Methods, devices, and systems for implementing quantum state factories in quantum circuits

Abstract

In a method for implementing a quantum state factory in a quantum circuit, it is determined for at least one qubit that the qubit is an idle and clean qubit within a sub-circuit of the quantum circuit. The qubit is idle if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit. The qubit is clean if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit. The at least one idle and clean qubit is assigned within the sub-circuit of the quantum circuit to a quantum state factory for generating at least one quantum state. The quantum state factory is implemented within the sub-circuit of the quantum circuit.

Description

METHODS, DEVICES, AND SYSTEMS FOR IMPLEMENTING QUANTUM STATE FACTORIES IN QUANTUM CIRCUITSCross-Reference to Related Applications

[0001] This application claims priority from US application No. 63 / 682597 filed13 August 2024 and entitled METHODS, DEVICES, AND SYSTEMS FOR IMPLEMENTING QUANTUM STATE FACTORIES IN QUANTUM CIRCUITS which is hereby incorporated herein by reference for all purposes. For purposes of the United States of America, this application claims the benefit under 35 U.S.C. §119 of US application No. No. 63 / 682597 filed 13 August 2024 and entitled METHODS, DEVICES, AND SYSTEMS FOR IMPLEMENTING QUANTUM STATE FACTORIES IN QUANTUM CIRCUITS which is hereby incorporated herein by reference for all purposes.Field

[0002] This disclosure generally relates to methods, devices, and systems for implementing a quantum state factory in a quantum circuit.Background

[0003] In the field of quantum computing, the efficiency of algorithms is significantly influenced by the number of required qubits and the execution time of quantum operations. Traditionally, complex quantum algorithms necessitate specific states, the generation and management of which demand additional resources. This limitation poses a significant challenge to the practical applicability of such algorithms, given the current technological constraints on the availability and control of qubits.

[0004] Quantum state factories are a concept designed to address the need for specific quantum states within a quantum circuit. These quantum state factories are mechanisms that create, distill, and teleport or inject the required states to the parts of the quantum circuit where they are needed.

[0005] Typically, quantum state factories operate on dedicated qubits that are reserved solely for the purpose of generating and managing these states throughout the execution of the quantum circuit. However, state factories require large numbers of qubits, which reduces the number of qubits available for computation.

[0006] Accordingly, there is a need for a more efficient implementation of state factories.Summary

[0007] The present disclosure has several aspects, including a method, a device, and an information processing system for implementing a quantum state factory in a quantum circuit.

[0008] A first aspect of the disclosure provides a method for implementing a quantum state factory in a quantum circuit. For at least one qubit, it is determined that the qubit is an idle and clean qubit within a sub-circuit of the quantum circuit. The qubit is an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit. The qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit. The at least one idle and clean qubit is assigned within the sub-circuit of the quantum circuit to a quantum state factory for generating at least one quantum state. The quantum state factory is implemented within the sub-circuit of the quantum circuit.

[0009] The method can reduce the runtime of quantum algorithms that need complex states without requiring additional qubits or at least requiring a reduced number of additional qubits. In general, many quantum circuits will include a significant number of idle and clean qubits. These qubits can be used to implement quantum state factories. The quantum state factories can be considered to be temporary quantum state factories in contrast to permanent quantum state factories that operate on dedicated qubits, i.e. , qubits that are only used to generate quantum states throughout the execution of a quantum circuit. In general, a quantum state factory can generate at least one specific state. That is, in some embodiments, a quantum state factory generates only a single state and in other embodiments, the quantum state factory generates a plurality of states (e.g., multiple instances of a specific state). Optionally, the quantum state factory may perform additional routines, such as distillation and / or synthillation.

[0010] Unlike permanent state factories that rely on dedicated qubits, temporary state factories leverage idle and clean qubits within the quantum circuit. These temporary factories generate, distill, and distribute specific states only when the qubits are notengaged in other computational tasks. This method maximizes the use of available qubits without the need for additional resources.

[0011] The method capitalizes on the significant number of idle and clean qubits present in many quantum circuits, such as quantum circuits that include a quantum read-only memory (QROM) e.g., quantum look-up circuits. By implementing temporary state factories, the method also effectively reduces the runtime of quantum algorithms that require complex states. This optimization is achieved without the need for additional qubits, thereby enhancing the efficiency and practicality of quantum computing.

[0012] According to the specification, it is also considered that “no quantum operation” operates on a qubit within a sub-circuit of the quantum circuit, if the subcircuit includes only an identity operator.

[0013] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the identification of idle and clean qubits and the implementation of the quantum state factory is performed before the quantum circuit is actually executed on a quantum hardware device. In the specification, the usage of a specific tense (e.g., “stores information”, “will store information”, and so on) does not necessarily imply when the respective actions are performed. In some embodiments, at least some of the method steps can be performed during execution of the quantum circuit.

[0014] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum circuit comprises a logical quantum circuit, wherein the at least one idle and clean qubit is a logical qubit of the logical quantum circuit. The quantum circuit can alternatively be a virtual or physical quantum circuit that implements the logical quantum circuit.

[0015] According to the specification, the term “logical quantum circuit” denotes a quantum computation. The logical quantum circuit generally comprises a sequence of operations, such as logical quantum gates, measurements, and initializations of logical qubits to predefined values. Herein, logical quantum gates are basic blocks that operate on a small number of logical qubits.

[0016] According to the specification, the term “virtual quantum circuit” denotes a quantum circuit comprising (virtual) physical qubits that is obtained by a mapping of the logical quantum circuit, based on a quantum error correction (QEC) code.

[0017] According to the specification, the term “QEC code” relates to a code space which is a vector subspace of a Hilbert space. The code space is spanned by so- called codewords of the QEC code. A codeword is a state which encodes some data and corresponds to a logical state of the QEC code. A QEC code is used to protect quantum information that is processed in the computation from errors due to quantum noise, e.g., decoherence.

[0018] A QEC code is in general a mapping of k qubits onto n qubits, where n > k. The quantum states on k qubits are elements of a Hilbert space of dimension 2k. The quantum states on n qubits are elements of a Hilbert space of dimension 2n. Herein, the k qubits are the “logical qubits” or “encoded qubits” that are to be protected from error, e.g., a threshold amount of error. The n qubits are the “physical qubits” implementing the logical qubits. The additional n - k qubits allow the k logical qubits to be stored in a redundant fashion so that the encoded information is less susceptible to noise or other disturbances.

[0019] According to the specification, the term “physical quantum circuit” denotes a quantum circuit comprising hardware physical qubits that is obtained after the (virtual) physical qubits of the virtual quantum circuit are mapped to the hardware physical qubits of a quantum hardware system. The physical quantum circuit is executed on the quantum hardware system to perform the quantum operation.

[0020] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum circuit is a virtual quantum circuit or a physical quantum circuit that implements the logical quantum circuit.

[0021] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the qubit is a logical qubit. The logical qubit can be determined to be an idle qubit within the sub-circuit of the quantum circuit if no logical quantum operation operates on the logical qubit within the sub-circuit of the quantum circuit. Similarly, the logical qubit can be determined to be a clean qubit within the sub-circuit of the quantum circuit if the logical qubit does not store information which is used within or after the sub-circuit of the quantum circuit.

[0022] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the qubit is a logical qubit. The logical qubit can be determined to be an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on a physical qubit implementing the logical qubit. Similarly, the logical qubit can be determined to be a clean qubit within the sub-circuit of the quantum circuit if the qubit is a logical qubit and at least one physical qubit implementing the qubit does not store information which is used within or after the sub-circuit of the quantum circuit.

[0023] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the qubit is a logical qubit. The logical qubit and at least one other logical qubit are both implemented by a plurality of physical qubits (e.g., the same plurality of physical qubits). The plurality of physical qubits can store information forming the state stored in the at least one other logical qubit. If the information stored in the at least one other logical qubit is used within or after the subcircuit of the quantum circuit, the at least one other logical qubit is not clean. Still, the logical qubit itself can be clean if there is no information stored in the logical qubit which is used within or after the sub-circuit of the quantum circuit. Therefore, in this embodiment, a logical qubit implemented by physical qubits can be clean even if the physical qubits also implement at least one other logical qubit which is not clean.

[0024] Additionally, or alternatively, a quantum operation may operate on the at least one other logical qubit within the sub-circuit of the quantum circuit. The at least one other logical qubit is therefore not idle within the sub-circuit of the quantum circuit. Still, the logical qubit itself can be idle if the quantum operation operating on the at least one other logical qubit does not disturb the state of the logical qubit. Therefore, in this embodiment, a logical qubit implemented by physical qubits can be idle even if the physical qubits also implement at least one other logical qubit which is not idle.

[0025] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a state that can be inserted into a qubit, e.g., by injection, and causes a non-Clifford gate to be implemented on that qubit.

[0026] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a state of a qubit that, when a Clifford circuit, a measurement and a conditional Cliffordgate are applied on that qubit and another qubit, results in the implementation of a non-Clifford gate on the other qubit.

[0027] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a state that can be inserted into a qubit, e.g., by injection, and causes a gate to be implemented on that qubit. Herein, the gate can be a gate that cannot otherwise be implemented fault tolerantly in the QEC code in which the logical quantum circuit is encoded.

[0028] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a pure non-stabilizer state distilled from mixed non-stabilizer states via one or more Clifford group operations.

[0029] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a magic state.

[0030] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a T state. According to the specification, the term “T state” denotes a qubit that is in a superposition of 0- and 1 -states separated by a phase of TT / 4. A T state can be used to apply a T gate on another target qubit by applying a CNOT to both qubits and measuring one of them. Creating T states usually requires creating many approximate T states and using a distillation procedure that probabilistically creates fewer high fidelity T states out of many low fidelity ones.

[0031] Examples of T state distillation protocols include the [[15,1 ,3]] Bravyi-Kitaev code which is explained in Bravyi and Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas”, Phys. Rev. A 71 , 022316, which is hereby incorporated by reference in its entirety.

