KR20220011380A - Quantum state measurment method and apparatus for performing the same - Google Patents

Abstract

Disclosed are a method for measuring a quantum state and a device for performing the same. As a method for a quantum computing device to measure the quantum state, the method for measuring the quantum according to one embodiment comprises: a step of obtaining a depolarization channel by performing a quantum channel twirl on a qubit; and a step of measuring the quantum state of the qubit based on the depolarization channel. Therefore, the present invention is capable of providing a technique to mitigate an occurrence of a measurement error.

Description

QUANTUM STATE MEASURMENT METHOD AND APPARATUS FOR PERFORMING THE SAME

The following embodiments relate to a quantum state measurement method and an apparatus for performing the same.

Quantum computing (Noisy Intermediate Scalable Quantum Computing (NISQC)) implemented with noisy quantum equipment includes various kinds of noise in all processes of quantum state preparation, processing and measurement.

Quantum algorithms that have advantages over conventional methods, such as quantum period-finding, quantum search, quantum factoring, and quantum oracle algorithms, are building blocks, quantum It can be realized by quantum Fourier transform (QFT) and quantum amplitude amplification (QAA).

Since building blocks consist of sequential entangling gates for multiple qubits, it is important to apply coherent quantum operations to multiple qubits. If the algorithm is realized as a NISQ device, the noise inherent in every step from preparation to measurement readout is uncontrolled and errors accumulate, and consequently quantum dominance cannot be achieved.

As a related prior art, there is Korean Patent Publication No. 10-2009-0090326 (Title of the Invention: Systems, Methods and Apparatus for Local Programming of Quantum Processor Elements).

Embodiments may provide a technique for mitigating a measurement error caused by noise in the process of measuring the quantum state of a qubit.

However, the technical tasks are not limited to the above-described technical tasks, and other technical tasks may exist.

In a method for a quantum computing device to measure a quantum state, a quantum measurement method according to an embodiment comprises the steps of: obtaining a depolarization channel by performing quantum channel twirl on qubits; , measuring the quantum state of the qubit based on the depolarization channel.

The obtaining includes: applying a first unitary transform to the quantum state of the qubit before the qubit passes through the noise channel; and applying a second unitary transform to the state.

The second unitary transformation may be a Hermitian conjugate of the first unitary transformation.

The first unitary transformation may be one of elements of a set of unitary transformations including a plurality of unitary transformations.

The obtaining may include calculating an average value of a depolarization channel obtained for each element of the set of unitary transformations.

The acquiring of the depolarization channel includes: performing collective channel twirl on a plurality of qubits included in the qubit; It may include the step of acquiring a depolarization channel for

The performing the collective quantum channel mixing includes: applying a first unitary transform to the quantum state of each of the plurality of qubits before the plurality of qubits pass through a noise channel; and applying a second unitary transform to a quantum state of each of the plurality of qubits after passing through the noise channel.

The second unitary transformation may be a Hermitian conjugate of the first unitary transformation.

The step of obtaining a depolarization channel for each of the plurality of qubits may include identifying an effect on the quantum state of the individual qubits for the plurality of qubits obtained as a result of the collective quantum channel mixing.

The quantum measurement method may further include removing an error in the measurement result of the quantum state.

A quantum measuring apparatus according to an embodiment includes a quantum preprocessor for obtaining a depolarization channel by performing quantum channel twirl on a qubit, and measuring the quantum state of the qubit based on the depolarization channel It includes a quantum detector that

The quantum preprocessor may apply a first unitary transform to the quantum state before the qubits pass through the noise channel, and apply a second unitary transform after the qubits pass through the noise channel.

The second unitary transformation may be a Hermitian conjugate of the first unitary transformation.

The first unitary transformation may be one of elements of a set of unitary transformations including a plurality of unitary transformations.

The quantum preprocessor may calculate an average value of a depolarization channel obtained for each element of the set of unitary transformations.

The quantum preprocessor performs collective channel twirl on a plurality of qubits included in the qubit, and obtains a depolarization channel for each of the plurality of qubits based on the collective quantum channel mixing result. can

The quantum preprocessor applies a first unitary transform to the quantum state of each of the plurality of qubits before the plurality of qubits pass through the noise channel, and applies a first unitary transform to the quantum state of each of the plurality of qubits after the plurality of qubits pass through the noise channel. 2 A unitary transform can be applied.

The second unitary transformation may be a Hermitian conjugate of the first unitary transformation.

The quantum preprocessor may determine the effect on the quantum state of individual qubits for a plurality of qubits obtained as a result of the collective quantum channel mixing.

