Methods of Operating Quantum Computing Systems for Amplitude Estimation

Patent metadata

Field	Value
Publication number	US-2026044762-A1
Application number	US-202418904466-A
Country	US
Kind code	A1
Filing date	Oct 2, 2024
Priority date	Nov 20, 2020
Publication date	Feb 12, 2026
Grant date	—

Abstract

This disclosure relates to enhanced methods of operating quantum computing systems to perform amplitude estimation. More than that, the methods may be tuned to accommodate for specific noise levels (e.g., in given a quantum device). Embodiments also enable quantum computing systems to perform amplitude estimation faster than amplitude estimation algorithms performed using a classical (non-quantum) computer.

First claim

1 . A non-transitory computer-readable storage medium storing instructions for determining θ of a quantum unitary operator U within an error ϵ, wherein U|0 t =cos(θ)|x, 0 +sin(θ)|x′, 1 , the instructions, when executed by a computing system, cause the computing system to perform operations comprising:
determining a parameter β∈(0,1) and N shots , where N shots is an integer greater than zero;
determining a probability distribution p(θ) for a set of angles θ;
for k=1 to K:
initializing N k0 =0 and N k1 =0;
for i=1 to N shtots :
instructing a quantum computer to sequentially execute the quantum unitary operator U

⌊

k

1
-
β

2
⁢
β

⌋

 times;
instructing the quantum computer to measure a qubit of the resulting quantum state; and
updating a value of N k0 or N k1 based on the measured value of the qubit; and

performing a Bayesian update to the probability distribution p(θ) based on the updated values of N k0 and N k1 ; and

determining θ based on the updated probability distribution.

2 . The non-transitory computer-readable storage medium of claim 1 , wherein a total number of times the quantum unitary operator U is executed on the quantum computer to determine θ scales as O(1/ϵ 1+β ).

3 . The non-transitory computer-readable storage medium of claim 1 , wherein the number of times the quantum unitary operator U is sequentially executed in a single run scales as

O
⁡
(

1

ϵ

1
-
β

)

.

4 . The non-transitory computer-readable storage medium of claim 1 , wherein determining the probability distribution p(θ) for the set of angles θ comprises determining a uniform distribution for a set of angles

θ
=

π
⁢
t
⁢
ϵ

2

,

where (t∈[0,1/ϵ]).

5 . The non-transitory computer-readable storage medium of claim 1 , wherein updating the value of N k0 or N k1 based on the measured value of the qubit comprises:
responsive to the measured value of the qubit being 0, updating the value of N k0 to be N k0 +1; and responsive to the measured value of the qubit being 1, updating the value of N k1 to be N k1 +1.

6 . The non-transitory computer-readable storage medium of claim 1 , wherein performing the Bayesian update includes p(θ)→p(θ) cos((2m k +1)θ) N k0 sin((2m k +1)θ) N k1 for θ=πtϵ/2 for integer t∈[0,1/ϵ], where

m
k

=

⌊

k

1
-
β

2
⁢
β

⌋

.

7 . The non-transitory computer-readable storage medium of claim 1 , wherein the determined θ based on the updated probability distribution corresponds to a highest probability of the updated probability distribution.

8 . The non-transitory computer-readable storage medium of claim 1 , wherein β is determined based on noise of the quantum computer.

9 . The non-transitory computer-readable storage medium of claim 1 , wherein θ is determined within error ϵ with probability at least 0.9.

10 . The non-transitory computer-readable storage medium of claim 1 , wherein

K
=

max
⁡
(

1

ϵ

2
⁢
β

,

log
⁢

(

1
/
ϵ

)

)

.

11 . A non-transitory computer-readable storage medium storing instructions for determining θ of a quantum unitary operator U within an error ϵ, wherein U|0 t =cos(θ)|x, 0 +sin(θ)|x′, 1 , the instructions, when executed by a computing system, cause the computing system to perform operations comprising:
determining integer parameters k and q, where k≥2 and 1≤q≤(k−1);
determining a set of k co-prime moduli (n 1 , n 2 , . . . , n k ), where N=Π i∈[k] n i is equal to or greater than π/ϵ;
partitioning the set of k co-prime moduli (n 1 , n 2 , . . . , n k ) into [k/q] groups π i of size at most q;
for i=1 to [k/q]:
for a number of iterations:
instructing a quantum computer to execute the quantum unitary operator U to generate a quantum state |ϕ (N-N i )/2N i defined by

|

ϕ
μ

〉

=

cos
⁡
(

(

2
⁢
μ

Assignees

• Goldman Sachs & Co Llc

Inventors

• Giurgica-Tiron Tudor
• Kerenidis Iordanis
• Labib Farrokh
• Prakash Anupam
• Zeng William Joseph

Classifications

• G06F17/18

  for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} · CPC title

• G06N10/00 Primary

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