[0032] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a double controlled phase, CCZ, state. A CCZ state can be consumed to implement aCCZ gate on a target qubit based on the states of two control qubits. According to the specification, the term “CCZ gate” can be written as:I ® I ® |0><0| + CZ ® |1><1| , where CZ denotes the controlled-Z gate that flips the phase of the target qubit if the control qubit is in the |1) state. The CCZ gate flips the phase of the target qubit if the control qubits are in the |11> state in the computational basis. In some embodiments, the state factory generates a logical CCZ state via catalyzed distillation of two T- states as explained in Gidney and Fowler, “Efficient magic state factories with a catalyzed \CCZ) to 2| > transformation”, Quantum, 2019, Vol. 3, p. 135, which is hereby incorporated by reference in its entirety.

[0033] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a Toffoli state. The T state, the CCZ state and the Toffoli state can be described as non-Clifford states, i.e. , states that can be used to implement a non-Clifford gate on another qubit. Non-Clifford states generally require magic state distillation or synthillation protocols to be implemented fault-tolerantly. This can be achieved by the state factory.

[0034] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a Bell pair. According to the specification, the term “Bell pair” denotes a pair of two maximally entangled qubits. According to some embodiments, the state factory generates the Bell pair using the Barrett-Kok protocol. In general, the actual Bell pair will deviate from being maximally entangled. The fidelity of the Bell pair indicates how close the two-qubit state is to a maximally entangled state. High-fidelity physical Bell pairs can be obtained from distillation of raw Bell pairs using extra qubits. It is expected that thousands of high-fidelity Bell pairs will be needed to execute a logical gate across two modules of a distributed quantum computing system. Thus, the state factory may be configured to generate a Bell pair by distilling Bell pairs.

[0035] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a Greenberger-Horne-Zeilinger, GHZ, state. According to the specification, a “GHZ state” denotes three or more maximally entangled qubits. According to someembodiments, the state factory generates a GHZ state consisting of n entangled and maximally connected qubits by applying a Hadamard gate to a first qubit and then, for each of the remaining n - 1 qubits, performing a controlled not (CNOT) gate between the respective qubit and the first qubit. Distillation protocols can also increase GHZ states fidelity by using raw GHZ states or Bell pairs and extra qubits.

[0036] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory is configured to generate a W state. According to the specification, a “W state” denotes an entangled state of three qubits which can be written as

[0037] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the step of implementing the quantum state factory within the sub-circuit of the quantum circuit depends on a number of idle and clean qubits assigned to the quantum state factory. For example, it can be determined how many idle and clean qubits are available. The quantum state factory can be selected which can be implemented with this number of idle and clean qubits. For example, if a plurality of quantum states is to be generated by different quantum state factories, different sub-circuits with idle and clean qubits may be identified. The state factories are then distributed to the sub-circuits such that all states can be generated. If one of the quantum state factories requires a large number of idle and clean qubits, a subcircuit with a large number of idle and clean qubits is assigned to this quantum state factory.

[0038] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the step of implementing the quantum state factory within the sub-circuit of the quantum circuit depends on a length of the sub-circuit of the quantum circuit. If one of the quantum state factories requires a large number of execution cycles, a sub-circuit with a large number of execution cycles, i.e., with a large length, is assigned to this quantum state factory. In some embodiments, a number of rounds of distillation can be adjusted based on the length of the sub-circuit of the quantum circuit. For example, based on the length of the sub-circuit of the quantum circuit, the number of rounds of distillation may be maximized (possibly up to some pre-defined upper bound). In some embodiments, a delay in computation canbe implemented such that the length of the sub-circuit of the quantum circuit is long enough for the state factory to generate the state.

[0039] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one qubit is determined to be a clean qubit if the qubit will not have been used in a quantum computation prior to the sub-circuit of the quantum circuit. If the qubit has not been used in a quantum computation, it will not store any useful information.

[0040] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one qubit is determined to be a clean qubit if the qubit will have been used in a quantum computation prior to the sub-circuit of the quantum circuit and will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit. The qubit may still be provisioned to be used in computation at a later stage after the sub-circuit of the quantum circuit as long as no information stored in the qubit is to be retrieved.

[0041] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one qubit is determined to be a clean qubit if neither the qubit nor another qubit entangled with the qubit is used for computation in and after the sub-circuit of the quantum circuit.

[0042] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one qubit is determined to be a clean qubit if it is not entangled.

[0043] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the step of determining that the qubit will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit comprises determining that the qubit will be measured prior to the sub-circuit of the quantum circuit. The measurement may be a destructive measurement. The destructive measurement leads to a collapse of the state into an eigenstate and removes any entanglement or superposition.

[0044] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the step of determining that the qubit will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit comprises determining that the qubit will be uncomputed priorto the sub-circuit of the quantum circuit. According to the specification, “uncomputing” a qubit denotes that the state of the qubit is restored to its state prior to the computation. When uncomputing a qubit, previously introduced entanglement of the qubit may be removed.

[0045] Uncomputation ensures that qubits do not interfere with the final measurement of the computation and are returned to a known state, e.g., the null state |0) in the computational basis. During the quantum computation, a sequence of operations is performed. The operations entangle the qubit with other qubits. Uncomputation can be implemented by performing an inverse of the sequence of operations. More generally, the computation sequence can comprise a plurality of operations. The uncomputation can then involve performing a sequence of the inverse operations. Herein, each inverse operation is an inverse of an operation performed in the original computation sequence. In some embodiments, uncomputation can also involve performing an inverse of the sequence of the operations without a one-to-one correspondence between the operations in the inverse sequence and the operations in the original sequence, as long as the uncomputation returns the state of the qubit to the state it was in prior to the original computation sequence being performed.

[0046] By applying the inverse operations, the entanglement is undone, and the qubit is disentangled from the other qubits. This ensures that the qubit is clean and does not hold any residual information that could affect final measurement of qubits.

[0047] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the step of determining that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit comprises identifying that an uncomputation sequence of quantum operations follows a computation sequence of quantum operations acting on the qubit. The uncomputation sequence of quantum operations corresponds to an inverse of the computation sequence of quantum operations. Often, an inverse sequence of quantum operations corresponds to “undoing” the original sequence of quantum operations.

[0048] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the uncomputation sequence is identified by identifying a symmetry of the quantum circuit. Such symmetries are present if a sequence of quantum operations is followed by an inverse of the sequence of the quantum operations.

[0049] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, determining that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit comprises determining whether the quantum circuit comprises a cleaning operation from a predefined set of cleaning operations. The cleaning operation operates on the qubit prior to the sub-circuit of the quantum circuit. Determining that a qubit is a clean qubit can involve storing the predefined set of cleaning operations in a memory (e.g., in form of a list) and comparing the quantum circuit to the elements of the set to identify parts of the quantum circuit that include any of those cleaning operations. The cleaning operations can be uncomputation operations.

[0050] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one qubit is determined to be a clean qubit if the qubit will have been used in a quantum computation prior to the sub-circuit of the quantum circuit and will not be used for computation (including measurement) in and after the sub-circuit of the quantum circuit. Such qubits can be identified by checking for qubits that have no gates (or only identity operators) operating on the qubits in and after the sub-circuit of the quantum circuit.

[0051] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the method further comprises the step of modifying the quantum circuit to include a cleaning operation operating on the at least one qubit before using the at least one qubit in the quantum state factory. This makes sure that no unwanted information, including unwanted entanglement of the qubits with other qubits, remains which might have undesired effects on final outcomes.

[0052] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the cleaning operation operating on the at least one qubit comprises a destructive measurement on the at least one qubit or initializing the at least one qubit. The destructive measurement destroys any usable information. By initializing the at least one qubit, the qubit is prepared in a predefined state.

[0053] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one qubit is determined to be a clean qubit if the qubit is a logical qubit in a logical quantum circuit and is flagged as a clean qubit. The identification of clean and idle qubits can be simplified by the specification (or description) of the logical circuit including flags indicating whether or not a qubit isclean. For example, a qubit can be considered to be flagged as a clean qubit if it is flagged as uncomputed. For example, the logical circuit may comprise flags that indicate “computation” and “uncomputation” of, e.g., Toffoli pairs.

[0054] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one qubit is physically implemented by at least one client-broker group which comprises a physical broker qubit and at least one physical client qubit. The at least one qubit is determined to be a clean qubit if at least one of the client qubits does not store information which is used within or after the sub-circuit of the quantum circuit. According to the specification, the term “physical broker qubit” denotes a physical qubit that acts as a broker of interactions with other physical qubits. The term “physical client qubit” denotes a physical qubit that stores quantum information. The state of a physical client qubit can be transferred to the state of the physical broker qubit. Each qubit can include many physical client-broker groups. Physical multi-qubit gates can be implemented by performing multi-qubit interactions between physical broker qubits and then swapping the state of the physical broker qubits to the physical client qubits, for example using an imaginary swap (iSWAP) gate. Herein, the term “iSWAP gate” denotes a gate which can be represented by the following matrix:

[0055] In some embodiments, the client-broker group is a client-broker pair, i.e. , it comprises a single physical broker qubit and a single physical client qubit.

[0056] In some embodiments, the client-broker group comprises a physical broker qubit and a plurality of physical client qubits. The qubit implemented by the clientbroker group is determined to be a clean qubit if at least one of the plurality of physical client qubits does not store information which is used in or after the subcircuit of the quantum circuit. This at least one physical client qubit can then be used for the state factory. The other physical client qubits may store information and are not used for the state factory.

[0057] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the determining that the qubit is an idle and clean qubitwithin a sub-circuit of a quantum circuit comprises determining that the qubit is an idle and clean qubit within a sub-circuit of a quantum circuit having a predefined length. The predefined length can depend on the quantum state factory which is to be implemented. In general, it takes a certain number of execution cycles to implement the quantum state factory. A qubit will be considered to be an idle and clean qubit within a sub-circuit of the quantum circuit only if the sub-circuit of the quantum circuit comprises a sufficient number of execution cycles to implement the quantum state factory.

[0058] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the predefined length is determined by a predefined number of execution cycles. The execution cycle may be defined in different ways. For example, an execution cycle can be defined with reference to the shortest operation for a particular architecture of a quantum hardware system implementing the quantum circuit, e.g., the time taken to reliably perform a particular excitation. This may usually take multiple execution attempts. The execution cycle can also be a time to send an optical, magnetic or an electric pulse, or an execution cycle can be a time unit of a classically operating metronome.

