Quantum-enabled server adapted for delegated quantum blind computing

Abstract

A quantum-enabled server adapted for delegated quantum blind computing, the quantum-enabled server comprising quantum storage means configured to store quantum states; quantum computing means comprising quantum state transformation and measurement hardware; a non-quantum hardware enclave configured to generate instructions for quantum state transformation and measurement and cause the instructions to be transmitted to the quantum computing means, wherein the quantum computing means are configured to generate measurement results by operating on one or more quantum states stored in the quantum storage means in accordance with the instructions and to provide measurement results to the non-quantum hardware enclave in response to the instructions, wherein the non-quantum hardware enclave is configured to execute a feedforward function for determining next instructions for quantum state transformation and measurement on the basis of the received measurement results and cause the next instructions to be transmitted to the quantum computing means.

Description

QUANTUM-ENABLED SERVER ADAPTED FOR DELEGATED QUANTUM BLIND COMPUTINGTECHNICAL FIELD

[0001] Various example embodiments relate generally to a quantum-enabled server adapted for delegated quantum blind computing, a system including such quantum-enabled server and a corresponding method.BACKGROUND

[0002] Quantum computers allow to efficiently solve computational tasks that are believed to be hard to solve by means of a classical computer, whereas the quantum internet allows to establish quantum communication over arbitrarily complex networks and far nodes. An element for the physical implementation of many quantum algorithms is a large-dimensional quantum system composed of highly interacting qubits as for instance a cluster state.

[0003] An important feature required by many quantum protocols, e.g. measurement-based quantum computing and quantum teleportation, is the feedforward adaptivity of quantum measurements, namely the ability to act over one reduced size subsystem of a given quantum system, that is, a subset of the qubit states of the overall quantum state according to the outcome of a quantum measurement performed on another subsystem, that is, another subset of the qubit states of the overall state. The signal analysis required by these tasks may be achieved by means of classical electronics and necessarily has to take into account the typical coherence times of the considered quantum platform, i.e. the time interval in which a system can maintain the quality of the prepared quantum states before being degraded by the interaction with the environment.

[0004] In some configurations, the computation is driven by a CPU in the server which provides to the client the measurement results after each qubit measurement. Thus, there is a round of communication between the CPU and the client. Here the latency comes from the classical communication between the client and the server. This communication occurs over a standard classical network. Each measurement requires a round of communication to compute next instructions by a feedforward function. This may take up to a few milliseconds, which requires the server to store the qubits coherently for that amount of time.

[0005] This generally represents a major issue, since typical coherence times may be significantly shorter than the time required for the transmission and readout of digital signals.SUMMARY

[0006] The scope of protection is set out by the independent claims. The embodiments, examples and features, if any, described in this specification that do not fall under the scope of the protection are to be interpreted as examples useful for understanding the various embodiments or examples that fall under the scope of protection.

[0007] In the context of the present description, the terms ”non-quantum” or “classical” are used interchangeably.

[0008] According to a first aspect, a quantum-enabled server adapted for delegated quantum blind computing is disclosed. The quantum-enabled server comprises: quantum storage means configured to store quantum states; quantum computing means comprising quantum state transformation and measurement hardware; a classical hardware enclave configured to generate instructions for quantum state transformation and measurement and cause the instructions to be transmitted to the quantum computing means, wherein the quantum computing means are configured to generate measurement results by operating on one or more quantum states stored in the quantum storage means in accordance with the instructions and to provide measurement results to the classical hardware enclave in response to the instructions; wherein the classical hardware enclave is configured to execute a feedforward function for determining next instructions for quantum state transformation and measurement on the basis of the received measurement results and cause the next instructions to be transmitted to the quantum computing means.

[0009] The quantum-enabled server may be adapted for delegated quantum blind of a sequence of logical operations. In embodiments, the feedforward function may be configured to control an execution of a sequence of quantum operations corresponding to the sequence of logical operations by determining the next instructions for quantum state transformation and measurement on the basis of the received measurement results.

[0010] The classical hardware enclave may be configured to receive, from the client, via a classical (i.e., non-quantum) communication channel, feedforward configuration data for configuring the feedforward function.

