, hidden in the details was a reference to a technology that is as rare as it is valuable. The fact is that the topological qubit that was generated could only have been done via ҹɫֱ��’s H-Series quantum processors due to their various qualities and functions of which measurement and ‘feed-forward’ is critical.

As we know, great advances are often built on the back of little-known utilities - functions and tools that rarely get mentioned. These are sometimes technological constructs that might seem simple on the surface, but which are difficult (in the case of feed-forward make that “very difficult” to create), and without which critical advances would remain merely theoretical.

As detailed in two manuscripts that have been uploaded onto the pre-print repository, arXiv, ҹɫֱ�� researchers and their collaborators successfully demonstrated, for the first time, a large-scale implementation of a long-standing theory in quantum information science; namely the use of measurement and (see below for a detailed explanation of what this means) to efficiently generate long-range entangled states.

The two experiments, conducted with research partners at the California Institute of Technology, Harvard University, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used ҹɫֱ��’s trapped ion quantum computers, Powered by Honeywell, to show how feed-forward enables success by dramatically reducing the resources required to produce highly-entangled quantum states and topologically ordered phases, one of the most exciting areas of research in modern physics.

Feed-forward uses selective measurements during the execution of a quantum circuit and adapts future operations depending on those measurement results. To be successful in running an adaptive quantum circuit, several challenging requirements must be met: (1) a select group of qubits must be measured in the middle of a circuit with high fidelity, and without accidentally measuring other qubits, and (2) the measurement results must be sent to a classical computer and quickly processed to create instructions to be fed-forward to the quantum computer on the fly - all of which must be done fast enough to prevent the active qubits from decohering.

Once these requirements are met, the feed-forward capabilities let quantum computers create long-range entangled states which are emerging as central to various branches of modern physics such as quantum error correction codes and the study of spin liquids in condensed matter. It is also the essential component of topological order and could enable the simulation of quantum systems beyond the reach of classical computation.

In the paper “”, ҹɫֱ��, working with colleagues from the California Institute of Technology and Harvard University use feed-forward to explore topologically ordered phases of matter. 

Separately, a different team of scientists from ҹɫֱ��, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used feed-forward to explore adaptive quantum circuits in “”.��

Two of ҹɫֱ��’s physicists who worked on both experiments, Henrik Dreyer and Michael Foss-Feig, offered some observations on the work.

“While it has been clear to theorists that feed-forward would be a useful primitive, doing it with low errors has turned out to be very challenging. The H-Series systems have made it possible to use this primitive efficiently,” said Henrik, managing director and scientific lead at ҹɫֱ��’s office in Munich, Germany.

Michael, who is based at ҹɫֱ��’s world-leading quantum computing laboratory outside of Denver, Colorado, also described feed-forward and adaptive quantum circuits as a jump toward meaningful simulations.

“This capability speeds up the timeline for new scientific discoveries,” he said.

These successful experiments proved that feed-forward operations reduce the quantum resources required for certain algorithms and are a valuable building block for more advanced research.

"I am really excited by the opportunities opened up by this demonstration: using wave-function collapse is a very powerful tool for preparing very exotic entangled states further down the road, where there are no good scalable alternatives," said Dr. Ruben Verresen, a physicist at Harvard University and a co-author of the topological order paper.

The authors note that “the primary technical challenge in implementing adaptive circuits is the requirement to perform partial measurements of a subset of qubits in the middle of a quantum circuit with minimal cross-talk on unmeasured qubits, return those results to a classical computer for processing, and then condition future operations on the results of that processing in real time.”

The paper describes how quantum hardware has now reached a state where adaptive quantum circuits are possible and can outperform unitary circuits. The experiment detailed in the paper “firmly establishes that given access to the same amount of quantum computational resources with respect to available gates and circuit depth, adaptive quantum circuits can perform tasks that are impossible for quantum circuits without feedback.”

Henrik and Michael noted that the adaptive circuit research provides concrete evidence not only that feed-forward works, but that it now works well enough to achieve tasks that would not be possible without it.

“We were trying to find a metric by which somebody can look at our data produced by a shallow adaptive circuit, and convince themselves it could not have been produced with a unitary circuit of the same depth,” Michael said. The metric proposed in the adaptive circuits paper achieved exactly that.

A good match: Trapped ion architecture and feed-forward 

Demonstrating this technique required significant performance from the H1-1. 

“It's a huge challenge to implement this in a way that works well,” Michael said. 

