Hardware-efficient syndrome extraction for entangled quantum states

Patent metadata

Field	Value
Publication number	US-9762262-B2
Application number	US-201414541779-A
Country	US
Kind code	B2
Filing date	Nov 14, 2014
Priority date	Jun 18, 2014
Publication date	Sep 12, 2017
Grant date	Sep 12, 2017

Abstract

A quantum-state-refresh module of a memory system is configured to detect an error in an entangled qubit state stored therein by performing a redundant measurement of syndrome values corresponding to a quantum stabilizer code, with the redundant measurement being based on a block error-correction code. The quantum-state-refresh module includes a plurality of measurement sub-modules, each configured to measure a respective syndrome value or a respective parity value corresponding to the entangled qubit state. The total number of the measurement sub-modules is smaller than the codeword length of the block error-correction code, and the initial approximation of the punctured syndrome values is replaced in the decoding process by erasure values. With the block error-correction code appropriately constructed for the use of erasure values, the quantum-state-refresh module is advantageously capable of providing reliable error detection with fewer quantum gates than that used for the full-length measurement of the codeword.

First claim

What is claimed is:

1. An apparatus comprising:
a register configured to store a coded entangled qubit state generated using a quantum stabilizer code;
a measurement circuit configured to perform a redundant measurement of a set of syndrome values corresponding to the coded entangled qubit state, wherein the redundant measurement is performed based on a block error-correction code;
an erasure-value generator configured to generate a set of erasure values; and
a decoder configured to determine a probable syndrome vector corresponding to the coded entangled qubit state using the block error-correction code and the redundant measurement of the set of syndrome values, and further configured to apply the set of erasure values generated by the erasure-value generator to a set of variable nodes not configured to receive a measured syndrome value from the measurement circuit.

2. The apparatus of claim 1 , further comprising a state-recovery circuit configured to correct an error in the coded entangled qubit state based on the probable syndrome vector determined by the decoder.

3. The apparatus of claim 2 , wherein the state-recovery circuit is further configured to:
determine, based on the probable syndrome vector, an error operator corresponding to a probable error in the coded entangled qubit state; and
process the coded entangled qubit state based on the error operator in a manner that corrects the probable error therein.

4. The apparatus of claim 3 , further comprising a qubit array configured to store a plurality of coded entangled qubit states, wherein the apparatus is configured to:
transfer a selected coded entangled qubit state from the qubit array to the register; and
transfer the selected coded entangled qubit state from the register to the qubit array in response to modifying the selected entangled qubit state based on the error operator.

5. The apparatus of claim 1 , wherein the measurement circuit comprises:
a first set of measurement modules coupled to the register, wherein each measurement module in the first set is configured to measure a respective syndrome value corresponding to the coded entangled qubit state based on a respective one of first binary vectors, each of said first binary vectors being a generator of the quantum stabilizer code; and
a second set of measurement modules coupled to the register, wherein each measurement module in the second set is configured to measure a respective parity value corresponding to the coded entangled qubit state based on a respective one of second binary vectors, wherein each parity value is related to a respective subset of syndrome values of the quantum stabilizer code as defined by the block error-correction code.

6. The apparatus of claim 5 , wherein a total number of the measurement modules in the first set is smaller than a total number of generators of the quantum stabilizer code.

7. The apparatus of claim 6 , wherein a total combined number of the measurement modules in the first set and the second set is smaller than a codeword length of the block error-correction code.

8. The apparatus of claim 5 , wherein a total combined number of the measurement modules in the first set and second set is smaller than a codeword length of the block error-correction code.

9. The apparatus of claim 5 , wherein:
a measurement module in the first set comprises a respective soft-output detector configured to generate the respective syndrome value as a log-likelihood-ratio (LLR) value; and
a measurement module in the second set comprises a respective soft-output detector configured to generate the respective parity value as an LLR value.

10. The apparatus of claim 1 ,
wherein the decoder is configured to determine the probable syndrome vector by executing a message-passing decoding algorithm corresponding to the block error-correction code; and
wherein the decoder is configured to initialize said message-passing decoding algorithm using the set of erasure values generated by the erasure-value generator.

11. The apparatus of claim 1 , wherein a measurement module in the measurement circuit comprises:
a sequence of quantum gates connected to the register and configured to process a reference multi-qubit state by coupling the coded entangled qubit state to the reference multi-qubit state; and
a logic circuit configured to estimate a syndrome value or a parity value corresponding to the coded entangled qubit state from measurements on the processed reference multi-qubit state performed by the sequence of quantum gates.

12. The apparatus of claim 11 , wherein the logic circuit is configured to:
estimate a respective binary syndrome sub-value or a respective binary parity sub-value from a measurement on individual qubits of the processed reference multi-qubit state; and
the circuit comprises a multi-input XOR gate configured to process said binary sub-values to estimate the syndrome value or the parity value.

13. The apparatus of claim 11 , wherein the logic circuit comprises a soft-output detector configured to generate a soft estimate of the syndrome value or of the parity value.

14. The apparatus of claim 1 , wherein the decoder is configured to determine the probable syndrome vector by executing a decoding algorithm corresponding to the block error-correction code.

15. The apparatus of claim 14 , wherein the decoder is configured to initialize said decoding algorithm using LLR values generated by the measurement circuit during the redundant measurement and further using the set of erasure values generated by the erasure-value generator.

16. The apparatus of claim 1 , wherein the decoder is configured to use the set of erasure values generated by the erasure-value generator as an initial approximation for punctured syndrome bits of the probable syndrome vector.

17. The apparatus of claim 1 , wherein the decoder is configured to use the set of erasure values generated by the erasure-value generator to construct an initial approximation of a codeword corresponding to the coded entangled qubit state, said codeword being a codeword of the block error-correction code.

18. The apparatus of claim 17 , wherein the decoder is further configured to use, in the initial approximation of the codeword corresponding to the coded entangled qubit state, LLR values generated by the measurement circuit during the redundant measurement.

19. A method of mitigating loss of fidelity of coded entangled qubit states stored in a memory system, the method comprising:
performing a redundant measurement of a set of syndrome values corresponding to a coded entangled qubit state generated using a quantum stabilizer code, wherein the redundant measurement is performed using a measurement circuit corresponding to a block error-correction code; and
determining a probable syndrome vector corresponding to the coded entangled qubit state using the block error-correction code and the redundant measurement of the set of syndrome values; and
wherein the step of determining comprises applying a set of erasure values to a set of variable nodes not configured to receive a measured syndrome value from the measurement circuit.

20. The method of claim 19 , wherein the step of determining further comprises using the set of erasure values to construct an initial approximation of a codeword corresponding to the coded entangled qubit state, said codeword being a codeword of the block error-correction code, wherein the initial approximation of the codeword includes LLR values generated during the redundant

Assignees

• Alcatel Lucent Usa Inc
• Alcatel Lucent

Inventors

• Ashikhmin Alexei

Classifications

• H03M13/005

  Electricity · mapped topic

• G06N99/002

  Physics · mapped topic

• H03M13/1575 Primary

  Direct decoding, e.g. by a direct determination of the error locator polynomial from syndromes and subsequent analysis or by matrix operations involving syndromes, e.g. for codes with a small minimum Hamming distance · CPC title

• H03M13/154

  Error and erasure correction, e.g. by using the error and erasure locator or Forney polynomial · CPC title

• G06N10/00 Primary

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