Efficient use of quantum bits 20-bit quantum computer successfully runs 80-bit algorithm

Scientists at Quantinuum have proposed a new method for reusing quantum bits that maximizes the size of programs that can run on quantum computers with a limited number of quantum bits. The team solved the 80-qubit maximum cut (MaxCut) quantum adiabatic optimization algorithm (QAOA) problem by experimenting on a 20-qubit Quantinuum H1-1 quantum processor. This approach is highly beneficial for algorithms in the NISQ era, and the company's researchers also expect it to scale as quantum computers gain more quantum bits and become less error-prone.

The paper, entitled "Quantum Bit Reuse Compilation with Intermediate Circuit Measurement and Reset" [1], was written by scientists Matthew DeCross, Eli Chertkov, Megan Kohagen and Michael Foss-Feig of Quantinuum (a Honeywell subsidiary) and is now online at arXiv.

01Technology Breakthrough Needed: Efficient Use of Quantum Bits

Many current quantum computers are limited by the number of quantum bits available for computation. To realize the computational advantages of quantum computers over classical computers for a variety of practical applications, researchers will need to make efficient use of quantum bits.

"Our motivation is primarily to increase the utility of the relatively small quantum computers we have today. But looking ahead to the early days of fault-tolerant quantum computing, there will be a point in time when we are trying to run circuits with 50 logical quantum bits and very low error rates," Foss-Feig said. "At that point in time, we will be short of logical quantum bits to solve many problems, so this approach will also be in that intermediate time period useful."

The new technique provides an automated framework for compiling circuits to operate on fewer quantum bits by using measurements and resets in the middle of the circuit to map the circuit to a compressed version of itself. According to the scientists, this technique will still be feasible when quantum systems reach several thousand quantum bits. It is also device-independent and can work on any circuit on any machine.

Quantum bit reuse is an essential element of scalable quantum error correction protocols that require repeated circuit intermediate measurements and resets to measure error complexes. Recently, reuse techniques have been used for experimental preparation and time evolution to capture the state of large tensor networks on ion quantum computers and to study nonequilibrium phase transitions.

Left: the case with no quantum bit reuse. The bottommost input quantum bit is used only after crossing the gray shaded area, while the adjacent quantum bits are no longer used after that area; Right: case with quantum bit reuse. The whole circuit can be executed with one less quantum bit, using mid-circuit measurements and resets.

02Automation of quantum bit reuse: two algorithms

Compiling programs with quantum bit reuse is a difficult combinatorial optimization problem and an under-explored area of quantum circuit design. The key principle of this approach is that, in many cases, only a partial execution of the circuit is required to measure a given output quantum bit. In order to measure a given output quantum bit, only the gates that have a causal effect on that output in the future need to be executed, a set of operations called the "causal cone" of the output. After executing only part of the original circuit, the output quantum bit may be reset and recycled as an input quantum bit elsewhere in the circuit.

Identification of the causal cone of the output quantum bit q2 in the displayed quantum circuit. Measuring and resetting q2 requires only the execution of gating between the four input quantum bits {q1, q2, q3, q4}. Performed between the four input quantum bits {q1, q2, q3, q4}, after which q2 can be reset and reused as q5.

Once the causal structure of the circuit has been determined, there are still many freedoms related to the order of the measured output quantum bits. Previous efforts to exploit the causal structure involved laborious manual processes for each new application and required the circuit to be simple enough to visually determine the causal cone and determine the best order of measurements. DeCross, the study's lead author, says their new technique automatically generates an exact logic rewrite circuit using as few quantum bits as possible, but with exactly the same number of gates.

In previous studies, Quantinuum researchers used this old labor-intensive method to build compressed circuits for quantum tensor network simulations of materials.

"In many cases, it's really hard to imagine scaling these techniques by inspection," says Foss-Feig [2], "You need an automated tool to do this kind of analysis, and our algorithm allows you to do that."

The team used two algorithms for quantum bit reuse compilation: an exact constrained programming optimization model and a heuristic algorithm that runs quickly to a large number of quantum bits and scales polynomially with the number of quantum bits. The team numerically benchmarked these algorithms on QAOA and applied them to the "maximum cut" problem on random triple regular graphs. They also studied several examples of highly structured circuits with recent relevance, including one- and two-dimensional time-evolving circuits and certain quantum tensor networks, and analytically solved the quantum bit reuse compilation problem in these cases.

A p=1 maximum cut QAOA circuit using 10 quantum bits.

The same circuit is compressed using quantum bit reuse. The final circuit is logically equivalent and can be executed with only 4 quantum bits instead of the original 10.

03Practical results of quantum bit reuse

The research team demonstrated the practical benefits of these quantum bit reuse compilation algorithms by experimentally solving the 80-bit maximum cut quantum adiabatic optimization algorithm (QAOA) problem on a 20-bit Quantinuum H1-1 quantum processor. Variational algorithms like QAOA and the Variational Quantum Solver (VQE) are natural use cases for such compilations because they have wide and shallow circuits and are run on NISQ devices.

The minimum number of quantum bits required to perform certain structured quantum circuits after quantum bit reuse is compiled. For k-layer circuits, 4k is assumed to be less than all dimensions.

During the experiment, the team performed the full QAOA optimization protocol on the quantum computer, whereas some previous experiments sometimes performed the optimization on the classical computer and only once on the quantum computer for the optimal parameters.

In response, DeCross said, "Our results show the application of quantum bit reuse compilation to an important benchmark problem, and demonstrate that the resulting circuits are feasible to operate and optimize at realistic noise levels."

Reference links

[1]https://arxiv.org/abs/2210.08039

[2]https://medium.com/quantinuum/quantinuum-scientists-find-new-approach-for-optimizing-and-automating-qubit-reuse-133f13532713