# US 10,311,174 B2 · Innermost data sharing method of lattice quantum chromodynamics calculation

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- Number: US 10,311,174 B2
- Document ID: US10311174B2
- Status: Granted
- Kind: B2
- Application number: 14/920,529
- Filed: 2015-10-22
- Published: 2017-04-27
- Granted: 2019-06-04
- Earliest claimed: 2015-10-22
- Assignees: International Business Machines Corporation
- Applicants: International Business Machines Corporation
- Inventors: Jun Doi
- Web page: https://patentgrep.com/patent/US10311174B2

## CPC

- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G06F 17/10: Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)}
- G06F 2111/10: Numerical modelling
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method for calculating lattice quantum chromodynamics (QCD) that includes loading an aligned spinor and gauge matrix, and constructing a half-spinor for plus and minus from the aligned spinors. In a following step, the method may include calculating a half spinor minus to be transferred to a positive neighbor of the gauge matrix by multiplying the gauge matrix and half-spinor for minus. The half-spinor for plus (Hp) and the half spinor minus may be stored in a shared memory. In a following step, the method may continue with calculating a half spinor plus to be transferred to a negative neighbor of the gauge matrix by multiplying the gauge matrix and the half-spinor for plus. Thereafter, the sum of half-spinors may be calculated.

## Claims

### Claim 1

A computer-implemented method for increasing processing efficiency when calculating lattice quantum chromodynamics (QCD) comprising:
loading an aligned spinor (W) array and gauge matrix (U) into a hardware processor;
constructing a half-spinor for plus (Hp) and half-spinor for minus (Hn) from the aligned spinor (W) array;
calculating a half spinor minus (Hn′) to be transferred to a positive neighbor of the gauge matrix by multiplying the gauge matrix (U) and half-spinor for minus (Hn) before storing in a shared memory;
storing the half-spinor for plus (Hp) and the half spinor minus (Hn′) in a shared memory;
calculating a half spinor plus (Hp′) to be transferred to a negative neighbor of the matrix by multiplying the gauge matrix (U) and the half-spinor for plus (Hp); and
calculating the sum of half-spinors from the half spinor minus (Hn′) to be transferred to the positive neighbor of the gauge matrix and the half spinor plus (Hp′) to be transferred to the negative neighbor of the gauge matrix.

### Claim 2 (depends on 1)

The method of claim 1, wherein calculating the sum of half-spinors comprises a Wilson-Dirac operator.

### Claim 3 (depends on 1)

The method of claim 1, wherein calculating the sum of half-spinors includes D=W−k(Hp′+Hn′), wherein D is a Wilson-Dirac operator, and k is equal to a constant kappa.

### Claim 4 (depends on 1)

The method of claim 1, wherein the calculation of the sum of half spinors is completed using a Wilson-Dirac operator for innermost data sharing (X) as follows:
D(n)=δ(n)−k·(1−γ1)U1(n)δ(n+1)Ul†(n−1)δ(n−1)
wherein D is an innermost Wilson-Dirac operator, n is equal to a lattice site, k is equal to a constant kappa, γ is a projector gamma matrix, δ is equal to a quark spinor, and U is equal to the gauge matrix, U† is a matrix orthogonal to U in one of 4 dimensions l.

### Claim 5 (depends on 1)

The method of claim 1, wherein the method for calculating QCD employs a symmetry for the gauge matrix of special unitary group of rank 3 (SU(3)) geometry.

### Claim 6 (depends on 5)

The method of claim 5, wherein the method comprises compressing a 4×3 spinor to a 2×3 half spinor using said SU(3) geometry.

### Claim 7 (depends on 1)

The method of claim 1, wherein the method employs a same spinor and gauge matrix for both plus and minus directions.

### Claim 8 (depends on 1)

The method of claim 1, wherein the method provides for sharing 2×3 spinors.

