US-20260127480-A1 - Fusing Logical Qubits to Implement Transversal Multi-Qubit Gates in Fault-Tolerant Quantum Computing Systems

US20260127480A1US 20260127480 A1US20260127480 A1US 20260127480A1US-20260127480-A1

Abstract

A method for operating a fault-tolerant quantum computing system (QCS), which includes a first set of physical qubits (PQs) that forms a first logical qubit (LQ) and a second set of PQs that forms a second LQ, is disclosed. A first subset of the first set of PQs is entangled with a second subset of the second set of PQs, forming a first set of entangled qubit-pairs. The entangled qubit-pairs are distributed across the first subset of PQs and the second subset of PQs. A fused LQ is formed that includes the first LQ, the second LQ is formed, and a set of fused stabilizers that spans the first LQ and the second LQ. The entangled qubit-pairs are employed as fused-measure qubits for the set of fused stabilizers. A quantum error correction (QEC) code is implemented on the fused LQ. The QEC code employs the fused stabilizers.

Inventors

Matthew James McEwen

Assignees

GOOGLE LLC

Dates

Publication Date: 20260507
Application Date: 20241101

Claims (20)

1 . A method for operating a fault-tolerant quantum computing system (QCS) that includes a first set of physical qubits (PQs) that forms a first logical qubit (LQ) and a second set of PQs that forms a second LQ, the method comprising: entangling a first subset of the first set of PQs with a second subset of the second set of PQs such that a first set of entangled qubit-pairs is formed and the first set of entangled qubit-pairs is distributed across the first subset of PQs and the second subset of PQs; forming a fused LQ that includes the first LQ and the second LQ, wherein the fused LQ further includes a set of fused stabilizers that spans the first LQ and the second LQ, and wherein at least a subset of the first set of entangled qubit-pairs is employed as a set of fused-measure qubits for the set of fused stabilizers; and implementing a quantum error correction (QEC) code on the fused LQ, wherein the QEC code employs the set of fused stabilizers.
2 . The method of claim 1 , wherein the first set of PQs includes a first set of data qubits for the first LQ and a first set of measure qubits for the first LQ, wherein the first subset of PQs is a first subset of the first set of measure qubits that is located on a first LQ boundary of the first LQ such that the first subset of PQs is a first set of boundary-measure qubits of the first LQ; and the second set of PQs includes a second set of data qubits for the second LQ and a second set of measure qubits for the second LQ, wherein the second subset of PQs is a second subset of the second set of measure qubits that is located on a second LQ boundary of the second LQ such that the second subset of PQs is a second set of boundary-measure qubits of the second LQ.
3 . The method of claim 2 , wherein the QCS further includes: a first set of transmission qubits that is associated with the first LQ, wherein each boundary-measure qubit in the first set of boundary-measure qubits is coupable to at least one transmission qubit of the first set of transmission qubits via one or more multi-qubit logic gate types; a second set of transmission qubits that is associated with the second LQ, wherein each boundary-measure qubit in the second set of boundary-measure qubit is coupable to at least one transmission qubit of the second set of transmission qubits via the one or more multi-qubit logic gate types; and a set of quantum transmission lines (QTLs) that couples each transmission qubit of the first set of transmission qubits to a corresponding transmission qubit of the second set of transmission qubits, wherein the set of QTLs is configured to transmit quantum information between the first set of transmission qubits and the second set of transmission qubits.
4 . The method of claim 3 , wherein the QCS further includes: a first module that includes the first set of PQs and the first set of transmission qubits; and a second module that includes the second set of PQs and the second set of transmission qubits, wherein the second module is physically separate from the first module and the set of QTLs quantumly couples the first module to the second module.
5 . The method of claim 3 , wherein entangling the first subset of PQs with the second subset of PQs comprises: generating the first set of entangled qubit-pairs such that the second set of transmission qubits includes a first qubit of each entangled qubit-pair of the first set of entangled qubit-pairs and the second set of boundary-measure qubits includes a second qubit of each entangled qubit-pair of the first set of entangled qubit-pairs, wherein when generating the first set of entangled qubit-pairs, the one or more multi-qubit logic gate types are employed to entangle the second set of boundary-measure qubits with the second set of transmission qubits; for each entangled qubit-pair of the first set of entangled qubit-pairs, transmitting a quantum state of the first qubit of the entangled qubit-pair, via a corresponding QLT of the set of QLTs, from the second set of transmission qubits to the first set of transmission qubits such that the first set of transmission qubits encodes the quantum state of the first qubit of each entangled qubit-pair of the set of entangled qubit-pairs and the second set of boundary-measure qubits encodes a quantum state of the second qubit of each entangled qubit-pair of the set of entangled qubit-pairs; and entangling, via the one or more multi-qubit logic gate types, the first set of transmission qubits with the first set of boundary-measure qubits such that the first set of boundary-measure qubits encodes the quantum state of the first qubit of each entangled qubit-pair of the first set of entangled qubit-pairs, resulting in an entanglement between the first subset of PQs and the second subset of PQs.
