US-12619898-B1 - Systems and methods for preparation of a quantum state encoding an approximate normal distribution

US12619898B1US 12619898 B1US12619898 B1US 12619898B1US-12619898-B1

Abstract

Systems, apparatuses, methods, and computer program products are disclosed for preparation of a quantum state encoding an approximate normal distribution (QSEAND) in a set of qubits. An example method includes initializing the set of qubits by preparing the set of qubits in an initial quantum state. The example method also includes encoding the approximate normal distribution in the quantum state of the set of qubits, wherein encoding the approximate normal distribution comprises preparing the set of qubits to be in a quantum state representing a plurality of Fourier coefficients, and applying an inverse quantum Fourier transform to the set of qubits in the quantum state representing the plurality of Fourier coefficients to obtain the QSEAND. The example method also includes utilizing the QSEAND, wherein the utilization alters or transfers the QSEAND.

Inventors

Constantin Gonciulea
Vanio Markov
Charlee Alexandra Stefanski
Abhijit Bhima Rao

Assignees

WELLS FARGO BANK, N.A.

Dates

Publication Date: 20260505
Application Date: 20220921

Claims (20)

1 . A method for preparation of a quantum state encoding an approximate normal distribution (QSEAND) in a set of qubits, the method comprising: initializing, via state initialization circuitry, the set of qubits by preparing the set of qubits in an initial quantum state; encoding, via state preparation circuitry, the approximate normal distribution in the quantum state of the set of qubits, wherein encoding the approximate normal distribution causes the set of qubits to be in the QSEAND, and wherein encoding the approximate normal distribution comprises: preparing, via the state preparation circuitry, the set of qubits to be in a quantum state representing a plurality of Fourier coefficients, and applying, via the state preparation circuitry, an inverse quantum Fourier transform to the set of qubits in the quantum state representing the plurality of Fourier coefficients to obtain the QSEAND; and utilizing, via state transformation circuitry, the QSEAND, wherein the utilization alters or transfers the QSEAND.
2 . The method of claim 1 , wherein the quantum state representing the plurality of Fourier coefficients represents three Fourier coefficients or five Fourier coefficients.
3 . The method of claim 1 , wherein utilizing the QSEAND comprises: measuring the QSEAND; storing information from the QSEAND; further transforming the QSEAND with a quantum circuit; or a combination thereof.
4 . The method of claim 1 , further comprising: before encoding the approximate normal distribution: transpiling, via transpilation circuitry, a quantum circuit to obtain a transpiled quantum circuit, wherein encoding the approximate normal distribution in the quantum state of the set of qubits uses the transpiled quantum circuit.
5 . The method of claim 1 , further comprising: acquiring, via communications hardware, user input providing attributes of the approximate normal distribution; wherein encoding the approximate normal distribution in the quantum state of the set of qubits proceeds according to the attributes of the approximate normal distribution from the user input.
6 . The method of claim 1 , wherein utilizing the QSEAND comprises: initializing, via the state initialization circuitry, a second set of qubits; entangling, via the state transformation circuitry, the set of qubits with the second set of qubits using a transformation derived from a payoff function of a financial product; applying a first transformation H, via the state transformation circuitry, to the set of qubits, wherein the first transformation H results in the set of qubits being in superposition; applying a second transformation U, via the state transformation circuitry, to the second set of qubits, wherein the Hermitian conjugate of U encodes a linear distribution function; and measuring, via the state transformation circuitry, a quantum state of the set of qubits and the second set of qubits to evaluate a price for the financial product.
7 . The method of claim 1 , wherein the QSEAND models a feature of a dataset used to build a linear classifier, wherein the distribution of the feature of the dataset lies within a pre-defined tolerance of values of the normal distribution.
8 . The method of claim 1 , wherein values of the approximate normal distribution lie within a pre-defined tolerance of values of the normal distribution.