### Claim 9

A non-transitory computer readable storage medium that includes a computer readable program for calculating lattice quantum chromodynamics (QCD), wherein the non-transitory computer readable program when executed on a computer causes the computer to perform the steps of calculating lattice quantum chromodynamics (QCD) that includes:
loading an aligned spinor (W) array and gauge matrix (U) into a hardware processor;
constructing a half-spinor for plus (Hp) and half-spinor for minus (Hn) from the aligned spinor (W) array;
calculating a half spinor minus (Hn′) to be transferred to a positive neighbor of the gauge matrix by multiplying the gauge matrix (U) and half-spinor for minus (Hn) before storing in a shared memory;
storing the half-spinor for plus (Hp) and the half spinor minus (Hn′) in a shared memory;
calculating a half spinor plus (Hp′) to be transferred to a negative neighbor of the gauge matrix by multiplying the gauge matrix (U) and the half-spinor for plus (Hp); and
calculating the sum of half-spinors from the half spinor minus (Hn′) to be transferred to the positive neighbor of the gauge matrix and the half spinor plus (Hp′) to be transferred to the negative neighbor of the gauge matrix.

### Claim 10 (depends on 9)

The non-transitory computer readable storage medium of claim 9, wherein said calculating the sum of half-spinors comprises a Wilson-Dirac operator.

### Claim 11 (depends on 9)

The non-transitory computer readable storage medium of claim 9, wherein said calculating the sum of half-spinors includes D=W−k(Hp′+Hn′), wherein D is a Wilson-Dirac operator, and k is equal to a constant kappa.

### Claim 12 (depends on 9)

The non-transitory computer readable storage medium of claim 9, wherein the calculation of the sum of half spinors is can be completed using a Wilson-Dirac operator for innermost data sharing (X) using:
D(n)=δ(n)−k·(1−γ1)U1(n)δ(n+1)Ul†(n−1)δ(n−1)
wherein D is an innermost Wilson-Dirac operator, n is equal to a lattice site, k is equal to a constant kappa, γ is a projector gamma matrix, δ is equal to a quark spinor, and U is equal to the gauge matrix, U† is a matrix orthogonal to U in one of 4 dimensions l.

### Claim 13 (depends on 9)

The non-transitory computer readable storage medium of claim 9, wherein the method for calculating QCD employs a symmetry for the gauge matrix of special unitary group of rank 3 (SU(3)) geometry.

### Claim 14 (depends on 13)

The non-transitory computer readable storage medium of claim 13, wherein the method for calculating QCD further comprises compressing a 4×3 spinor to a 2×3 half spinor using said SU(3) geometry.

### Claim 15 (depends on 9)

The non-transitory computer readable storage medium of claim 9, wherein the method employs a same spinor and gauge matrix for both plus and minus directions.

### Claim 16 (depends on 9)

The non-transitory computer readable storage medium of claim 9, wherein the method provides for sharing 2×3 spinors.

### Claim 17

A system for calculating lattice quantum chromodynamics (QCD) comprising:
a loading module for loading an aligned spinor (W) array and gauge matrix (U) into a hardware processor;
a half-spinor constructor module for constructing a half spinor for plus (Hp) and half-spinor for minus (Hn) from the aligned spinors (W) array;
a calculation module for calculating a half spinor minus (Hn′) to be transferred to a positive neighbor of the gauge matrix by multiplying the gauge matrix (U) and half-spinor for minus (Hn) before storing in a shared memory;
a storage module storing the half-spinor for plus (Hp) and minus (Hn′) in the shared memory;
a calculating module for calculating a half spinor plus (Hp′) to be transferred to a negative neighbor of the gauge matrix by multiplying the gauge matrix (U) and the half-spinor for plus (Hp); and
a calculating module for calculating the sum of half-spinors from the half spinor minus (Hn′) to be transferred to the positive neighbor of the gauge matrix and the half spinor plus (Hp′) to be transferred to the negative neighbor of the gauge matrix.

### Claim 18 (depends on 17)

The system of claim 17, wherein calculating the sum of half-spinors comprises a Wilson-Dirac operator.

### Claim 19 (depends on 17)

The system of claim 17, wherein calculating the sum of half-spinors includes D=W−k(Hp′+Hn′), wherein D is a Wilson-Dirac operator, and k is equal to a constant kappa.

### Claim 20 (depends on 17)

The system of claim 17, wherein the calculation of the sum of half spinors is completed using a Wilson-Dirac operator for innermost data sharing (X) as follows:
D(n)=δ(n)−k·(1−γ1)U1(n)δ(n+1)Ul†(n−1)δ(n−1),
wherein D is an innermost Wilson-Dirac operator for innermost, n is equal to a lattice site, k is equal to a constant kappa, γ is a projector gamma matrix, δ is equal to a quark spinor, and U is equal to the gauge matrix, U† is a matrix orthogonal to U in one of 4 dimensions l.