6 . The method of claim 5 , wherein the one or more multi-qubit logic gate types includes a CNOT gate.
7 . The method of claim 5 , wherein generating the first set of entangled qubit-pairs comprises: generating a first set of Bell pairs via the one or more multi-qubit logic gate types, wherein the first set of entangled qubit-pairs is the first set of Bell pairs, the first qubit of each entangled qubit pair of the first set of entangled qubit-pairs is a first-half of a separate Bell pair of the first set of Bell pairs and the second qubit of each entangled qubit pair of the first set of entangled qubit-pairs is a second-half of the separate Bell pair of the first set of Bell pairs such that the first-half of each Bell pair of the first set of Bell pairs is included in the second set of transmission qubits and the second-half of each Bell pair of the first set Bell pairs is included in the second set of boundary-measure qubits.
8 . The method of claim 7 , wherein transmitting the quantum state of the first qubit of the entangled qubit-pair from the second set of transmission qubits to the first set of transmission qubits comprises: transmitting, via a uni-directional transmission over the corresponding QTL of the set of QTLS, the second-half of each Bell pair of the first set of Bell pairs, from the second set of transmission qubits to the first set of transmission qubits.
9 . The method of claim 8 , wherein entangling the first set of transmission qubits with the first set of boundary-measure qubits comprises: transferring, via the one or more multi-qubit logic gate types, the second-half of each Bell pair of the first set of Bell pairs, from the first set of transmission qubits to the first set of measure qubits via the one or more multi-qubit logic gate types.
10 . The method of claim 5 , wherein implementing the QEC code on the fused LQ comprises: measuring each measure qubit in the first set of measure qubits, wherein the first set of measure qubits are employed as measure qubits for the set of fused stabilizers.
11 . The method of claim 3 , wherein: there is a first one-to-one correspondence between the first set of measure qubits and the first set of transmission qubits; there is a second one-to-one correspondence between the second set of measure qubits and the second set of transmission qubits; there is a third one-to-one correspondence between the first set of transmission qubits and the second set of transmission qubits; and there is a fourth one-to-one correspondence between the first set of measure qubits and the second set of measure qubits via the first one-to-one correspondence, the second one-to-one correspondence, and the third one-to-one correspondence.
12 . The method of claim 11 , the method further comprising: performing a first reset operation on a first measure qubit of the first set of measure qubits, wherein the first reset operation is performed in a first measurement-basis; performing a second reset operation on a first transmission qubit of the first set of transmission qubits, wherein the second reset operation is performed in a second measure-basis that is orthogonal to the first measurement-basis and the first measure qubit corresponds to the first transmission qubit via the first one-to-one correspondence; performing a third reset operation on a second measure qubit of the second set of measure qubits, wherein the third reset operation is performed in the first measurement-basis; and performing a fourth reset operation on a second transmission qubit of the second set of transmission qubits, wherein the fourth reset operation is performed in the second measurement-basis, the second measure qubit corresponds to the second transmission qubit via the second one to correspondence, and the first transmission qubit corresponds to the second transmission qubit via the third one-to-one correspondence.
13 . The method of claim 3 , wherein entangling the first subset of PQs with the second subset of PQs comprises: generating the first set of entangled qubit-pairs such that the second set of transmission qubits includes a first qubit of each entangled qubit-pair of the first set of entangled qubit-pairs and the second set of boundary-measure qubits includes a second qubit of each entangled qubit-pair of the first set of entangled qubit-pairs, wherein when generating the first set of entangled qubit-pairs, the one or more multi-qubit logic gate types are employed to entangle the second set of boundary-measure qubits with the second set of transmission qubits; generating a second set of entangled qubit-pairs such that the first set of transmission qubits includes a first qubit of each entangled qubit-pair of the second set of entangled qubit-pairs and the first set of boundary-measure qubits includes a second qubit of each entangled qubit-pair of the second set of entangled qubit-pairs, wherein when generating the second set of entangled qubit-pairs, the one or more multi-qubit logic gate types are employed to entangle the first set of boundary-measure qubits with the first set of transmission qubits; swapping quantum states, via bi-directional swap operations along the set of QLTs, between the first qubits of the first set of entangled qubit-pairs and the first qubits of the second set of entangled qubit-pairs such quantum states of the first qubits of the first set of entangled qubit-pairs are encoded in the first set of transmission qubits, quantum states of the second qubits of the first set of entangled qubit-pairs are encoded in the second set of of boundary-measure qubits, quantum states of the first qubits of the second set of entangled qubit-pairs are encoded in the second set of transmission qubits, and quantum states of the second qubits of the second set of entangled qubit-pairs are encoded in the first set of boundary-measure qubits; measuring the second set of transmission qubits; and performing a set of flag operations for the bi-directional swap operations based on measuring the second set of transmission qubits, wherein the set of flag operations are configured to detect transmission errors occurring in the bi-directional swap operations.
