Quantum Circuit Compilation via Pauli String Segmentation
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Solution Overview
Problem
The Unitary Coupled Cluster (UCC) ansatz for quantum computing scales poorly with the size of molecules, leading to long computation times and high error rates due to increased circuit depth and entangling gate count, which hampers the efficiency of algorithms like VQE on NISQ devices.
Innovation Solution
A compilation strategy that partitions Pauli strings into mutually commuting sets, generates Pauli gadgets through Trotterization, diagonalizes them into phase gadgets, and transforms these into one- and two-qubit native gates, significantly reducing circuit depth and entangling gate count.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the UCC ansatz is used to generate quantum circuits for molecular systems, then chemical accuracy is improved, but circuit depth scales poorly with molecule size leading to long computation times
Solution Approach 1:
The patent partitions the Hamiltonian into multiple Pauli string terms and groups them into commuting sets. Each set can be evaluated independently and in parallel, segmenting the overall computation into smaller manageable units that reduce the sequential circuit depth while maintaining the full UCC ansatz accuracy.
Solution Approach 2:
The patent employs periodic measurement cycles where different commuting sets of Pauli strings are measured in alternating sequences. This periodic action allows the system to accumulate measurement data from multiple sets over time, enabling accurate energy estimation without requiring all measurements to be performed in a single deep circuit.
2Measurement precision
If the UCC ansatz is used to generate quantum circuits for molecular systems, then chemical accuracy is improved, but the error rate increases due to more entangling gates
Solution Approach 1:
By dividing the Hamiltonian into commuting sets of Pauli strings, the patent reduces the number of entangling gates required within each individual circuit. Each segmented circuit operates with fewer entangling gates, thereby reducing the error rate per measurement while the full accuracy is recovered through aggregation of results from multiple sets.
Solution Approach 2:
The patent measures each commuting set separately and accumulates results over multiple partial measurements rather than attempting to measure all Pauli strings simultaneously in a single excessive-depth circuit. This partial action approach reduces the error accumulation that would occur in a single deep circuit while still achieving the complete energy estimation.
3Measurement precision
If more Pauli strings are included in the UCC ansatz to improve accuracy, then chemical precision is enhanced, but the number of entangling gates increases leading to higher error rates
Solution Approach 1:
The patent segments the complete set of Pauli strings from the UCC ansatz into multiple commuting sets. This segmentation allows the system to include all the Pauli strings necessary for chemical accuracy in the ansatz while distributing them across multiple simpler circuits, each with a manageable number of entangling gates.
Solution Approach 2:
The patent implements periodic measurement of different commuting sets of Pauli strings. By cycling through multiple sets over time and aggregating results, the system achieves the precision benefits of including all Pauli strings in the UCC ansatz without requiring all of them to be present simultaneously in a single circuit, thus managing the entangling gate count effectively.
Data Source
AI summary
Concepts, systems and methods are described for generating a quantum circuit from a Unitary Coupled Cluster (UCC) ansatz which represents the excitation of a reference state by a parameterised operator including excitation operators. The UCC ansatz includes multi-qubit Pauli operators, referred to as Pauli strings, determined from each excitation operator. The method comprises partitioning the Pauli strings into mutually commuting sets and sequencing the Pauli strings by set. Pauli gadgets are then generated from the Pauli strings by Trotterization, the Pauli gadgets having the same sequencing by set as the Pauli strings. Each set of Pauli gadgets is diagonalised to convert the Pauli gadgets into phase gadgets which are then transformed into one- and two-qubit native gates to generate the quantum circuit.