The quantum measurement apparatus may further include a post-processor for removing an error in the measurement result of the quantum state.

1 is a diagram for conceptually explaining a quantum measuring apparatus according to an embodiment.
FIG. 2 is a schematic block diagram of the quantum measuring apparatus shown in FIG. 1 .
FIG. 3 is a view for explaining a quantum measurement operation of the quantum measurement apparatus shown in FIG. 1 .
FIG. 4 is a flowchart for explaining a quantum measurement operation of the quantum measurement apparatus shown in FIG. 1 .

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. However, since various changes may be made to the embodiments, the scope of the patent application is not limited or limited by these embodiments. It should be understood that all modifications, equivalents and substitutes for the embodiments are included in the scope of the rights.

The terms used in the examples are used for the purpose of description only, and should not be construed as limiting. The singular expression includes the plural expression unless the context clearly dictates otherwise. In this specification, terms such as "comprise" or "have" are intended to designate that a feature, number, step, operation, component, part, or a combination thereof described in the specification exists, but one or more other features It should be understood that this does not preclude the existence or addition of numbers, steps, operations, components, parts, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiment belongs. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with the meaning in the context of the related art, and should not be interpreted in an ideal or excessively formal meaning unless explicitly defined in the present application. does not

In addition, in the description with reference to the accompanying drawings, the same components are given the same reference numerals regardless of the reference numerals, and the overlapping description thereof will be omitted. In describing the embodiment, if it is determined that a detailed description of a related known technology may unnecessarily obscure the gist of the embodiment, the detailed description thereof will be omitted.

In addition, in describing the components of the embodiment, terms such as first, second, A, B, (a), (b), etc. may be used. These terms are only for distinguishing the elements from other elements, and the essence, order, or order of the elements are not limited by the terms. When it is described that a component is "connected", "coupled" or "connected" to another component, the component may be directly connected or connected to the other component, but another component is between each component. It will be understood that may also be "connected", "coupled" or "connected".

Components included in one embodiment and components having a common function will be described using the same names in other embodiments. Unless otherwise stated, descriptions described in one embodiment may be applied to other embodiments as well, and detailed descriptions within the overlapping range will be omitted.

FIG. 1 is a diagram for conceptually explaining a quantum measuring apparatus according to an embodiment, and FIG. 2 is a schematic block diagram of the quantum measuring apparatus shown in FIG. 1 .

The quantum measuring apparatus 100 may measure a quantum state of a qubit. The quantum measuring apparatus 100 may be designed to obtain an optimized measurement result through a standard basis. When the quantum states before measurement include noise, the result obtained by the quantum measurement apparatus 100 by measuring with a standard basis may include an error.

The quantum measuring apparatus 100 may mitigate a measurement error caused by noise existing in a process of measuring a quantum state of a qubit. The quantum measuring apparatus 100 may improve a measurement error by performing quantum pre-processing before measurement. For example, the quantum measuring apparatus 100 may reduce a measurement error by performing quantum preprocessing on a noise channel that generates noise in a quantum state before measurement.

The quantum measuring apparatus 100 may include a quantum preprocessor 200 , a quantum detector 300 , and a postprocessor 400 .

The quantum preprocessor 200 may perform quantum preprocessing on the quantum state before measurement. The quantum preprocessor 200 performs quantum preprocessing on the quantum state before measurement, so that the measurement with the standard basis becomes the optimal measurement again.

The quantum preprocessor 200 may include quantum gates capable of manipulating qubits. For example, the quantum preprocessor 200 may include a logic gate that applies a unitary transform to a quantum state. However, the present invention is not limited thereto, and the quantum preprocessor 200 may be implemented through various devices capable of performing quantum computing.

The quantum preprocessor 200 may perform quantum channel twirl on the quantum state before measurement. For example, the quantum preprocessor 200 may perform quantum channel mixing to obtain a depolarization channel.

The quantum preprocessor 200 may perform quantum channel mixing to obtain a depolarization channel so that any noise present in the _{quantum state ρ y} ^{(k) to be measured can be controlled as a type of depolarization form.} Optimization of quantum measurements can be preserved through the quantum preprocessing operation of the quantum preprocessor 200 .

The quantum preprocessor 200 may perform quantum channel mixing by applying unitary transformation to _{the quantum state ρ y} ^{(k) of the qubit.} For example, the quantum preprocessor 200 may apply a first unitary transform 210 to the quantum state of the qubits before they pass through the noise channel 500 , and the qubits may be converted into the noise channel 500 . ), the second unitary transform 230 may be applied to the quantum state of the qubit. In this case, the second unitary transform 230 may be a Hermitian conjugate of the first unitary transform 210 .