[0059] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the predefined number of execution cycles depends on a number of execution cycles required for operating the quantum state factory. The number of execution cycles required for operating the quantum state factory can be a number of execution cycles needed to generate and distill one or more particular states by the quantum state factory. The number of execution cycles required for operating the quantum state factory can be a hardcoded value.

[0060] In some embodiments, the qubit must be idle for a number of execution cycles which is at least equal to the number of execution cycles required for operating the quantum state factory.

[0061] In some embodiments, the qubit must be idle for a number of execution cycles which exceeds the number of execution cycles required for operating the quantum state factory by a predefined number of execution cycles. These additional execution cycles might be necessary to perform additional operations, e.g., cleaning the qubits.

[0062] In some embodiments, the quantum state factory generates a single quantum state. In this case, the number of execution cycles required for operating the quantum state factory can be a number of execution cycles needed to generate and distill a single particular quantum state.

[0063] In other embodiments, the quantum state factory generates a plurality of quantum states. The number of execution cycles required for operating the quantum state factory may depend on a number of quantum states the quantum circuit is expected to need. For example, it could be determined that the circuit involves a logical CCZ gate which requires two T-states. In this context, a qubit can be determined to be idle if the qubit is idle for long enough to generate the two required T-states.

[0064] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the number of execution cycles required for operating the quantum state factory depends on hardware properties of a quantum hardware system for executing the quantum circuit. For example, when optical link losses drop below a particular threshold, the number of execution cycles required for generating a high-fidelity state (e.g., a Bell pair) may increase. The number of execution cycles required for operating the quantum state factory may also depend on a QEC code and / or physical locations of the qubits.

[0065] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the number of execution cycles required for operating the quantum state factory depends on a required fidelity of the quantum states generated by the quantum state factory. In general, if the required fidelity of the quantum states generated by the quantum state factory is higher, more rounds of distillation are required. The qubits will need to be idle for longer to be repurposed for generating high-fidelity quantum states.

[0066] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the step of implementing the quantum state factory within the sub-circuit of the quantum circuit comprises modifying the logical quantum circuit to implement an operation to transport the at least one quantum state generated by the quantum state factory to a further qubit. The quantum state prepared by the quantum state factories are usually needed at different locations. Therefore,transporting the at least one quantum state can bring the quantum state to the right location.

[0067] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one quantum state is transported by quantum teleportation. Teleportation of a quantum state from a source qubit to a target qubit causes the current state of the target qubit to be overwritten with the state of the source qubit.

[0068] According to the specification, the expression “teleportation” means that the state of the target qubit after transportation depends only on the state that was transported to it. This can also be referred to as teledata.

[0069] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one quantum state is transported by state insertion. According to the specification, the expression “state insertion” means that the state of the target qubit after transportation depends on the state of the target qubit prior to transportation and the state that was transported to it. This can also be referred to as telegate or gate teleportation because it causes a gate corresponding to the transported state to be applied to the target qubit.

[0070] Inserting a quantum state of a source qubit to a target qubit causes a gate corresponding to the quantum state to be applied to the target qubit. This means the resulting state of the target qubit depends on the states of the target qubit prior to injection and the injected state.

[0071] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the at least one idle and clean qubit is a physical qubit of a physical quantum circuit. For example, the physical quantum circuit can be a noisy intermediate-scale quantum (NISQ) circuit that does not implement error correction.

[0072] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the physical quantum circuit implements a logical quantum circuit. The physical quantum circuit can implement the logical quantum circuit according to a QEC code.

[0073] The at least one idle and clean qubit can also be a physical qubit of a virtual quantum circuit that implements the logical quantum circuit, i.e. , before the physical qubits are mapped to actual hardware physical qubits. For example, if the statefactory generates Bell pairs or GHZ states, the idle and clean qubit may be identified at the level of the virtual quantum circuit or physical quantum circuit. Physical operations are inserted that implement the state factory into the virtual quantum circuit or physical quantum circuit.

[0074] In some embodiments, the connectivity of the physical qubits can be taken into account. For example, swap operations with intermediate qubits can be included to perform two-qubit operations for the state factory between qubits that are not directly connected.

[0075] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, a cleaning operation is implemented in the quantum circuit for cleaning the at least one qubit after using the at least one qubit in the quantum state factory. In this way, the qubit will again be clean and can be used, e.g., for quantum computations or in another quantum state factory.

[0076] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum circuit is executed on at least one modular quantum hardware system having a plurality of quantum modules.

[0077] According to the specification, the term “modular quantum hardware system” relates to a quantum hardware system comprising a plurality of modules or sub-units which can be physically separate entities, e.g., arranged on different chips. The modules are interconnected. For example, inter-modular operations can be performed by entangling physical qubits on different modules, e.g., using photon-mediated entanglement.

[0078] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, all of the at least one idle and clean qubit that implement the quantum state factory are mapped to a same quantum module. Quantum computation can be distributed, with each modular quantum hardware system including multiple modules that may each have hundreds or thousands of physical qubits. Qubits may be assigned to modules at the logical level. That is, after a logical circuit is obtained, sub-circuits of the logical circuit can be assigned to different modules. Inter-modular communications can be a blocking factor for quantum circuit execution, and implementing a state factory on a single module can significantly reduce the number of inter-modular communications. In some embodiments, the typeof the quantum state factory that will be implemented can depend on this requirement together with a number of logical cycles that idle and clean qubits are available, as well as, optionally, on immediate resource requirements of the algorithm.

[0079] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the quantum state factory generates an entangled quantum state between a first source qubit and a second source qubit. Entanglement between the first source qubit and the second source qubit is transferred to entangle a first target qubit and a second target qubit. A communication cost between the first source qubit and the first target qubit is smaller than a communication cost between the first source qubit and the second source qubit. State transferring (e.g., teleportation or insertion) typically requires entanglement. State factories combined with state transferring is advantageous if the number of computing cycles for state transferring is smaller than the number of computing cycles for directly generating the state without a state factory. This may occur when the cost of remote entanglement is significantly higher than the cost of local entanglement. In some embodiments, there are inexpensive entanglement mechanisms which are only available for neighboring qubits (i.e. , directly located next to each other). In this case, the first source qubit and the first target qubit can be neighboring qubits and the second source qubit and the second target qubit can be neighboring qubits. The distance between the first source qubit and the second source qubit can be larger, i.e., they are not directly neighboring qubits. After generating entanglement between the first source qubit and the second source qubit, the (inexpensive) local entanglement mechanisms can be used for transferring the entanglement to the first target qubit and the second target qubit.

[0080] Herein, the communication cost can be expressed in terms of a physical distance, link quality, number of hops, entanglement rate and / or fidelity, and the like.

[0081] According to an embodiment of the method for implementing a quantum state factory in a quantum circuit, the first source qubit and the first target qubit are implemented on a first module of a modular quantum hardware system. The second source qubit and the second target qubit are implemented on a second module of the modular quantum hardware system. Accordingly, the first pair of the first source qubit and the first target qubit and the second pair of the second source qubit and the second target qubit can be located on different modules. Generally, it is hard to achieve high-fidelity entangled states needed for fault-tolerant quantum computation.This means that generating high-fidelity entanglement between qubits on different modules is expected to require entanglement purification. Herein, entanglement purification refers to a process of using multiple low-fidelity entangled states to produce a high-fidelity entangled state. Executing cross-module operations requires sharing multiple high-fidelity entanglement across modules. By transferring entanglement, such high-fidelity entanglement can be achieved.

[0082] Herein, the expression that a target qubit is “implemented on” a module for physical qubits denotes that the physical qubit is located in the module. For logical qubits it may denote that the qubit is physically implemented in the module, e.g., by a plurality of hardware physical qubits.

[0083] A second aspect of the disclosure provides a computer program product comprising executable program code configured to, when executed by a computing device, perform the method for implementing a quantum state factory in a quantum circuit according to the first aspect.

[0084] A third aspect of the disclosure provides a non-transitory, computer-readable storage medium comprising executable program code configured to, when executed by a computing device, perform the method for implementing a quantum state factory in a quantum circuit according to the first aspect.

[0085] A fourth aspect of the disclosure provides a device for implementing a quantum state factory in a quantum circuit. The device comprises at least one processor and at least one tangible computer-readable storage device communicatively coupled to the at least one processor and which stores processorexecutable instructions. When executed by the at least one processor, the processorexecutable instructions cause the at least one processor to determine, for at least one qubit, that the qubit is an idle and clean qubit within a sub-circuit of the quantum circuit. The qubit is an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit. The qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit. The processor assigns the at least one idle and clean qubit within the subcircuit of the quantum circuit to a quantum state factory for generating at least one quantum state. The processor implements the quantum state factory within the subcircuit of the quantum circuit.

[0086] A fifth aspect of the disclosure provides an information processing system for implementing a quantum state factory in a quantum circuit. The information processing system comprises a quantum hardware system, at least one processor and at least one tangible computer-readable storage device communicatively coupled to the at least one processor and which stores processor-executable instructions. When executed by the at least one processor, the processor-executable instructions cause the at least one processor to determine, for at least one qubit, that the qubit is an idle and clean qubit within a sub-circuit of the quantum circuit. The qubit is an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit. The qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit. The processor assigns the at least one idle and clean qubit within the sub-circuit of the quantum circuit to a quantum state factory for generating at least one quantum state. The processor implements the quantum state factory within the sub-circuit of the quantum circuit. The processor controls the quantum hardware system to run the quantum circuit.