9 . An apparatus for preparing a QSEAND in a set of qubits, the apparatus comprising: state initialization circuitry configured to: initialize the set of qubits by preparing the set of qubits in an initial quantum state; state preparation circuitry configured to: encode an approximate normal distribution in the quantum state of the set of qubits, wherein encoding the approximate normal distribution causes the set of qubits to be in the QSEAND, and wherein encoding the approximate normal distribution comprises: preparing, via the state preparation circuitry, the set of qubits to be in a quantum state representing a plurality of Fourier coefficients, and applying, via the state preparation circuitry, an inverse quantum Fourier transform to the set of qubits in the quantum state representing the plurality of Fourier coefficients to obtain the QSEAND; and state transformation circuitry configured to: utilize the QSEAND, wherein the utilization alters or transfers the QSEAND.
10 . The apparatus of claim 9 , wherein the quantum state representing the plurality of Fourier coefficients represents three Fourier coefficients or five Fourier coefficients.
11 . The apparatus of claim 9 , wherein utilizing the QSEAND comprises: measuring the QSEAND; storing information from the QSEAND; further transforming the QSEAND with a quantum circuit; or a combination thereof.
12 . The apparatus of claim 9 , further comprising: transpilation circuitry configured to: before encoding the approximate normal distribution: transpile a quantum circuit to obtain a transpiled quantum circuit, wherein the state transformation circuitry is further configured such that encoding the approximate normal distribution in the quantum state of the set of qubits uses the transpiled quantum circuit.
13 . The apparatus of claim 9 , further comprising: communications hardware configured to: acquire user input providing attributes of the approximate normal distribution, wherein encoding the approximate normal distribution in the quantum state of the set of qubits proceeds according to the attributes of the approximate normal distribution from the user input.
14 . The apparatus of claim 9 , wherein utilizing the QSEAND comprises: initializing a second set of qubits; entangling the set of qubits with the second set of qubits using a transformation derived from a payoff function of a financial product; applying a first transformation H to the set of qubits; wherein the first transformation H creates a superposition quantum state in the set of qubits; applying a second transformation U to the second set of qubits, wherein the Hermitian conjugate of U encodes a linear distribution function; and measuring a quantum state of the set of qubits and second set of qubits to evaluate a price for the financial product.
15 . The apparatus of claim 9 , wherein the QSEAND models a feature of a dataset used to build a linear classifier, wherein the distribution of the feature of the dataset lies within a pre-defined tolerance of values of the normal distribution.
16 . The apparatus of claim 9 , wherein values of the approximate normal distribution lie within a pre-defined tolerance of values of the normal distribution.
17 . A computer program product for preparing a QSEAND in a set of qubits, the computer program product comprising at least one non-transitory computer-readable storage medium storing software instructions that, when executed, cause an apparatus to: initialize the set of qubits by preparing the set of qubits in an initial quantum state; encode an approximate normal distribution in the quantum state of the set of qubits, wherein encoding the approximate normal distribution causes the set of qubits to be in the QSEAND, and wherein encoding the approximate normal distribution comprises: preparing the set of qubits to be in a quantum state representing a plurality of Fourier coefficients, and applying an inverse quantum Fourier transform to the set of qubits in the quantum state representing the plurality of Fourier coefficients to obtain the QSEAND; and utilize the QSEAND, wherein the utilization alters or transfers the QSEAND.
18 . The computer program product of claim 17 , wherein values of the approximate normal distribution lie within a pre-defined tolerance of values of the normal distribution.
19 . The computer program product of claim 17 , wherein the software instructions, when executed, further cause the apparatus to: before encoding the approximate normal distribution: transpiling a quantum circuit to obtain a transpiled quantum circuit, wherein encoding the approximate normal distribution in the quantum state of the set of qubits uses the transpiled quantum circuit.
20 . The computer program product of claim 17 , wherein utilizing the QSEAND comprises: initializing a second set of qubits; entangling the set of qubits with the second set of qubits using a transformation derived from a payoff function of a financial product; applying a first transformation H to the set of qubits, wherein the first state preparation transformation H creates a superposition quantum state in the set of qubits; applying a second transformation U to the second set of qubits, wherein the Hermitian conjugate of U encodes a linear distribution function; and measuring a quantum state of the set of qubits and the second set of qubits to evaluate a price for the financial product.