14 . The method of claim 3 , wherein entangling the first subset of PQs with the second subset of PQs comprises: generating the first set of entangled qubit-pairs such that the second set of transmission qubits includes a first qubit of each entangled qubit-pair of the first set of entangled qubit-pairs and the second set of boundary-measure qubits includes a second qubit of each entangled qubit-pair of the first set of entangled qubit-pairs, wherein when generating the first set of entangled qubit-pairs, the one or more multi-qubit logic gate types are employed to entangle the second set of boundary-measure qubits with the second set of transmission qubits; and generating a second set of entangled qubit-pairs such that the first set of transmission qubits includes a first qubit of each entangled qubit-pair of the second set of entangled qubit-pairs and the first set of boundary-measure qubits includes a second qubit of each entangled qubit-pair of the second set of entangled qubit-pairs, wherein when generating the second set of entangled qubit-pairs, the one or more multi-qubit logic gate types are employed to entangle the first set of boundary-measure qubits with the first set of transmission qubits.
15 . The method of claim 14 , wherein: each transmission qubit of the first set of transmission qubits corresponds to two separate measure qubits of the first set of measure qubits; each transmission qubit of the second set of transmission qubits corresponds to two separate measure qubits of the second set of measure qubits; each measure qubit of the first set of measure qubits corresponds to a single transmission qubit of the first set of transmission qubits; each measure qubit of the second set of measure qubits corresponds to a single transmission qubit of the second set of transmission qubits; there is a first one-to-one correspondence between the first set of transmission qubits and the second set of transmission qubits; and there is a second one-to-one correspondence between the first set of measure qubits and the second set of measure qubits.
16 . The method of claim 15 , the method further comprising: performing a first reset operation on a first measure qubit of the first set of measure qubits, wherein the first reset operation is performed in a first measurement-basis; performing a second reset operation on a second measure qubit of the first set of measure qubits, wherein the second reset operation is performed in a second measurement-basis that is orthogonal to the first measurement-basis; performing a third reset operation on a first transmission qubit of the first set of transmission qubits, wherein the third reset operation is performed in the second measurement-basis and the first transmission qubit corresponds to each of the first measure qubit and the second measure qubit; performing a fourth reset operation on a third measure qubit of the second set of measure qubits, wherein the fourth reset operation is performed in the first measurement-basis; performing a fifth reset operation on a fourth measure qubit of the second set of measure qubits, wherein the fifth reset operation is performed in the second measurement-basis; performing a sixth reset operation on a second transmission qubit of the second set of transmission qubits, wherein the sixth reset operation is performed in the first measurement-basis, the second transmission qubit corresponds to each of the third measure qubit and the fourth measure qubit, and the first transmission qubit corresponds to the second transmission qubit via the first one-to-one correspondence, and wherein the first measure qubit corresponds to the third measure qubit via the second one-to-one correspondence and the second measure qubit corresponds to the fourth measure qubit via the second one-to-one correspondence.
17 . The method of claim 16 , wherein: a first entangled-qubit pair of the first set of entangled qubit pairs includes the third measure qubit and the second transmission qubit; and a second entangled-qubit pair of the second set of entangled qubit pairs includes the first measure qubit and the first transmission qubit.
18 . The method of claim 1 , the method further comprising: performing a transversal multi-qubit logic gate between the first LQ and the second LQ by employing local qubit-interactions across the fused LQ.
19 . The method of claim 1 , wherein the QEC code is a surface code.
20 . A computing system, comprising: a first set of physical qubits (PQs) that forms a first logical qubit (LQ); a second set of PQs that forms a second LQ; one or more processor devices; one or more memory devices, the one or more memory devices storing computer-readable instructions that when executed by the one or more processor devices cause the one or more processor devices to perform operations for implementing fault-tolerant quantum computing, the operations comprising: entangling a first subset of the first set of PQs with a second subset of the second set of PQs such that a first set of entangled qubit-pairs is formed and the first set of entangled qubit-pairs is distributed across the first subset of PQs and the second subset of PQs; forming a fused LQ that includes the first LQ and the second LQ, wherein the fused LQ further includes a set of fused stabilizers that spans the first LQ and the second LQ, and wherein at least a subset of the first set of entangled qubit-pairs is employed as a set of fused-measure qubits for the set of fused stabilizers; and implementing a quantum error correction (QEC) code on the fused LQ, wherein the QEC code employs the set of fused stabilizers.