[0087] The disclosure relates to all combinations of the above features, even if these are recited in different aspects or different claims. In particular, the device for implementing a quantum state factory in a quantum circuit may be configured to execute each or a combination of the described embodiments of the method for implementing a quantum state factory in a quantum circuit.Brief Description of the Drawings

[0088] In the following, further aspects and exemplary embodiments will be described with reference to the accompanying drawings. However, the present disclosure is not limited to the described exemplary embodiments and may be modified in various different ways. Consequently, the drawings and description are intended to be illustrative in nature and not limiting.Fig. 1 schematically shows a block diagram illustrating an information processing system according to an embodiment of the disclosure;Fig. 2 schematically shows logical quantum circuits to illustrate computation and uncomputation of a Toffoli gate;Fig. 3 schematically shows logical quantum circuits to illustrate the implementation of a Toffoli compute of a Toffoli computation- uncomputation pair;Fig. 4 schematically shows logical quantum circuits to illustrate the implementation of a Toffoli uncompute of a Toffoli computation- uncomputation pairFig. 5 schematically shows logical quantum circuits to illustrate another implementation of a Toffoli computation circuit;Fig. 6 schematically shows logical quantum circuits to illustrate the implementation of another Toffoli computation circuit;Fig. 7 schematically shows a logical quantum circuit illustrating state teleportation;Fig. 8 schematically shows two modules of a quantum hardware system; andFig. 9 shows a flow diagram illustrating a method for implementing a quantum state factory in a quantum circuit according to an embodiment of the disclosure.Detailed Description

[0089] Figure 1 schematically shows a block diagram illustrating an information processing system 100.

[0090] The information processing system 100 comprises a quantum hardware system 400 for performing quantum operations. The quantum hardware system 400 can optionally be a modular system and can comprise a plurality of interconnected chips or modules 401 . The quantum hardware system 400 comprises coupling devices 402 for coupling the modules 401 . The coupling devices 402 can comprise optical links or one or more optical networks to connect the modules 401 .

[0091] Whereas the quantum hardware system 400 in Figure 1 is a modular quantum hardware system, the specification is not restricted to this case. In other embodiments, the quantum hardware system 400 has only a single chip or module 401.

[0092] The quantum hardware system 400 is a physical device or machine which can be used to implement quantum algorithms (e.g., a quantum computer). The quantum hardware system 400 operates the multiple modules 401 when executing a quantum process and can perform “intra-modular” and “inter-modular” operations. The term “intra-modular operation” relates to operations (e.g., gates) between physical qubits of the same module 401 . The term “inter-modular operation” relates to operations (e.g., gates) between physical qubits of different modules 401 . In certain applications, it can be advantageous to link multiple modules 401 instead of building ever-larger monolithic quantum supercomputers (i.e., having only a single chip or module). Herein, the modules 401 are separate components and different modules 401 can be spatially separated.

[0093] The quantum hardware system 400 can be a non-locally connected quantum hardware system, as described in Simmons, “Scalable Fault-Tolerant Quantum Technologies with Silicon Colour Centres”, arXiv:2311 .04858, 2023, and in Afzal et al., “Distributed Quantum Computing in Silicon”, arXiv: 2406.01704, which are hereby incorporated by reference in their entirety.

[0094] The modules 401 may comprise a plurality of physical qubits having at least first and second quantum states that can be used to represent quantum information and which can exist in a quantum superposition.

[0095] Both the modules 401 and the coupling devices 402 comprise hardware components such as optical paths, optical links, optical networks, grating couplers, optical switches, Bell State Analyzers (BSAs) and / or detectors for facilitating optical connection between the physical qubits of the modules 401 . Accordingly, the coupling devices 402 may be configured to establish optical coupling between the modules 401 . In other embodiments, the modules 401 can be coupled non-optically. Similarly, inter-modular connections can be optical or non-optical. In some embodiments, there can be both optical and non-optical connections. Intra-module connections may comprise optical interconnects, microwave interconnects, physical ion transport, and the like. Inter-modular connections (i.e., the coupling devices 402) can comprise optical interconnects, microwave interconnects (with or without microwave to optical transduction), and the like.

[0096] Optical links can be used in connecting the physical qubits of the modules 401 with switches and detectors and can further connect switches and detectors to eachother. Similarly, the switches can be controlled to select specific optical links for connecting a physical qubit of the modules 401 to at least one other physical qubit of the modules 401 , either of the same module 401 or of another module 401 . In some embodiments, by controlling the hardware components in a suitable manner, any pair of physical qubits of the modules 401 may be connected to each other.

[0097] The detectors can be used in generating entanglement between the physical qubits of the modules 401 based on a photon detection pattern of photon states associated with said physical qubits of the modules 401 . The entanglement may be generated according to an entanglement protocol, such as the Barrett-Kok protocol.

[0098] The physical qubits of the modules 401 can be matter qubits or photonic qubits. Examples comprise luminescent defects, trapped ions, trapped atoms, neutral atoms, superconducting qubits, quantum dots, quantum wells, nuclear spins within dissolved molecules, trapped atoms coupled to high-finesse cavities, Bose-Einstein condensates, and the like.

[0099] The quantum hardware system 400 may comprise a photon interface (photonic interface). One possible example is a spin-photon interface. Spins generally have long coherence times, so information can be stored for long times. For example, the quantum hardware system 400 may comprise a semiconductor body with luminescent defects which form the physical qubits of the modules 401 . The semiconductor body may comprise silicon or similar semiconductor materials. For example, the semiconductor material may include natural silicon, silicon carbide, silicon germanium, isotopically purified paramagnetic silicon, a so-called silicon vacuum or combinations thereof. The semiconductor body may be processed to remove a large fraction of non-paramagnetic isotopes (e.g., silicon-29). The semiconductor body may comprise enriched or purified silicon that has been processed to remove some to nearly all non-zero-nuclear spin isotopes, such as silicon-29. Purified silicon includes material enriched to various levels of silicon-28, such as, 99%, 99.9%, and 99.99%. Purified silicon includes material enriched with silicon-28. Purified silicon includes silicon where spectroscopic linewidths are at least ten to hundred times sharper than in natural silicon. The semiconductor body may also comprise an epilayer of isotopically purified silicon, grown on top of a natural silicon wafer.

[0100] The luminescent defects may comprise luminescence centres or colour centres. The luminescent defects may comprise radiation damage centres. Theluminescent defects may comprise T centres, as described in any of US 2022 / 0366290 A1 , US 2022 / 0327416 A1 , and US 2024 / 0012749 A1 , which are hereby incorporated by reference in their entirety.

[0101] In embodiments where the physical qubits of the modules 401 are associated with T centres, pairs of T centres may be optically connected by means of a telecom photonic interface (i.e. , operating in the telecom frequency band, such as the telecom O-band) of the T centre in the silicon substrate. In some embodiments, each T centre can be optically connected to any other T centre, i.e., all-to-all optical connection between the T centres is possible. The optical connection between a pair of T centres may comprise at least one photonic waveguide integrated in the silicon substrate (“on-chip”). In addition or alternatively, the optical connection can also comprise optical fibres or other components which can be external to the silicon substrate (“off- chip”). In particular, the modules 401 can be arranged in different chips and the coupling devices 402 can comprise at least some off-chip hardware components for coupling physical qubits on different modules 401 .

[0102] The optical connection may be configured to facilitate entanglement between T centres. The entanglement can be generated and / or distributed by photons which are transmitted over the optical connections connecting the T centres. The quantum hardware system 400 can be configured to prepare maximally entangled Bell pairs, using the T centres.

[0103] The quantum hardware system 400 may further include means for generating and applying pulses for manipulating the state of physical qubits of the modules 401 . For example, the quantum hardware system 400 may include one or more antennas 403 for providing optical and / or microwave pulses for manipulating the state of physical qubits of the modules 401 .

[0104] The quantum hardware system 400 may be used for any practical application in quantum sensing, quantum computing or quantum communication.

[0105] Quantum sensing comprises measurements which utilize quantum effects such as entanglement, interference or quantum state squeezing.

[0106] Quantum computing comprises any processing of information based on quantum effects, such as superpositions of physical qubits of the modules 401 and (de-)coherence or entanglement of physical qubits of the modules 401 .

[0107] Quantum communication comprises the transmission of classical information or of quantum states between different devices, e.g., between the quantum hardware system 400 and another quantum hardware system based on quantum effects as described above.

[0108] Quantum circuits of the quantum hardware system 400 are designed for carrying out the necessary steps of a given quantum algorithm. Logical quantum circuits can be implemented by physical quantum circuits. Logical quantum circuits comprise a plurality of logical operators, such as gates.

[0109] In order to implement the logical quantum circuit, the logical qubits are implemented by (a generally larger number of) physical qubits of the quantum hardware system 400.

[0110] The physical operator implementation of a logical operator denotes a physical gate or more generally a sequence of physical gates that implement the logical operator. The physical gates are not necessarily already gates acting on hardware physical qubits of the quantum hardware system 400. Rather, the physical gates can act on “physical” (or virtual) qubits of a virtual circuit which is implemented on a physical circuit (i.e. , the quantum hardware system 400) at a subsequent stage.

[0111] The information processing system 100 further comprises a device 200 for implementing a quantum state factory. The device 200 for implementing a quantum state factory comprises at least one processor 203, and at least one memory 204 (i.e., a tangible computer-readable, or processor-readable storage device) communicatively coupled to the at least one processor 203.

[0112] The processor 203 can be a logic processing unit and can comprise a central processing unit (CPU), a graphics processing unit (GPU), a microcontroller (pC), an integrated circuit (IC), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), a program logic unit (PLU), a network processor (NP) or a combination thereof.

[0113] The memory 204 can comprise at least one of a magnetic hard disk, an optical disc (e.g., compact disc, digital video disc, Blu-ray disc), a solid state disc (SSD), a magneto-optical memory or a hard disc drive (HDD). For example, the memory 204 can comprise a volatile semiconductor or solid state memory, e.g., a random access memory (RAM), dynamic RAM (DRAM), or static RAM (SRAM). The memory 204 cancomprise a non-volatile semiconductor or solid state memory, e.g., a read only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), or the like.

[0114] The memory 204 stores processor-executable instructions and / or processor- readable data associated with the operation of the device 200 for implementing a quantum state factory. The processor-executable instructions and / or processor- readable data can comprise an operating system, peripheral drivers, server instructions, application instructions, calibration instructions, or communication channel instructions.

[0115] The device 200 for implementing a quantum state factory further comprises a user interface 205, having at least one of a display, a keyboard, a touch screen, a mouse, buttons, a microphone, loudspeakers and the like. A user may provide or receive information regarding the operation of the information processing system 100 via the user interface 205.