The noise channel 500 may be a concept encompassing various types of noise generated in all processes such as preparation, processing, and measurement of a quantum state in a quantum computing device. Accordingly, the quantum state before passing through the noise channel 500 may mean the quantum state of qubits arriving at the quantum measurement apparatus 100 , and the quantum state after passing through the noise channel 500 is the queue immediately before measurement. It may mean the quantum state of a bit.

The operation of the quantum preprocessor 200 will be described in more detail with reference to FIG. 3 below.

The quantum detector 300 may measure the quantum state of the qubit. For example, the quantum detector 300 may obtain a measurement result of a quantum state (P _(id,D) [x _k | k]) based on the depolarization channel. The measurement result (P _(id,D) [x _k |k]) may be a distribution of quantum state measurement values.

The quantum detector 300 may be designed to obtain an optimized measurement result through the standard basis {|0>, |1>}, but may still perform the optimized quantum measurement under the noise of the depolarization channel. That is, the optimized nature of the quantum measurement of the quantum detector 300 under the depolarization channel may be invariant.

The post-processor 400 may remove an error in the _{quantum state measurement result (P (id,D)} [x _{k |k]).} For example, the post-processor 400 _{calculates a distribution (P (id,id)} [x _k] of a measurement value that does not include an error based on the _{quantum state measurement result (P (id,D)} [x _{k | k])} |k]) can be obtained.

As a result of the quantum preprocessing operation of the quantum preprocessor 200, the quantum state measurement result (P _(id,D) [x _k k]) and the distribution of the measurement value without error (P _(id,id) [x _k | k]), a relation such as Equation 1 may be established.

는 2% 내지 8% 사이의 값을 가질 수 있다.At this time,

may have a value between 2% and 8%.

로 2% 내지 8% 사이의 값을 선택하여 수학식 2와 같은 연산을 수행할 수 있다. 예를 들어, 후처리기(400)는 미리 입력된 2% 내지 8% 사이의 값을

으로 설정하여 수학식 2와 같은 연산을 수행할 수 있다.The post-processor 400 is

By selecting a value between 2% and 8%, the operation shown in Equation 2 may be performed. For example, the post-processor 400 uses a pre-entered value between 2% and 8%.

By setting to , the same operation as in Equation 2 can be performed.

The post-processor 400 performs an operation as in Equation 2 and _{distributes the measurement value without error from the quantum state measurement result (P (id,D)} [x _k | k]) to the distribution (P _{(id, id)} [x _k k]) can be estimated.

FIG. 3 is a view for explaining a quantum measurement operation of the quantum measurement apparatus shown in FIG. 1 .

Although FIG. 3 shows the operation of the quantum measuring apparatus 100 for a plurality of qubits, a quantum preprocessing process for a single qubit will be described first for convenience of description.

The quantum preprocessor 200 may perform quantum channel mixing by utilizing three unitary transforms. The quantum preprocessor 200 may obtain a depolarization channel (D _η [ρ _y ]) by performing quantum channel mixing.

_{A depolarization channel (D η} [ρ _y ]) obtained for a single qubit in the quantum preprocessor 200 may be expressed as Equation (3).

는 잡음 채널을 의미하고, ρ_y는 측정 전의 가능한 양자 상태를 의미하고, G는 유니타리 변환을 나타낸다.At this time,

denotes a noise channel, ρ _y denotes a possible quantum state before measurement, and G denotes a unitary transformation.

Hereinafter, the operation of the quantum preprocessor 200 represented by Equation 3 will be described.

중 하나일 수 있다. 유니타리 변환 G가 적용된 양자 상태 ρ_y는

로 나타낼 수 있다.The quantum preprocessor 200 may apply the unitary transform G to _{the quantum state (ρ y} ) of the qubits arriving at the measurement equipment. In this case, the unitary transform G is each selected from _{the sets U 1} , U ₂ and U _{3 represented by Equations 4 to 6}

can be one of _{The quantum state ρ y} to which the unitary transform G is applied is

can be expressed as

In Equations 4 to 6, X, Y, and Z represent Pauli matrices.

를 적용할 수 있다. 유니타리 변환

는 유니타리 변환 G의 허미션 공액(Hermitian conjugate)일 수 있다. 잡음채널

를 지나 유니타리 변환

가 적용된 양자 상태 ρ_y는

로 나타낼 수 있다.The quantum preprocessor 200 unitary transforms the quantum state of the qubit immediately before measurement.

can be applied. unitary conversion

may be a Hermitian conjugate of the unitary transformation G. noise channel

unitary transformation through

The quantum state ρ _y to which is applied is

can be expressed as

The quantum preprocessor 200 may perform quantum channel mixing on all elements of the {U, V, W} set. For example, the quantum preprocessor may calculate an average value of results obtained by performing quantum channel mixing by selecting all elements of the {U, V, W} set as unitary transform G, respectively. In this case, the calculated average value may be the depolarization channel (D _η [ρ _y ]).

