Quantum Computing (QC) is a new calculation paradigm that promised significant speedup over classic computing on some problem. Quantum calculations are often representation as complex circuits that intact quantum “gates”, which are analogous to the logic ports in Convental Computers.
However, the difficulty of building quantum computers means that the circuits available in the current quantum hardware are relatively simple. Quantum compilators Are programs that map the complex circuit of quantum calculation specifications on the simpler circuits available today.
Circuit mapping often involves vigorous use of Swap Gate that swaps conditions with two adjacent quantum bits or quubits. Through one or more swaps, a QUBIT mode can move through the circuit unit as it adjacent to the next Qubit it needs to interact with. But swap ports are expensive and faulty, so the compiler shouts minimizes them.
In a paper we presented at 27Th International conference on theory and uses of sweetness -testing (SAT), we offer a new method that uses automated reasoning to find circulatory mapping that minimizes the number of swap gates. Satisfaction (SAT) Problems are problems that may be statistics of boooolean (binary) variables and logical operations, and the question is where there is an allocation of values ​​to the variables that Satisfy The logical limitations of the expression.
In our method, a limit for the number of swap gates is one of the restrictions that must be met, and a set solver tells us whatever whether it can be or not. In a comprehensive evaluation of practical cases over various quantum units and algorithms, our approach appeared 26 times as fast as advanced solver -based methods, reducing the gathering time from hours to minutes for important quantum applications. Compared to current heuristic algorithms, our method on average reduces the swap count by 26%.
This is a joint project between Amazon’s automated rage group (ARG) and Quantum Team (Amazon Braket). I was a student trainee who was done by the work, so we were eligible for SAT 2024 Best Student Paper Award, and we ended as runners.
Mapping Circuit
Just as logical gates are the basic building blocks for classic calculation, quantum gates are the building blocks for quantum calculation. But quantum port involves manipulating a quantum system on one or application At certain times. The swap port is one of the basic quantum gates; Others include the Hadamard gate that puts a QUBIT in superposition (mix of different possible states) and the rotation sport.
We illustrate the problem of mapping quantum circuits with an example. In the figure below, the schematic on the left qbit connections (part of) represents the strict Aspen M-3 quantum computer. Circles are physical quubits and lines are physical compounds that allow the use of two-quubit gates.
The figure on the right is the circuit diagram for a three-hented quantum circuit for the famous Quantum Fourier Transform (QFT) algorithm. The three horizontal lines take the schedules for quantum gates on the three algorithmic quubits. The boxes labeled H. Indicates en-quobit hadamard ports, and the boxes labeled R.With connections to fixed dots, two-square-controlled rotation ports reproduce. The QFT circuit has a two-packed rotation port between every two-packed subgroup of the three quubits.
Performing the QFT circuit on the Aspen M-3 unit requires a quantum compilation to perform circuit mapping. Introductive Mapping Circuit Two Steps: Initial Qubit Location and QBIT Routing. Initial under the qued location, the quantum compilator maps each algorithmic QUBIT in the circuit to a physical QUBIT on the device, as shown below.
The QFT cycle requires that each algorithmic Qubit interact with the other two. However, on the quiet connection graph of Aspen M-3, however, no undergradior forms a three-skirt ring that allows in pairs QUBIT interaction. As a result, the QFT cycle after the first QUBIT location (left in the fig below) cannot be performed directly. This type of limitation necessitates the second step in circuit mapping: QBIT routing.
Quibit routing is performed by inserting quantum swap ports. After a swap, any gates that are targeted at one of the swapped Qubits in the calculation special The right figure below describes swap insertion as two intersections connected with a vertical line. From the example we can see that swap gates can change the connection requirements to the calculation special to match them with the QUBIT connection of the underlying quantum hardware.
Optimization
Currently, there are two primary approaches to the circulatory card problem, solver-based and heuristics-based algorithms. Both approaches have their disadvantages: Solver-based algorithms achieve optimal swap numbers, but suffer from long assembly time; Heuristic algorithms are fast, but the swap cohents are unsetted suboptimal.
We offer a new circuit mapping method based on step by step and parallel solution for Boolian satisfaction (SAT). The figure presents the framework for our method. We like to find the smallest number of swap ports that can accommodate the circulatory card requirement by iteratively reducing the swap gate country and controlling the feasibility with a SAT solver.
Given three inputs – a quantum circuit, a quantum device (QPU) and an initial swap country (S.) -We codes for quantum-circuit mapping problem in a SAT formula in conjunctive normal form (CNF). A SAT solver takes CNF as input and controls its saffaibility. A satisfactory (SAT) result indicates that there is a valid mapping that does not use more than S. Swap gates. In this case we reduce the swap center S. And continue the loop to search for a mapping with fewer swap gates. We leave the loop when the solver returns Unsat, which indicates that we cannot reduce the swap count. Finlly we decorate a MAPD circuit from the best result we have achieved so far.
We developed an effective implementation to solve the coded circuit mapping problem. We use an incremental set that encodes iteratively to reduce Swap Counte S. and solve the problem without recovering the eligible problem of any iteration. Therefore, the solver can reuse the internal state of the previous iterations to reduce the overall run -time across iterations. We also designed a tailor -made solvent to use parallel solution techniques to improve the step -by -step solution.
An understanding evaluation of the real quantum of algorithms and devices shows that our method is 26 times as fast as the existing solver -based approach and produces better results. Our method also improved on the heuristic approach of 76% of the occurrences and achieved an average of 26% reduction in swapant numbers.