Variational Quantum Optimization With Fewer Qubits
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Solution Overview
Problem
Current Noisy-Intermediate Scale (NISQ) quantum devices are limited by the number of qubits, restricting their ability to optimize cost functions with a large number of discrete variables, as they convert discrete variables into bit variables, necessitating a qubit for each bit variable.
Innovation Solution
Utilize maximally orthogonal states of a qubit to represent the values of a variable, reducing the number of qubits needed by associating each qubit with a variable, and using quantum state tomography to measure and calculate the cost function iteratively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If discrete variables are reduced to bit variables with one qubit per bit variable, then the cost function can be minimized using current NISQ devices, but the number of qubits required increases significantly
Solution Approach 1:
The patent merges multiple discrete variable values into a single qubit by utilizing non-orthogonal quantum states. Instead of requiring separate qubits for each bit variable, the invention combines the representation of p different discrete values into one qubit's quantum state space, thereby reducing the total qubit count from m×N to N qubits.
Solution Approach 2:
The patent transitions from a classical binary representation (orthogonal basis states) to a quantum dimensional representation using non-orthogonal states on the Bloch sphere. This dimensional change allows a single qubit to encode p different discrete values through its continuous quantum state space, rather than requiring multiple discrete bit variables.
2Quantity of substance
If one qubit is assigned to each variable with p maximally orthogonal states, then the number of qubits is reduced to N, but the complexity of measuring and calculating the cost function increases
Solution Approach 1:
The patent replaces direct quantum measurement of non-orthogonal states with a classical calculation approach. Instead of measuring the quantum state directly to determine discrete variable values, the system calculates the cost function by evaluating the quantum state's overlap with reference states, substituting complex quantum measurement with classical computational procedures.
Solution Approach 2:
The patent introduces an intermediary classical calculation step between quantum state preparation and cost evaluation. The quantum computer prepares states representing discrete variables, but the cost function calculation is performed classically by computing overlaps or expectations, acting as an intermediary that bridges quantum and classical processing.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables the solution of larger optimization problems despite the qubit limitation by reducing the required number of qubits, allowing for more complex cost functions to be minimized effectively.
Implementation Method 1
a quantum state measuring step wherein the quantum computer measures individually the final quantum state of each of the qubits in the quantum circuit by means of quantum state tomography
Data Source
AI summary
Method for solving a variational quantum optimization problem in a hybrid quantum-classical computing system that includes a classical digital computer and a quantum computer by minimizing a cost function. The cost function comprises N variables, and each of the variables can take up to p different values. The quantum computer includes as many qubits as variables in the cost function, each qubit having p maximally orthogonal states, and a quantum circuit configured for performing a plurality of operations on said qubits. Each qubit represents each of the variables of the cost function, and each maximally orthogonal state of a qubit represents each of the values that the corresponding variable can have.