[0116] Although the user interface 205 is illustrated as a component of the device 200 for implementing a quantum state factory, the user interface 205 can also be an external device of the information processing system 100. For example, the device 200 for implementing a quantum state factory can be implemented as a remote server which a user can access via the user interface 205.

[0117] An interface 202 is provided for connecting the processor 203 with the quantum hardware system 400, a cooling device 500 and an actuator device 300. The interface 202 can be any port or link or interface capable of communicating information to another system, e.g., a wired connection or a wireless connection (e.g., wireless LAN, Bluetooth®, ethernet, or the like).

[0118] All of the components of the device 200 for implementing a quantum state factory described above can be controlled and / or can communicate over at least one bus 201 . The processor 203 may be configured to control the interface 202 and user interface 205 of the device 200 for implementing a quantum state factory.

[0119] The cooling device 500 may maintain the quantum hardware system 400 at a predefined operating temperature of the quantum hardware system 400. The operating temperature may be a cryogenic temperature, e.g., in a range from about 1 mK to 77 K, or more particularly in a range from about 1 .5 K to 4 K. In someembodiments, the cooling device 500 may be omitted. The quantum hardware system 400 may, optionally, also be kept at constant air pressure, e.g., a stable vacuum.

[0120] The actuator device 300 can comprise a plurality of actuators. For example, the actuator device 300 can comprise an electromagnet to apply a time-invariant electric field, a time-varying electric field, or a pulsed electric field to the quantum hardware system 400.

[0121] The processor 203 may obtain a specification (e.g., a description) of a quantum circuit and may determine whether the quantum circuit comprises idle and clean qubits within at least one sub-circuit of the quantum circuit. Herein, the quantum circuit can be a logical quantum circuit, a virtual quantum circuit or a physical quantum circuit. Accordingly, the qubits can be logical qubits or physical qubits.

[0122] The qubit is an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit.

[0123] The qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit.

[0124] For example, the processor 203 may determine that a qubit is a clean qubit if the qubit will not have been used in a quantum computation prior to the sub-circuit of the quantum circuit. If the qubit will have been used in a quantum computation prior to the sub-circuit of the quantum circuit, the qubit can still be determined to be a clean qubit if it will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit. This can be the case if the qubit is measured prior to the sub-circuit of the quantum circuit or if it is uncomputed prior to the sub-circuit of the quantum circuit.

[0125] The processor 203 may identify uncomputed qubits by determining whether the quantum circuit comprises an uncomputation sequence of quantum operations that follows a computation sequence of quantum operations acting on the qubit. The uncomputation sequence of quantum operations may correspond to an inverse of the computation sequence of quantum operations. The identification of such an uncomputation sequence may be based on a symmetry of the quantum circuit. Uncomputation may involve specific cleaning operations which can be identified by the processor 203.

[0126] The qubit may also be determined to be a clean qubit if it will have been used in a quantum computation prior to the sub-circuit of the quantum circuit but will not be used for computation in and after the sub-circuit of the quantum circuit. In such cases, the processor 203 may further modifying the quantum circuit to include a cleaning operation operating on the qubit before using the qubit in the quantum state factory to destroy potentially remaining unwanted information or entanglement. The cleaning operation may comprise a destructive measurement, e.g., using antennas 403 of the quantum hardware system 400, or an initialization of the qubit.

[0127] The processor 203 may further modify the quantum circuit to include a time delay to allow completing a factory cycle, i.e. , having qubits idle and clean for long enough to allow the quantum state factory to generate a state.

[0128] The processor 203 may also determine that a qubit is a clean qubit if the qubit is flagged as a clean qubit, e.g., in a specification of a logical quantum circuit.

[0129] In some embodiments, the processor 203 may determine that a qubit is an idle and clean qubit within a sub-circuit of a quantum circuit only if the sub-circuit of a quantum circuit has at least a predefined length (e.g., a predefined number of execution cycles) which is sufficiently long to implement the quantum state factory and / or to generate quantum states with some predefined required fidelity.

[0130] In some embodiments, the at least one qubit is a qubit that is physically implemented by at least one client-broker group. A client-broker group comprises a physical broker qubit and at least one physical client qubit. The at least one qubit is determined to be a clean qubit if at least one of the client qubits does not store information which is used within or after the sub-circuit of the quantum circuit.

[0131] In some embodiments, the qubit can be physically implemented in a module 401 using luminescence defects, such as T centres that include two carbon-12 atoms. An electron spin can be used as a physical broker qubit. An advantage is that the electron spin is optically addressable. A hydrogen nuclear spin can be used as a physical client qubit. This has the advantage that the hydrogen nuclear spin has a much longer coherence time than the electron spin.

[0132] In some embodiments, the qubit can be physically implemented in a module 401 using luminescence defects, such as T centres that include two carbon-13 atoms. Each T centre will be able to host four physical qubits: a free electron spin, ahydrogen nuclear spin and two carbon nuclear spins. One of the nuclear spins might not store information which is used in or after the sub-circuit of the quantum circuit. That nuclear spin can therefore be used as a physical qubit in the state factory. The other nuclear spins can be used for storing useful quantum information. In some embodiments, a nuclear spin can store the state generated by the state factory before it is transferred to another location.

[0133] The processor 203 assigns the at least one idle and clean qubit within the subcircuit of the quantum circuit to a quantum state factory for generating at least one quantum state. The processor 203 implements the quantum state factory within the sub-circuit of the quantum circuit. The implementation of the quantum state factory may include the modification of the logical quantum circuit to include an operation to transport the at least one quantum state generated by the quantum state factory to a further qubit, e.g., by quantum teleportation or state insertion.

[0134] The processor 203 may further include a cleaning operation in the quantum circuit for cleaning the at least one qubit after using the at least one qubit in the quantum state factory.

[0135] The processor 203 controls the quantum hardware system 400 to execute the quantum circuit on the quantum hardware system 400. Herein, all idle and clean qubits that implement the quantum state factory can be mapped to the same module 401 . In other embodiments, at least some qubits that implement the quantum state factory are implemented on different modules 401 .

[0136] In some embodiments, the quantum state factory generates an entangled quantum state between a first source qubit and a second source qubit. Entanglement between the first source qubit and the second source qubit is transferred to entangle a first target qubit and a second target qubit. A communication cost between the first source qubit and the first target qubit is smaller than a communication cost between the first source qubit and the second source qubit. For example, the first source qubit and the first target qubit are implemented on a first module of the modules 401 of the quantum hardware system 400. The second source qubit and the second target qubit are implemented on a second module of the modules 401 of the quantum hardware system 400. An example of this is described in more detail below in respect of Figure 8.

[0137] Figure 2 shows logical quantum circuits to illustrate computation and uncomputation of a Toffoli gate. The logical quantum circuits are equivalent. In the logical quantum circuit on the left-hand side of the equation, a first Toffoli gate is implemented on a first qubit, a second qubit and a third qubit corresponding to the first to third horizontal lines. Some arbitrary operations controlled by the third qubit are applied to at least one qubit, indicated by the three dots. A second Toffoli gate is then implemented on the first qubit, the second qubit and the third qubit. The implementation of the first Toffoli gate corresponds to the computation of the Toffoli gate and the implementation of the second Toffoli gate corresponds to a cleaning process by uncomputation.

[0138] The logical quantum circuit on the right-hand side of the equation shows the effect of the uncomputation. If the initial state of the third qubit is a zero state |0) in the computational basis, then the state of the third qubit after the uncomputation is again the zero state |0>.

[0139] The uncomputation circuit can be identified by determining that the quantum circuit has a symmetry because some quantum computation is framed by an initial Toffoli computation circuit and a final Toffoli uncomputation circuit.

[0140] Figure 3 shows logical quantum circuits to illustrate the implementation of a Toffoli computation circuit of a Toffoli pair. The Toffoli computation gate is schematically shown on the left-hand side and one specific way to implement it is shown on the right-hand side. The implementation comprises four T states in T-depth two, where the T-depth denotes a number of columns that at least have one T gate. The T-depth is a relevant quantity because the implementation of T gates takes generally much longer to apply in quantum circuits as compared to the implementation of Clifford gates.

[0141] More specifically, a third qubit is prepared in a T state, e.g., by state injection. A first CNOT gate operates on the first qubit and the third qubit, where the first qubit acts as control qubit. A second CNOT gate operates on the second qubit and the third qubit, where the second qubit acts as control qubit. A controlled-NOT-NOT gate (CXX gate) is applied to the first to third qubits, where the third qubit acts as control qubit. Adjoints of a T gate are applied to the first qubit and the second qubit, respectively. A T gate is applied to the third qubit. Another CXX gate is applied, where the third qubitacts as control qubit. A sequence of a Hadamard gate H and a S gate is applied to the third qubit.

[0142] Figure 4 shows logical quantum circuits to illustrate the implementation of a Toffoli uncomputation circuit. The Toffoli uncomputation gate is schematically shown on the left-hand side and a specific implementation is shown on the right-hand side. The implementation comprises a measurement gate and a conditional gate. The measurement gate acts on a third qubit and a conditional CZ gate is applied to the first qubit and the second qubit depending on the measurement result a of the measurement on the third qubit, where the first qubit acts as control qubit.

[0143] Figure 5 shows a Toffoli computation circuit using a CCZ state. The Toffoli computation gate is schematically shown on the left-hand side and a specific implementation is shown on the right-hand side. The specific implementation comprises first to fifth qubits. Third to fifth qubits are prepared in a CCZ state. A first CNOT gate is applied to the first qubit and the third qubit, where the first qubit is the control qubit. A second CNOT gate is applied to the second qubit and the fourth qubit, where the second qubit acts as control qubit. A Hadamard gate operates on the fifth qubit. A first measurement gate acts on the third qubit and a second measurement gate acts on the fourth qubit. A first conditional CX gate is applied to the second qubit and the fifth qubit depending on the measurement result a of the measurement on the third qubit, where the second qubit acts as control qubit. A second conditional CX gate is applied to the first qubit and the fifth qubit depending on the measurement result b of the measurement on the fourth qubit, where the first qubit acts as control qubit. A conditional X gate is applied to the fifth qubit depending on the product of the measurement result a of the measurement on the third qubit and the measurement result b of the measurement on the fourth qubit.