ҹɫֱ��’s H-Series has the capabilities that are crucial to this work: high fidelity gates, low state preparation and measurement (SPAM) error, low memory error, the ability to perform mid-circuit measurement, and all-to-all connectivity.

The feed-forward theory has been well-known for years but challenging to execute in practice, and as the paper states:

“While individual elements of this triad have been demonstrated in the context of error correction and topological order, combining all of these ingredients into one experimental platform has proven elusive since the inception of this idea more than a decade ago. Here, we demonstrate for the first time the deterministic, high-fidelity preparation of long-range entangled quantum states using a protocol with constant depth, using ҹɫֱ��’s H-Series programmable Ytterbium ion trap quantum computer.”

The authors also note that “the all-to-all connectivity of the device was vital for the implementation of the periodic two-dimensional geometry and the conditional dynamics.”

In summary – these papers showcase state-of-the-art demonstrations of what can be done with quantum computers today but are only a preview of what will be done tomorrow.

ҹɫֱ�� has unveiled our new optics and electromechanical engineering laboratory space at our largest operating site, in Broomfield Colorado.

Not only is the new space more than twice as big as the space we occupy today, but it will also house a clean, quiet, temperature controlled, state-of-the-art laboratory that befits the excellence of the work we do here.

Our hardware engineering and teams are focused on optimizing, customizing, and miniaturizing the components that power the H-Series quantum computers, demanding that our teams blur the boundaries between discrete disciplines, such as bulk optics and micro photonics, or embedded software and control electronics. Getting the handover right between different deeply skilled experts requires proximity and an intimate understanding of how one workflow blends into the other.

This is why this new lab space will make such a powerful contribution to our hardware success: because it is built around the needs of deeply connected, multidisciplinary teams, entirely focused on our goal of designing and building the first truly useful, breakaway quantum computer.

Six things you need to know about ҹɫֱ��’s new lab

1. State-of-the-Art Facility: Our new lab, with its state-of-the-art design and facilities, creates an environment for collaboration that will spur advances in the fields of optics, photonics, electromechanical engineering, and others.
   
   
2. Expansive and Efficient Space: The lab is not only going to be much larger than what we have today, it is also highly functional, with high ceilings and cloud superstructures over optics benches for better movement and workflow, which will afford our teams greater flexibility and access to every angle of the technology they are creating.
   
   
3. Advancing Micro and Nano Optics: As we aim to reduce our beam delivery size, we're drawing together the work of different teams, creating a dynamic environment where optics transitions into photonics, yielding new potential in terms of size, scale and performance. The location of certain teams will enable such cross-disciplinary workflows.
   
   
4. Custom Fabrication Capabilities: The new optics lab, together with our highly capable chip and trap fabrication capabilities, is designed to enable generational transitions from off-the-shelf, multipurpose optical components to fabricating more compact and fit-for-purpose devices: Think of moving from Functionality on a Table, through Functionality on a Chip, to Functionality on a Trap.
   
   
5. Greater Collaboration and Integration: The new laboratory layout improves the way some teams are co-located, with an eye always toward helping to enhance collaboration. For example, the new engineering space was designed to facilitate close cooperation between the electronics and software teams who design our control systems, as well as the mechanical teams who package the hardware and the test teams who validate it.  Such proximity between disciplines supports faster decision-making and more efficient resolution of interdisciplinary challenges, leading to a virtuous circle of accelerated design and development, faster innovation, and better quantum computers.
   
   
6. Ready for Future Expansion: As we prepare for the next stage of the journey towards fault-tolerant quantum computing, where demand for quantum compute will scale exponentially everywhere, this new laboratory space is fit for the future as well as meeting the demands of today.

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ҹɫֱ��’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 ҹɫֱ��’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 () architecture, which the H-Series is built on, the hardware team at ҹɫֱ�� 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, “,” 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 , 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, ҹɫֱ�� 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

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

To quantify the impact of these hardware and design improvements, ҹɫֱ�� 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, ҹɫֱ�� 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 ҹɫֱ�� 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
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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, ҹɫֱ�� 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 ҹɫֱ��, explain their advances in a new paper, “” published on arXiv. This is one of several papers published at the launch of ҹɫֱ��’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 ҹɫֱ��’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 ҹɫֱ�� 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 ����dzٲ�.��

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.

ҹɫֱ�� 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 ҹɫֱ��’s algorithm has significantly better runtime than 1-layer QAOA.