Quantum circuits for matrix trace estimation

Patent metadata

Field	Value
Publication number	US-12561594-B2
Application number	US-202217863508-A
Country	US
Kind code	B2
Filing date	Jul 13, 2022
Priority date	Jul 13, 2022
Publication date	Feb 24, 2026
Grant date	Feb 24, 2026

Abstract

Systems and methods for operating a quantum system are described. A controller of a quantum system can generate a command signal. The quantum system can include quantum hardware having a plurality of qubits. An interface of the quantum system can control the quantum hardware based on the command signal to generate a random state vector represented by the plurality of qubits. The random state vector can include a specific number of independent entries. The interface can control the quantum hardware to determine moments of a matrix based on the random state vector. The controller can be further configured to output the moments of the matrix to a computing device to estimate a trace of the matrix using the moments.

First claim

What is claimed is:

1 . An apparatus comprising:
a controller configured to generate a command signal; quantum hardware including at least a first set of qubits, a second set of qubits, and a plurality of Hadamard gates; and an interface connected to the controller and the quantum hardware, the interface being configured to convert the command signal received from the controller into a quantum operation to control the quantum hardware to: generate a random state vector represented by a plurality of qubits, wherein the random state vector comprises a specific number of independent entries of independent states of the random state vector, and the random state vector is a superposition of multiple states of the random state vector having different Hamming weights; determine moments of a matrix based on the random state vector, wherein elements of the matrix are inaccessible to the apparatus; and the controller being further configured to output the moments of the matrix to a computing device to estimate a trace of the matrix using the moments.

2 . The apparatus of claim 1 , wherein the specific number of independent entries is four entries.

3 . The apparatus of claim 1 , wherein the matrix corresponds to a Laplacian of simplices of a specific order in a simplicial complex, and a determination of Betti numbers of the simplicial complex is based on the estimated trace.

4 . The apparatus of claim 1 , wherein the matrix is a Hermitian matrix.

5 . The apparatus of claim 1 , wherein the matrix is an n×n matrix representing a dataset of n data points.

6 . The apparatus of claim 1 , wherein the matrix is an n×n matrix, and the quantum circuit is configured to generate the random state vector by randomly sampling a column of a 2{circumflex over ( )}n×2{circumflex over ( )}n Hadamard matrix.

7 . The apparatus of claim 1 , wherein the quantum hardware comprises a quantum t-design circuit including a layer of parallel Hadamard gates followed by a set of Toffoli gates, the interface is configured to control the quantum t-design circuit to output pseudo-random states that are indistinguishable from states drawn from a random Haar measure to sample the random state vector.

8 . The apparatus of claim 1 , wherein the interface is configured to control the quantum hardware to:
determine a quantum state that represents an application of the matrix to the random state vector; determine a complex conjugate of the random state vector; and determine an inner product between the quantum state and the complex conjugate to determine the moments.

9 . The apparatus of claim 1 , wherein the matrix corresponds to a Laplacian of simplices of a specific order in a simplicial complex, and the quantum circuit is configured to:
determine a quantum state that represents an application of the Laplacian to the random state vector; and determine a norm of the quantum state to determine the moments.

10 . The apparatus of claim 1 , wherein estimation of the trace comprises averaging the moments over a number of samples used for generating the random state vector.

11 . A system comprising:
a first computing device configured to process data encoded in binary data; a second computing device configured to be in communication with the first computing device, the second computing device being configured to process data encoded in qubits, the second computing device comprises: a controller configured to generate a command signal; quantum hardware including at least a first set of qubits, a second set of qubits, and a plurality of Hadamard gates; and an interface connected to the controller and the quantum hardware, the interface being configured to convert the command signal received from the controller into a quantum operation to control the quantum hardware to: generate a random state vector represented by a plurality of qubits, wherein the random state vector comprises a specific number of independent entries of independent states of the random state vector, and the random state vector is a superposition of multiple states of the random state vector having different Hamming weights; determine moments of a matrix based on the random state vector, wherein elements of the matrix are inaccessible to the apparatus; and the controller being further configured to output the moments of the matrix to the first computing device to estimate a trace of the matrix using the moments.

12 . The system of claim 11 , wherein the specific number of independent entries is four entries.

13 . The system of claim 11 , wherein the matrix corresponds to a Laplacian of simplices of a specific order in a simplicial complex, and a determination of Betti numbers of the simplicial complex is based on the estimated trace.

14 . The system of claim 11 , wherein the matrix is a Hermitian matrix.

15 . The system of claim 11 , wherein the matrix is an n×n matrix representing a dataset of n data points.

16 . The system of claim 11 , wherein the matrix is an n×n matrix, and the quantum circuit is configured to generate the random state vector by randomly sampling a column of a 2{circumflex over ( )}n×2{circumflex over ( )}n Hadamard matrix.

17 . The system of claim 11 , wherein the second computing device comprises a quantum t-design circuit including a layer of parallel Hadamard gates followed by a set of Toffoli gates, and the interface is configured to control the quantum t-design circuit to output pseudo-random states that are indistinguishable from states drawn from a random Haar measure to sample the random state vector.

18 . The system of claim 11 , wherein the second computing device is configured to:
determine a quantum state that represents an application of the matrix to the random state vector; determine a complex conjugate of the random state vector; and determine an inner product between the quantum state and the complex conjugate to determine the moments.

19 . The system of claim 11 , wherein the matrix corresponds to a Laplacian of simplices of a specific order in a simplicial complex, and the second computing device is configured to:
determine a quantum state that represents an application of the Laplacian to the random state vector; and determine a norm of the quantum state to determine the moments.

20 . The system of claim 11 , wherein the first computing device is configured to determine an average of the moments over a number of samples used for the generation of the random state vector to estimate the trace.

21 . A method of operating a quantum system, the method comprising:
receiving, by a controller of a quantum system, an instruction; generating, by the controller of the quantum system, a command signal based on the instruction; converting, by an interface of the quantum system, the command signal into a quantum operation; and based on the quantum operation, controlling, by the interface of the quantum system, quantum hardware of the quantum system including a plurality of Hadamard gates to:
generate a random state vector represented by a plurality of qubits, the random state vector comprising a specific number of independent entries of independent states of the random state vector, and the random state vector is a superposition of multiple states of the random state vector having different Hamming weights;
determine moments of a matrix based on the random state vector, wherein elements of the matrix are inaccessible to the apparatus; and
outputting, by the controller of the qu

Assignees

• IBM

Inventors

• Ubaru Shashanka
• Clarkson Kenneth Lee
• Akhalwaya Ismail Yunus
• Squillante Mark S
• Kalantzis Vasileios
• Horesh Lior

Classifications

• G06N10/00

  Quantum computing, i.e. information processing based on quantum-mechanical phenomena · CPC title

• G06F17/16 Primary

  Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} · CPC title

• G06N10/40 Primary

  Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control · CPC title