[0144] Figure 6 shows another Toffoli computation circuit using a CCZ state. A Toffoli computation gate is schematically shown on the left-hand side and a specific implementation is shown on the right-hand side. The specific implementation comprises first to sixth qubits. Fourth to sixth qubits are prepared in a CCZ state. The third qubit is prepared in a zero state 10>. A first CNOT gate is applied to the first qubit and the fourth qubit, where the first qubit is the control qubit. A second CNOT is applied to the second qubit and the fifth qubit, where the second qubit acts as control qubit. A Hadamard gate operates on the sixth qubit. A third CNOT gate is applied tothe third qubit and the sixth qubit, where the sixth qubit is the control qubit. A Hadamard gate operates on the sixth qubit. A first measurement gate acts on the fourth qubit, a second measurement gate acts on the fifth qubit, and a third measurement gate acts on the sixth qubit. A conditional Z gate is applied to the third qubit depending on the measurement result c of the measurement on the sixth qubit. A first conditional CX gate is applied to the second qubit and the third qubit depending on the measurement result a of the measurement on the fourth qubit, where the second qubit acts as control qubit. A second conditional CX gate is applied to the first qubit and the third qubit depending on the measurement result b of the measurement on the fifth qubit, where the first qubit acts as control qubit. A conditional X gate is applied to the third qubit depending on the product of the measurement result a of the measurement on the fourth qubit and the measurement result b of the measurement on the sixth qubit.

[0145] The specific circuits in Figures 3 to 6 are examples of circuits that can be stored in a database. If one of these circuits is found in the logical quantum circuit, a respective computation or uncomputation is identified.

[0146] Figure 7 shows a logical quantum circuit illustrating state teleportation. The logical quantum circuit comprises first to third qubits. The first qubit is in some state \i ) which is to be teleported to the third qubit. The second and third qubits are in the zero state 10>. A Hadamard gate operates on the third qubit. A first CNOT is applied to the second qubit and the third qubit, where the third qubit acts as control qubit. A second CNOT is applied to the first qubit and the second qubit, where the second qubit acts as control qubit. A Hadamard gate operates on the first qubit. A first measurement gate acts on the first qubit and a second measurement gate acts on the second qubit. A conditional X gate is applied to the third qubit depending on the measurement result b of the measurement on the second qubit. A conditional Z gate is applied to the third qubit depending on the measurement result a of the measurement on the first qubit.

[0147] Figure 8 schematically illustrates two different modules 801 , 901 of a quantum hardware system. A first module 801 comprises a first source qubit 802 and a first target qubit 803 and a second module 901 comprises a second source qubit 902 and a second target qubit 903.

[0148] A state factory is used to generate an entangled state by entangling the first source qubit 802 and the second source qubit 902. The state factory can first produce an entangled state of two local qubits on the same module, e.g., the first module 801 . The entangled state may initially have a low-fidelity. The entangled state may then be purified to obtain a high-fidelity entangled state. Alternatively, the fidelity of the entangled state may be sufficiently high such that purification is not required. The entangled state is distributed between two qubits located on different modules 801 , 901 , i.e. , the first source qubit 802 and the second source qubit 902. That entanglement is then transported to the first target qubit 803 and the second target qubit 903 via local operations which are computationally inexpensive.

[0149] That is, once high-fidelity entanglement is achieved between first source qubit 802 and second source qubit 902, only local operations between the first source qubit 802 and the first target qubit 803, as well as local operations between the second source qubit 902 and the second target qubit 903, are required to establish high- fidelity entanglement between the first target qubit 803 and the second target qubit 903.

[0150] The number of cycles required for intra-modular entanglement is lower than for inter-modular entanglement. Therefore, it is quicker to generate the inter-modular entanglement between the first source qubit 802 and the second source qubit 902 in advance, and then later generate the intra-modular entanglements required to transport the entangled state to the first target qubit 803 and the second target qubit 903.

[0151] Figure 9 shows a flow diagram illustrating a method for implementing a quantum state factory in a quantum circuit. The method can be carried out by a quantum information system, such as the information processing system 100 illustrated in Figure 1. In turn, the information processing system 100 of Figure 1 may be configured to carry out the following method.

[0152] In step S101 , a logical quantum circuit is determined. The logical quantum circuit can be predetermined or the logical quantum circuit can be obtained. In some embodiments, a user can submit the logical quantum circuit to a job handler of a Quantum as a Service (QaaS) platform. The logical quantum circuit, or a specification of the logical quantum circuit, can be provided in any computer-readable form, e.g., in Open Quantum Assembly Language (OpenQASM), in Q#, in Quantum IntermediateRepresentation (QI ), or in a graph-based format such as a directed acyclic graph (DAG) with metadata. The metadata can provide a mapping between logical quantum gates of the logical quantum circuit and corresponding nodes in the graph.

[0153] Alternatively, a selection of parameters of an algorithm can be obtained from a user. A logical quantum circuit may be built based on the algorithm with the selected parameters. For example, a user may upload a molecular structure, identify a molecular charge and spin, and submit a job to calculate the ground- or excited-states energies or molecular properties.

[0154] In addition, a QEC code for encoding logical qubits of the logical quantum circuit in physical qubits can be determined. A user may submit the QEC code. In some embodiments, the user may select between a plurality of predefined QEC codes.

[0155] In step S102, idle and clean qubits in the quantum logical circuit are determined. In some embodiments, it is checked for each qubit individually whether the qubit is both idle and clean. All qubits can be checked in parallel or in sequence. In some embodiments, all idle qubits are determined first and then the clean qubits are selected out of the idle qubits. In other embodiments it is the other way around, i.e. , all clean qubits are determined first and then the idle qubits are selected out of the clean qubits.

[0156] For a given qubit, it is determined that the qubit is an idle qubit within a subcircuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit.

[0157] The qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit. In some embodiments, if the qubit is a logical qubit, it can be sufficient that at least one physical qubit implementing the qubit does not store information which is used within or after the sub-circuit of the quantum circuit. In other embodiments, a logical qubit may only be considered clean if the logical qubit does not store information which is used within or after the sub-circuit of the quantum circuit.

[0158] Multiple criteria can be applied to determine whether the qubit is clean. For example, a qubit is clean within a sub-circuit of the quantum circuit if the qubit is notintended for use in a quantum computation prior to the sub-circuit of the quantum circuit.

[0159] If the qubit is intended for use in a quantum computation prior to the sub-circuit of the quantum circuit, the qubit can be determined to be a clean qubit if it will not store information for retrieval in a quantum computation within or after the sub-circuit of the quantum circuit. Criteria for this to be the case can be that the qubit is to be measured prior to the sub-circuit of the quantum circuit or that the qubit is to be uncomputed prior to the sub-circuit of the quantum circuit. For example, the last operation to be performed on the qubit prior to the sub-circuit may be a measurement or an uncomputation.

[0160] An uncomputation operation can be identified by searching for uncomputation sequences that are pre-stored in a data base or are identified based on a symmetry of the quantum circuit.

[0161] The qubit may also be determined to be a clean qubit if it is intended for use in a quantum computation prior to the sub-circuit of the quantum circuit but is not used for computation in and after the sub-circuit of the quantum circuit or if no other qubit entangled with the qubit is used for computation in and after the sub-circuit of the quantum circuit. The quantum circuit can be modified to include a cleaning operation operating on the qubit before using the qubit in the quantum state factory, e.g., a destructive measurement or an initialization of the qubit.

[0162] The qubit can also be flagged as a clean qubit, e.g., in a specification of the logical quantum circuit, such as a specification of the quantum circuit determined in step S101 .

[0163] In step S103, idle and clean qubits within the same sub-circuit are assigned to a quantum state factory for generating at least one quantum state. In some embodiments, it is determined whether there is a sufficient number of qubits which are both idle and clean at least within some sub-circuit of the quantum circuit to generate some state of a predetermined fidelity with the quantum state factory.

[0164] In some embodiments, the qubit is a qubit that is physically implemented by at least one client-broker group. A client-broker group comprises a physical broker qubit and at least one physical client qubit. The qubit is determined to be a clean qubit if atleast one of the client qubits does not store information which is used within or after the sub-circuit of the quantum circuit.

[0165] In step S104, the quantum state factory is implemented within the sub-circuit of the quantum circuit. Additional operations such as gates and measurements corresponding to the quantum state factory are inserted into the logical quantum circuit to generate quantum states and distill the quantum states to the desired fidelity.

[0166] The implementation can be predefined in a database or can be identified at compilation time by using an identifier algorithm (e.g., a machine-learning based algorithm) and can depend on the specific state. The state can be a magic state, a T state, a CCZ state, a Bell pair, a GHZ pair, a Toffoli state, a W state or the like. The logical quantum circuit can also be modified to implement an operation to transport the quantum state generated by the quantum state factory to a further qubit, e.g., by quantum teleportation or state insertion. Further, at least one cleaning operation can be implemented in the quantum circuit for cleaning the at least one qubit assigned to the quantum state factory after using the at least one qubit in the quantum state factory.

[0167] The quantum hardware system can be a modular quantum hardware system, as explained with reference to Figure 1 . In this case, all idle and clean qubits that implement the quantum state factory can be mapped to the same module of the modular quantum hardware system.

[0168] In some embodiments, the quantum state factory generates an entangled quantum state between a first source qubit and a second source qubit. The first source qubit and the second source qubit are entangled. Entanglement can be generated using any of various entanglement protocols, such as the Barrett-Kok protocol. For example, the physical qubits can be associated with T centres. The electron spins of two T centres can be prepared in a superposition of spin-up and spin-down states, and are triggered to emit a photon resonant with the spin-up transition. After interfering with a beam splitter, the photonic modes are detected. After inverting the spin states, emission and detection is repeated. A maximally- entangled Bell pair is obtained by using exactly one photon detection in each of the first and second optical cycles as a herald signal. If the physical qubits (e.g., associated with T centres) are arranged on different modules, inter-modularentanglement is achieved. The likelihood of success of entanglement depends on the optical path losses between modules, the emission probability (i.e., how likely a photon is to be emitted after excitation), and the excitation probability.