Now, the quantum preprocessing process for a plurality of qubits will be described with reference to the quantum preprocessing process for a single qubit. Although three qubits are illustrated in FIG. 3 , the present invention is not limited thereto, and in general, an operation for n qubits will be described.

The quantum preprocessor 200 may perform collective channel twirl by utilizing three unitary transforms. The quantum preprocessor 200 may perform collective quantum channel mixing to obtain a depolarization channel D _η [ρ _y ].

The depolarization channel (D _η [ρ _k ]) obtained for each quantum state (ρ _{y ) included in the quantum state (ρ 1??n} ) of the n-qubit in the quantum preprocessor 200 is obtained by Equation 7 and It can be expressed through Equation 8.

)는 개별 큐비트에 대해 탈분극 채널과 동일할 수 있다.The result obtained by the quantum preprocessor 200 performing collective quantum channel mixing (

) can be equal to the depolarization channel for individual qubits.

Hereinafter, the operation of the quantum preprocessor 200 represented by Equations 7 and 8 will be described.

을 적용하는 동작으로 나타낼 수 있다. 이때, G는 수학식 2 내지 수학식 4로 표현되는 집합 U₁, U₂ 및 U₃에서 각각 선택된

중 하나일 수 있고, 유니타리 변환

=

은 G를 n번 텐서곱한 결과로서 n개 양자 시스템 각각에 동일한 유니타리 변환 G가 적용되는 동작을 의미할 수 있다.The quantum preprocessor 200 may apply the same unitary transform G (210-1 to 210-3) to each of the n qubits arriving at the measurement equipment. The operation of applying the same unitary transform G to n qubits is a unitary transform to the quantum state (ρ _1??n ) of n-qubits.

It can be expressed as an action to apply . At this time, G is each selected from _{the sets U 1} , U ₂ and U _{3 represented by Equations 2 to 4}

can be one of the unitary transforms

=

is a result of tensor multiplication of G, and may mean an operation in which the same unitary transform G is applied to each of n quantum systems.

(230-1 내지 230-3)을 적용할 수 있다. 유니타리 변환

는 유니타리 변환 G의 허미션 공액(Hermitian conjugate)일 수 있고, 유니타리 변환

은

로 n개 양자 시스템 각각에 동일한 유니타리 변환

가 적용되는 동작을 의미할 수 있다.The quantum preprocessor 200 unitary transforms the quantum state into each of the n qubits immediately before measurement.

(230-1 to 230-3) can be applied. unitary conversion

may be a Hermitian conjugate of the unitary transformation G, and the unitary transformation

silver

the same unitary transformation for each of the n quantum systems with

may mean an operation to which is applied.

The quantum preprocessor 200 may perform the aforementioned collective quantum channel mixing on all elements of the {U, V, W} set. The quantum preprocessor can perform collective quantum channel mixing by selecting all elements of the {U, V, W} set as unitary transform G, respectively. The overall state of the qubits before measurement obtained as a result of the quantum channel mixing by the quantum preprocessor 200 may be expressed as Equation (7). In this case, the state of each qubit can be expressed as in Equation (8). That is, the quantum preprocessor 200 may perform quantum channel mixing on all qubits to obtain a depolarization channel (D _η [ρ _k ]) for _{the state (ρ y ) of each individual qubit.}

FIG. 4 is a flowchart for explaining a quantum measurement operation of the quantum measurement apparatus shown in FIG. 1 .

The quantum measuring apparatus 100 may perform quantum pre-processing before measurement ( 410 ). For example, the quantum preprocessor 200 may obtain a depolarization channel by performing quantum channel mixing on the quantum state of the qubit to be measured.

The quantum measuring apparatus 100 may measure a quantum state based on the depolarization channel ( 430 ). For example, the quantum detector 300 may perform an optimized quantum measurement under noise of a depolarization channel.

The quantum measuring apparatus 100 may perform post-processing on the measurement result ( S450 ). For example, the post-processor 400 may calculate a distribution of measured values in which the amount of error is mitigated based on a relational expression obtained as a result of the quantum pre-processing operation.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiment, or may be known and available to those skilled in the art of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic such as floppy disks. - includes magneto-optical media, and hardware devices specially configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

Software may comprise a computer program, code, instructions, or a combination of one or more thereof, which configures a processing device to operate as desired or is independently or collectively processed You can command the device. The software and/or data may be any kind of machine, component, physical device, virtual equipment, computer storage medium or apparatus, to be interpreted by or to provide instructions or data to the processing device. , or may be permanently or temporarily embody in a transmitted signal wave. The software may be distributed over networked computer systems and stored or executed in a distributed manner. Software and data may be stored in one or more computer-readable recording media.