Description

FIELD The present disclosure relates generally to quantum computing and information processing systems, and more particularly to fusing logical qubits to implement transversal multi-qubit gates in fault-tolerant quantum computing systems. BACKGROUND Quantum computing is a computing method that takes advantage of quantum effects, such as superposition of basis states and entanglement to perform certain computations more efficiently than a classical digital computer. In contrast to a digital computer, which stores and manipulates information in the form of bits, e.g., a “1” or “0,” quantum computing systems can manipulate information using quantum bits (“qubits”). A qubit can refer to a quantum device that enables the superposition of multiple states, e.g., data in both the “0” and “1” state, and/or to the superposition of data, itself, in the multiple states. In accordance with conventional terminology, the superposition of a “0” and “1” state in a quantum system may be represented, e.g., as a |0+b |1 The “0” and “1” states of a digital computer are analogous to the |0 and |1 basis states, respectively of a qubit. SUMMARY Aspects and advantages of embodiments of the present disclosure will be set forth in part in the following description, or can be learned from the description, or can be learned through practice of the embodiments. One example aspect of the present disclosure is directed to a method for operating a fault-tolerant quantum computing system (QCS). The QCS includes a first set of physical qubits (PQs) that forms a first logical qubit (LQ). The QCS further includes a second set of PQs that forms a second LQ. The method includes entangling a first subset of the first set of PQs with a second subset of the second set of PQs. A first set of entangled qubit-pairs is formed by entangling the first subset of PQ and the second set of PQs. The first set of entangled qubit-pairs is distributed across the first subset of PQs and the second subset of PQs. A fused LQ that includes the first LQ and the second LQ is formed. The fused LQ further includes a set of fused stabilizers that spans the first LQ and the second LQ. At least a subset of the first set of entangled qubit-pairs is employed as a set of fused-measure qubits for the set of fused stabilizers. A quantum error correction (QEC) code is implemented on the fused LQ. The QEC code employs the set of fused stabilizers. Other aspects of the present disclosure are directed to various systems, methods, apparatuses, non-transitory computer-readable media, computer-readable instructions, and computing devices. These and other features, aspects, and advantages of various embodiments of the present disclosure will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate example embodiments of the present disclosure and, together with the description, explain the related principles. BRIEF DESCRIPTION OF THE DRAWINGS Detailed discussion of embodiments directed to one of ordinary skill in the art is set forth in the specification, which refers to the appended figures, in which: FIG. 1 depicts an example quantum computing system according to example embodiments of the present disclosure; FIG. 2A illustrates a set of logical qubits that may be fused, according to various embodiments; FIG. 2B shows a non-limiting example of a fused logical qubit, according to various embodiments; FIG. 3A shows a uni-directional transmission of quantum information along a quantum transmission line, according to various embodiments; FIG. 3B shows a bi-directional transmission of quantum information along a quantum transmission line, according to various embodiments; FIG. 4A shows a set of logical qubits, according to various embodiments; FIG. 4B shows a fused logical qubit comprised of the first logical qubit and the second logical qubit of FIG. 4A, according to various embodiments; FIG. 5 shows a first quantum circuit that configures a fused logical qubit, according to various embodiments; FIG. 6 shows a second quantum circuit that configures a fused logical qubit, according to various embodiments; FIG. 7 shows a third quantum circuit that configures a fused logical qubit, according to various embodiments; and FIG. 8 depicts a flow chart diagram of an example method for operating a fault-tolerant quantum computing system, according to various embodiments. DETAILED DESCRIPTION Example aspects of the present disclosure are directed to methods, architectures, and hardware configurations that enable fusing logical qubits (LQs). For example, quantum error correction (QEC) codes form LQs from multiple physical qubits (PQs), where the PQs redundantly encode the quantum information. Somewhat similar to classical error correction (CEC) codes, this redundant encoding of quantum information provides for detecting and correcting qubit errors. More partic