Description

BACKGROUND Quantum computers promise to provide significant advantages for solving particular problems that are difficult or costly for classical computers to solve. However, the loading of data onto a quantum computer remains a computationally difficult problem that threatens to negate many of the advantages gained by utilizing quantum algorithms. In particular, the normal distribution is widely used but notoriously difficult to load on quantum computers. BRIEF SUMMARY Although still in its infancy, quantum computing and its potential applications are of rapidly increasing interest to a broad array of industrial sectors, including complex simulation, artificial intelligence, healthcare, and financial services. Unlike classical computers, which process information in bits that can only represent one of two binary information states at a time, quantum computers process information in quantum bits (qubits) that can represent a coherent superposition of both binary information states at the same time. Two or more qubits may be entangled so that their physical properties are correlated even when separated by large distances, and quantum computers may simultaneously perform a vast number of operations on these entangled qubits. These features allow quantum computers to perform incredibly complex calculations at speeds not realizable today and solve certain classes of problems that are beyond the capability of existing classical computers. Quantum computing is one of an array of emerging quantum technologies that present a wide field of potential applications. Quantum sensing and quantum communications are expected to have wide-ranging technological impact, and advances in the field of quantum computing may enable or find further applications in these fields. While quantum computers promise to outperform classical computers on a number of computationally intensive tasks, several hurdles prevent their widespread use. One such hurdle is the computational complexity of loading data into a quantum state. A quantum state encoding of the normal distribution is desirable for numerous computations, so there is a need for methods that efficiently load the normal distribution—or a reasonable approximation of the normal distribution—on a quantum computer. Systems, apparatuses, methods, and computer program products are disclosed herein for preparation of a quantum state encoding an approximate normal distribution (QSEAND). The systems, apparatuses, methods, and computer program products disclosed herein provide solutions that enable the efficient loading of quantum states. These solutions enable the operation of quantum computers by eliminating a common type of computational bottleneck in state preparation. In one example embodiment, a method is provided for preparation of a QSEAND in a set of qubits. The method includes initializing, via state initialization circuitry, the set of qubits by preparing the set of qubits in an initial quantum state. The method also includes encoding, via state preparation circuitry, the approximate normal distribution in the quantum state of the set of qubits, wherein encoding the approximate normal distribution causes the set of qubits to be in the QSEAND, and wherein encoding the approximate normal distribution comprises preparing, via the state preparation circuitry, the set of qubits to be in a quantum state representing a plurality of Fourier coefficients, and applying, via the state preparation circuitry, an inverse quantum Fourier transform to the set of qubits in the quantum state representing the plurality of Fourier coefficients to obtain the QSEAND. The method also includes utilizing, via the state transformation circuitry, the QSEAND, wherein the utilization alters or transfers the QSEAND. In another example embodiment, an apparatus is provided for preparing a QSEAND in a set of qubits. The apparatus includes state initialization circuitry configured to initialize the set of qubits by preparing the set of qubits in an initial quantum state. The apparatus also includes state preparation circuitry configured to encode the approximate normal distribution in the quantum state of the set of qubits, wherein encoding the approximate normal distribution causes the set of qubits to be in the QSEAND, and wherein encoding the approximate normal distribution comprises preparing, via the state preparation circuitry, the set of qubits to be in a quantum state representing a plurality of Fourier coefficients, and applying, via the state preparation circuitry, an inverse quantum Fourier transform to the set of qubits in the quantum state representing the plurality of Fourier coefficients to obtain the QSEAND. The apparatus also includes state transformation circuitry configured to utilize the QSEAND, wherein the utilization alters or transfers the QSEAND. In another example embodiment, a computer program product is provided for preparing a QSEAND in a set of qubits, the computer program product co