As described above, although the embodiments have been described with reference to the limited drawings, those skilled in the art may apply various technical modifications and variations based on the above. For example, the described techniques are performed in an order different from the described method, and/or the described components of the system, structure, apparatus, circuit, etc. are combined or combined in a different form than the described method, or other components Or substituted or substituted by equivalents may achieve an appropriate result.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

Claims (20)

A method for a quantum computing device to measure a quantum state, comprising:
obtaining a depolarization channel by performing quantum channel mixing (channel twirl) on qubits;
Measuring the quantum state of the qubit based on the depolarization channel
Including, a quantum measurement method.
According to claim 1,
The obtaining step is
applying a first unitary transform to the quantum state of the qubit before the qubit passes through a noise channel; and
applying a second unitary transform to the quantum state of the qubit after the qubit has passed through the noise channel;
Including, a quantum measurement method.
3. The method of claim 2,
The second unitary transformation is
A Hermitian conjugate of the first unitary transform, a quantum measurement method.
3. The method of claim 2,
The first unitary transformation is
A quantum measuring method, which is one of the elements of a set of unitary transforms including a plurality of unitary transforms.
5. The method of claim 4,
The obtaining step is
calculating an average value of depolarization channels obtained for each element of the set of unitary transformations
Including, a quantum measurement method.
According to claim 1,
The step of obtaining the depolarization channel comprises:
performing collective channel twirl on a plurality of qubits included in the qubits; and
obtaining a depolarization channel for each of the plurality of qubits based on a result of the collective quantum channel mixing;
A quantum measurement method comprising a.
7. The method of claim 6,
The step of performing the collective quantum channel mixing comprises:
applying a first unitary transform to the quantum state of each of the plurality of qubits before the plurality of qubits pass through a noise channel; and
applying a quantum state second unitary transform of each of the plurality of qubits after the plurality of qubits have passed through the noise channel;
Including, a quantum measurement method.
8. The method of claim 7,
The second unitary transformation is
A Hermitian conjugate of the first unitary transform, a quantum measurement method.
7. The method of claim 6,
The step of obtaining a depolarization channel for each of the plurality of qubits comprises:
Investigating the effect on the quantum state of individual qubits for a plurality of qubits obtained as a result of the collective quantum channel mixing
A quantum measurement method comprising a.
According to claim 1,
removing an error in the measurement result of the quantum state
Further comprising, a quantum measurement method.
a quantum preprocessor for obtaining a depolarization channel by performing quantum channel twirl on qubits; and
A quantum detector that measures the quantum state of the qubit based on the depolarization channel
Including, quantum measurement device.
12. The method of claim 11,
The quantum preprocessor,
applying a first unitary transform to the quantum state before the qubits pass through the noise channel, and applying a second unitary transform after the qubits pass through the noise channel.
13. The method of claim 12,
The second unitary transformation is
A Hermitian conjugate of the first unitary transform, a quantum measuring device.
14. The method of claim 13,
The first unitary transformation is
A quantum measuring device, which is one of the elements of a set of unitary transforms including a plurality of unitary transforms.
15. The method of claim 14,
The quantum preprocessor,
A quantum measuring device for calculating an average value of a depolarization channel obtained for each of all elements of the set of unitary transformations.
12. The method of claim 11,
The quantum preprocessor,
A quantum measuring apparatus for performing collective channel twirl on a plurality of qubits included in the qubit, and obtaining a depolarization channel for each of the plurality of qubits based on a result of collective quantum channel mixing.
17. The method of claim 16,
The quantum preprocessor,
A first unitary transform is applied to the quantum state of each of the plurality of qubits before the plurality of qubits pass through the noise channel, and a second unitary transform is performed after the plurality of qubits pass through the noise channel. Applied, quantum measuring device.
18. The method of claim 17,
The second unitary transformation is
A Hermitian conjugate of the first unitary transform, a quantum measuring device.
17. The method of claim 16,
The quantum preprocessor,
Quantum measurement apparatus for examining the effect on the quantum state of individual qubits for a plurality of qubits obtained as a result of the collective quantum channel mixing.
12. The method of claim 11,
A post-processor that removes an error in the measurement result of the quantum state
Further comprising a, quantum measurement device.

Images