[0169] Entanglement between the first source qubit and the second source qubit is transferred to entangle a first target qubit and a second target qubit. A communication cost (e.g., a physical distance or link quality) between the first source qubit and the first target qubit is smaller than a communication cost between the first source qubit and the second source qubit. For example, the first source qubit and the first target qubit are implemented on a first module of a modular quantum hardware system, and the second source qubit and the second target qubit are implemented on a second module of the modular quantum hardware system.

[0170] In step S105, a virtual quantum circuit is provided, which comprises physical qubits and sequences of operations and measurements, based on the logical quantum circuit and the QEC code. Herein, the operations are based on the physical operator implementations of the logical gates of the logical quantum circuit. That is, the logical operations in the logical quantum circuit can be replaced with their respective physical implementations, in the determined QEC code.

[0171] For example, logical quantum state preparations, logical quantum gates, and logical circuit measurements in the logical quantum circuit are replaced by physical quantum state preparations, physical quantum gates, and physical circuit measurements. Moreover, stabilizer measurements are introduced that extract information about the locations of errors without disturbing the protected logical information.

[0172] In step S106, the logical quantum circuit is executed on the quantum hardware system, using the QEC code and the determined physical operator implementations. In order to implement the logical quantum circuit, the corresponding virtual quantum circuit is mapped to the hardware of the quantum hardware system. In particular, each physical qubit in the virtual quantum circuit is mapped to a corresponding hardware physical qubit in the quantum hardware system.

[0173] The virtual quantum circuit is thereby mapped to a physical quantum circuit executed on the quantum hardware system. The mapping may be based on hardware considerations, i.e., based on the characterization of the quantum hardware system.

[0174] The quantum hardware system compiles the physical quantum circuit to obtain an executable i.e., converts it into machine code that is readable by a controller of the quantum hardware system. The executable is then output to a controller of the quantum hardware system for execution.

[0175] In other embodiments, the idle and clean qubits are identified in the virtual quantum circuit or in the physical quantum circuit.

[0176] In some embodiments, the method is performed using the information processing system 100 of Figure 1 . Steps S101 to S105 may be performed by the device 200 for implementing a quantum state factory. More specifically, all computations may be performed by the processor 203. The processor 203 may also act as the controller of the quantum hardware system 400 and may control the quantum hardware system 400 to execute step S106. In other embodiments, the device 200 for implementing a quantum state factory can be an external device and the quantum hardware system 400 may come equipped with its own controller. The processor 203 may then provide the executable to the controller of the quantum hardware system 400.

[0177] More generally, steps S101 to S106 may be performed by a single device or at least some of the steps may be performed by different devices, e.g., in a distributed system. For example, steps S101 to S105 may be performed by an external device for implementing a quantum state factory (e.g., a remote server) and the execution of the logical quantum circuit in step S106 can be performed locally on the quantum hardware system 400.

[0178] In summary, the invention provides methods, devices and systems for implementing temporary quantum state factories in quantum circuits. Instead of statically assigning fixed qubits to the state factories, idle and clean qubits are identified and assigned to the state factory. Thus, the qubit reservoir can be used more efficiently.

[0179] The devices, apparatuses and systems described in the present disclosure may comprise electronic components and circuits known to those skilled in the art. Therefore, details of the circuitry and its components have not be explained in any greater extent than that considered necessary for the understanding and appreciation of the underlying concepts of the present disclosure.

[0180] Where reference is made to a component, such as a device, component, software module or the like, the reference to that component is intended to include as equivalents any component being functionally equivalent, i.e. , performing the same function, even though the component is not necessarily structurally equivalent to the component that performs in the exemplary embodiments.

[0181] In the above description, embodiments have been described with reference to specific details, e.g., parts of a method, components, materials, and the like. A person skilled in the art will understand that embodiments may be implemented without one or more of these specific details.

[0182] All of the US patents, US patent application publications, US patent applications, foreign patents, foreign patent applications, and non-patent publications referred to in this specification, or referred to on any application data sheet, are incorporated by reference in their entireties for all purposes herein.

[0183] A person skilled in the art may understand that certain method steps may be described or depicted in a particular order of occurrence while such specificity with respect to sequence is not actually required.

[0184] Phrases like “an embodiment” and “another embodiment” are used in the sense that particular features described in connection with the embodiment are included in at least one embodiment. Those phrases do not necessarily all refer to the same embodiment. Terms such as “first”, “second”, “third”, and so on, are used to distinguish between the elements described by these terms. These terms do not necessarily imply any temporal or other prioritization of such elements.

[0185] As used herein, the singular forms “a”, “one,” and “the “ are also intended to encompass the plural forms unless the context indicates otherwise. In addition, it is understood that the expressions “includes” and / or “including” when used in this specification relates to the presence of features, numbers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more features, numbers, steps, operations, elements and / or combinations thereof. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed elements.

[0186] Terms such as “horizontal”, “vertical”, “upper”, “lower”, “above”, “below”, “forward” and “backward” refer to particular orientations of components and / or eventsin time and / or space. The skilled person understands that may therefore depend on the specific orientation and may change if the components and / or events are oriented differently.

[0187] In this specification, the present disclosure has been described with reference to the accompanying drawings, in which exemplary embodiments are shown. However, the present disclosure is not limited to the described exemplary embodiments described and may be modified in various different ways.Consequently, the drawings and description are intended to be illustrative in nature and not limiting. Identical reference numbers denote identical elements in the specification.

[0188] As used herein, the terms “about,” “approximately,” or “substantially” refer to a value, amount, or property that is close to the specified value, amount, or property. The value, amount, or property is such that a desired function or result is still achieved. According to an example, an amount may be less than 10%, 5%, 1%, or 0.1% of the specified amount, respectively.

[0189] Even if the disclosure has been described and illustrated with reference to illustrative embodiments, various modifications may be made without departing from the scope of the present disclosure as defined in the claims. Such modifications may comprise replacement of features, components and / or method steps with equivalent features, components and / or method steps; mixing of features, components and / or method steps from different embodiments; and / or omitting or combining features, components and / or method steps from described embodiments. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.

Claims

WHAT IS CLAIMED IS:1 . A method for implementing a quantum state factory in a quantum circuit, the method comprising the steps of: determining, for at least one qubit, that the qubit is an idle and clean qubit within a sub-circuit of the quantum circuit, wherein the qubit is an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit, and wherein the qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit; assigning the at least one idle and clean qubit within the sub-circuit of the quantum circuit to a quantum state factory for generating at least one quantum state; and implementing the quantum state factory within the sub-circuit of the quantum circuit.

2. The method of claim 1 , wherein the quantum state factory is configured to generate a magic state.

3. The method of claim 2, wherein the magic state is a T state.

4. The method of claim 2, wherein the magic state is a double controlled phase,CCZ, state.

5. The method of claim 2, wherein the magic state is a Toffoli state.

6. The method of claim 1 , wherein the quantum state factory is configured to generate a Bell pair.

7. The method of claim 1 , wherein the quantum state factory is configured to generate a Greenberger-Horne-Zeilinger, GHZ, state.

8. The method of any of the preceding claims, wherein the step of implementing the quantum state factory within the sub-circuit of the quantum circuit depends on a number of idle and clean qubits assigned to the quantum state factory.

9. The method of any of the preceding claims, wherein the step of implementing the quantum state factory within the sub-circuit of the quantum circuit depends on a length of the sub-circuit of the quantum circuit.

10. The method of any of the preceding claims, wherein the at least one qubit is determined to be a clean qubit if the qubit will not have been used in a quantum computation prior to the sub-circuit of the quantum circuit.11 . The method of any of the preceding claims, wherein the at least one qubit is determined to be a clean qubit if the qubit will have been used in a quantum computation prior to the sub-circuit of the quantum circuit and will not store information which is retrieved in a quantum computation within or after the subcircuit of the quantum circuit.

12. The method of claim 11 , wherein the step of determining that the qubit will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit comprises: determining that the qubit will be measured prior to the sub-circuit of the quantum circuit.

13. The method of claim 11 or 12, wherein the step of determining that the qubit will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit comprises the step of: determining that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit.

14. The method of claim 13, wherein the step of determining that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit comprises the step of: identifying that an uncomputation sequence of quantum operations follows a computation sequence of quantum operations acting on the qubit, wherein the uncomputation sequence of quantum operations corresponds to an inverse of the computation sequence of quantum operations.

15. The method of claim 14, wherein the uncomputation sequence is identified by identifying a symmetry of the quantum circuit.

16. The method of any of claims 13 to 15, wherein determining that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit comprises the step of: determining whether the quantum circuit comprises a cleaning operation from a predefined set of cleaning operations, wherein the cleaning operation operates on the qubit prior to the sub-circuit of the quantum circuit.

17. The method of any of the preceding claims, wherein the at least one qubit is determined to be a clean qubit if the qubit will have been used in a quantum computation prior to the sub-circuit of the quantum circuit and will not be used for computation in and after the sub-circuit of the quantum circuit.

18. The method of claim 17, further comprising the step of modifying the quantum circuit to include a cleaning operation operating on the at least one qubit before using the at least one qubit in the quantum state factory.

19. The method of claim 18, wherein the cleaning operation operating on the at least one qubit comprises a destructive measurement on the at least one qubit or initializing the at least one qubit.

20. The method of any of the preceding claims, wherein the at least one qubit is determined to be a clean qubit if the qubit is a logical qubit in a logical quantum circuit and is flagged as a clean qubit.21 . The method of any of the preceding claims, wherein the at least one qubit is physically implemented by at least one client-broker group which comprises a physical broker qubit and at least one physical client qubit, wherein the at least one qubit is determined to be a clean qubit if at least one of the client qubits does not store information which is used within or after the sub-circuit of the quantum circuit.

22. The method of any of the preceding claims, wherein the determining that the qubit is an idle and clean qubit within a sub-circuit of a quantum circuit comprises determining that the qubit is an idle and clean qubit within a sub-circuit of a quantum circuit having a predefined length.

23. The method of claim 22, wherein the predefined length is determined by a predefined number of execution cycles.

24. The method of claim 23, wherein the predefined number of execution cycles depends on a number of execution cycles required for operating the quantum state factory.

25. The method of claim 24, wherein the number of execution cycles required for operating the quantum state factory depends on hardware properties of a quantum hardware system for executing the quantum circuit.

26. The method of claim 24 or 25, wherein the number of execution cycles required for operating the quantum state factory depends on a required fidelity of the quantum states generated by the quantum state factory.

27. The method of any of the preceding claims, wherein the quantum circuit comprises a logical quantum circuit, wherein the at least one idle and clean qubit is a logical qubit of the logical quantum circuit.

28. The method of claim 27, wherein the step of implementing the quantum state factory within the sub-circuit of the quantum circuit comprises the step of: modifying the logical quantum circuit to implement an operation to transport the at least one quantum state generated by the quantum state factory to a further qubit.

29. The method of claim 28, wherein the at least one quantum state is transported by quantum teleportation.

30. The method of claim 28, wherein the at least one quantum state is transported by state insertion.31 . The method of any of the preceding claims, wherein the at least one idle and clean qubit is a physical qubit of a physical quantum circuit.

32. The method of claim 31 , wherein the physical quantum circuit implements a logical quantum circuit.

33. The method of any of the preceding claims, further comprising the step of implementing a cleaning operation in the quantum circuit for cleaning the at least one qubit after using the at least one qubit in the quantum state factory.

34. The method of any of the preceding claims, wherein the quantum circuit is executed on at least one modular quantum hardware system having a plurality of quantum modules.

35. The method of claim 34, wherein all of the at least one idle and clean qubit that implement the quantum state factory are mapped to a same quantum module.

36. The method of any of the preceding claims, wherein the quantum state factory generates an entangled quantum state between a first source qubit and a second source qubit, wherein the method further comprises: transferring entanglement between the first source qubit and the second source qubit to entangle a first target qubit and a second target qubit, wherein a communication cost between the first source qubit and the first target qubit is smaller than a communication cost between the first source qubit and the second source qubit.

37. The method of claim 36, wherein the first source qubit and the first target qubit are implemented on a first module of a modular quantum hardware system, and wherein the second source qubit and the second target qubit are implemented on a second module of the modular quantum hardware system.

38. A computer program product comprising executable program code configured to, when executed by a computing device, perform the method for implementing a quantum state factory in a quantum circuit according to any of claims 1 to 37.

39. A non-transitory, computer-readable storage medium comprising executable program code configured to, when executed by a computing device, perform the method for implementing a quantum state factory in a quantum circuit according to any of claims 1 to 37.

40. A device for implementing a quantum state factory in a quantum circuit, comprising: at least one processor; and at least one tangible computer-readable storage device communicatively coupled to the at least one processor and which stores processor-executable instructions which, when executed by the at least one processor, cause the at least one processor to: determine, for at least one qubit, that the qubit is an idle and clean qubit within a sub-circuit of the quantum circuit, wherein the qubit is an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit, and wherein the qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit; assign the at least one idle and clean qubit within the sub-circuit of the quantum circuit to a quantum state factory for generating at least one quantum state; and implement the quantum state factory within the sub-circuit of the quantum circuit.41 . The device of claim 40, wherein the quantum state factory is configured to generate a magic state.

42. The device of claim 41 , wherein the magic state is a T state.

43. The device of claim 41 , wherein the magic state is a double controlled phase,CCZ, state.

44. The device of claim 41 , wherein the magic state is a Toffoli state.

45. The device of claim 40, wherein the quantum state factory is configured to generate a Bell pair.

46. The device of claim 40, wherein the quantum state factory is configured to generate a Greenberger-Horne-Zeilinger, GHZ, state.

47. The device of any of claims 40 to 46, wherein the processor is configured to implement the quantum state factory within the sub-circuit of the quantum circuit depending on a number of idle and clean qubits assigned to the quantum state factory.

48. The device of any of claims 40 to 47, wherein the processor is configured to implement the quantum state factory within the sub-circuit of the quantum circuit depending on a length of the sub-circuit of the quantum circuit.

49. The device of any of the claims 40 to 48, wherein the processor is configured to determine that the at least one qubit is a clean qubit if the qubit will not have been used in a quantum computation prior to the sub-circuit of the quantum circuit.

50. The device of any of the claims 40 to 49, wherein the processor is configured to determine that the at least one qubit is a clean qubit if the qubit will have been used in a quantum computation prior to the sub-circuit of the quantum circuit and will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit.51 . The device of claim 50, wherein the processor is configured to determine that the qubit will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit by: determining that the qubit will be measured prior to the sub-circuit of the quantum circuit.

52. The device of claim 50 or 51 , wherein the processor is configured to determine that the qubit will not store information which is retrieved in a quantum computation within or after the sub-circuit of the quantum circuit by: determining that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit.

53. The device of claim 52, wherein the processor is configured to determine that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit by: identifying that an uncomputation sequence of quantum operations follows a computation sequence of quantum operations acting on the qubit, wherein the uncomputation sequence of quantum operations corresponds to an inverse of the computation sequence of quantum operations.

54. The device of claim 53, wherein the processor is configured to identify the uncomputation sequence by identifying a symmetry of the quantum circuit.

55. The device of any of claims 52 to 54, wherein the processor is configured to determine that the qubit will be uncomputed prior to the sub-circuit of the quantum circuit by: determining whether the quantum circuit comprises a cleaning operation from a predefined set of cleaning operations, wherein the cleaning operation operates on the qubit prior to the sub-circuit of the quantum circuit.

56. The device of any of claims 40 to 55, wherein the processor is configured to determine that the at least one qubit is a clean qubit if the qubit will have been used in a quantum computation prior to the sub-circuit of the quantum circuit and will not be used for computation in and after the sub-circuit of the quantum circuit.

57. The device of claim 56, wherein the processor is further configured to modify the quantum circuit to include a cleaning operation operating on the at least one qubit before using the at least one qubit in the quantum state factory.

58. The device of claim 57, wherein the cleaning operation operating on the at least one qubit comprises performing a destructive measurement on the at least one qubit or initializing the at least one qubit.

59. The device of any of claims 40 to 58, wherein the processor is configured to determine that the at least one qubit is a clean qubit if the qubit is a logical qubit in a logical quantum circuit and is flagged as a clean qubit.

60. The device of any of claims 40 to 59, wherein the at least one qubit is physically implemented by at least one client-broker group which comprises a physical broker qubit and at least one physical client qubit, wherein the processor is configured to determine that the at least one qubit is a clean qubit if at least one of the client qubits does not store information which is used within or after the sub-circuit of the quantum circuit.61 . The device of any of claims 40 to 60, wherein the processor is configured to determine that the qubit is an idle and clean qubit within a sub-circuit of a quantum circuit within a sub-circuit of a quantum circuit having a predefined length.

62. The device of claim 61 , wherein the predefined length is determined by a predefined number of execution cycles.

63. The device of claim 62, wherein the predefined number of execution cycles depends on a number of execution cycles required for operating the quantum state factory.

64. The device of claim 63, wherein the number of execution cycles required for operating the quantum state factory depends on hardware properties of a quantum hardware system for executing the quantum circuit.

65. The device of claim 63 or 64, wherein the number of execution cycles required for operating the quantum state factory depends on a required fidelity of the quantum states generated by the quantum state factory.

66. The device of any of claims 40 to 65, wherein the quantum circuit comprises a logical quantum circuit, wherein the at least one idle and clean qubit is a logical qubit of the logical quantum circuit.

67. The device of claim 66, wherein the processor is configured to implement the quantum state factory within the sub-circuit of the quantum circuit by: modifying the logical quantum circuit to implement an operation to transport the at least one quantum state generated by the quantum state factory to a further qubit.

68. The device of claim 67, wherein the processor is configured to implement that the at least one quantum state is transported by quantum teleportation.

69. The device of claim 67, wherein the processor is configured to implement that the at least one quantum state is transported by state insertion.

70. The device of any of claims 40 to 69, wherein the at least one idle and clean qubit is a physical qubit of a physical quantum circuit.71 . The device of claim 70, wherein the physical quantum circuit implements a logical quantum circuit.

72. The device of any of the claims 40 to 71 , wherein the processor is further configured to implement a cleaning operation in the quantum circuit for cleaning the at least one qubit after using the at least one qubit in the quantum state factory.

73. The device of any of the claims 40 to 72, wherein the processor is configured to control at least one modular quantum hardware system having a plurality of quantum modules to execute the quantum circuit.

74. The device of claim 73, wherein the processor is configured to map all of the at least one idle and clean qubit that implement the quantum state factory to a same quantum module.

75. The device of any of claims 40 to 74, wherein the quantum state factory is configured to generate an entangled quantum state between a first source qubit and a second source qubit, wherein the processor is further configured to: transfer entanglement between the first source qubit and the second source qubit to entangle a first target qubit and a second target qubit, wherein a communication cost between the first source qubit and the first target qubit is smaller than a communication cost between the first source qubit and the second source qubit.

76. The device of claim 75, wherein the processor is configured to implement the first source qubit and the first target qubit on a first module of a modular quantum hardware system, and to implement the second source qubit and the second target qubit on a second module of the modular quantum hardware system.

77. An information processing system comprising: a quantum hardware system; at least one processor communicatively coupled to the quantum hardware system; and at least one tangible computer-readable storage device communicatively coupled to the at least one processor and which stores processor-executable instructions which, when executed by the at least one processor, cause the at least one processor to: determine, for at least one qubit, that the qubit is an idle and clean qubit within a sub-circuit of the quantum circuit, wherein the qubit is an idle qubit within the sub-circuit of the quantum circuit if no quantum operation operates within the sub-circuit of the quantum circuit on the qubit, and wherein the qubit is a clean qubit within the sub-circuit of the quantum circuit if the qubit does not store information which is used within or after the sub-circuit of the quantum circuit; assign the at least one idle and clean qubit within the sub-circuit of the quantum circuit to a quantum state factory for generating at least one quantum state;implement the quantum state factory within the sub-circuit of the quantum circuit; and control the quantum hardware system to run the quantum circuit.

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