[0011] The quantum-enabled server may comprise an electronic driving interface for driving the quantum computing means and a processor configured to control the electronic driving interface, wherein to cause the instructions to be transmitted to the quantum computing means, the classical hardware enclave is configured to transmit the instructions to the processor. The processor may be configured to cause the instructions to be transmitted to the quantum computing means via the electronic driving interface.

[0012] The classical hardware enclave may include a driving circuitry, wherein to cause the instructions to be transmitted to the quantum computing means, the classical hardware enclave is configured to transmit the instructions to the quantum computingmeans via the driving circuitry; wherein the driving circuitry unit is configured to cause the instructions to be transmitted the quantum computing means. The driving circuitry may be a FPGA coupled with a trusted execution environment of the classical hardware enclave.

[0013] The quantum computing means may be configured to cause the measurement results to be transmitted to the classical hardware enclave via the driving circuitry.

[0014] The quantum-enabled server may comprise an electronic driving interface adapted for driving the quantum computing means and a processor configured to control the electronic driving interface, wherein the quantum computing means are configured to cause the measurement results to be transmitted to the classical hardware enclave via the electronic driving interface.

[0015] The classical hardware enclave may be secured by a trusted execution environment adapted to run software code configured to execute the feedforward function to generate the instructions.

[0016] The classical hardware enclave may comprise a digital-to-analogue converter for converting the instructions into one or more analogue control signals carrying the instructions and adapted to be transmitted to the quantum computing means by the driving circuitry directly or via the electronic driving interface.

[0017] The quantum states may be quantum states transformed by a client from quantum states generated by a quantum source.

[0018] According to a second aspect, a method for operating a quantum-enabled server adapted for delegated quantum blind computing is disclosed. The method comprises: generating, by a classical hardware enclave of the quantum-enabled server, instructions for quantum state transformation and measurement; causing, by the classical hardware enclave, transmission of the instructions to quantum computing means of the quantum- enabled server via electronic driving interface; generating, by the quantum computing means, measurement results by operating on quantum states stored in quantum storage means of the quantum-enabled server in accordance with the instructions; receiving, by the classical hardware enclave, the measurement results; executing, by the classical hardware enclave, a feedforward function for determining next instructions for quantum state transformation and measurement on the basis of the received measurement results; causing, by the classical hardware enclave, the next instructions to be transmitted to the quantum computing means.

[0019] The method may be adapted for delegated quantum blind of a sequence of logical operations. In embodiments, the feedforward function may be configured to control an execution of a sequence of quantum operations corresponding to the sequence of logicaloperations by determining the next instructions for quantum state transformation and measurement on the basis of the received measurement results.

[0020] The method may comprise: receiving from a client, via a classical communication channel, feedforward configuration data for configuring the feedforward function and configuring, by the classical hardware enclave the feedforward function based on the received feedforward configuration data.BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Example embodiments will become more fully understood from the detailed description given herein below and the accompanying drawings, which are given by way of illustration only and thus are not limiting of this disclosure.

[0022] FIG. 1 is a block diagram of an architecture of a quantum computing system according to an example.

[0023] FIG. 2 is a block diagram of an architecture of a quantum computing system according to an example.

[0024] FIG. 3 is a block diagram of an architecture of a quantum computing system according to an example.

[0025] FIG. 4 is a flow diagram illustrating schematically a protocol for delegating quantum computation by two clients to a server according to an example.

[0026] FIG. 5 is a flowchart illustrating a method for operating a quantum-enabled server adapted for delegated quantum blind computing according to an example.

[0027] It should be noted that these drawings are intended to illustrate various aspects of devices, methods and structures used in example embodiments described herein. The use of similar or identical reference numbers in the various drawings is intended to indicate the presence of a similar or identical element or feature.DETAILED DESCRIPTION

[0028] Detailed example embodiments are disclosed herein. However, specific structural and / or functional details disclosed herein are merely representative for purposes of describing example embodiments and providing a clear understanding of the underlying principles. However, these example embodiments may be practiced without these specific details. These example embodiments may be embodied in many alternate forms, with various modifications, and should not be construed as limited to only the embodiments set forth herein. In addition, the figures and descriptions may have been simplified to illustrate elements and I or aspects that are relevant for a clear understanding of the present invention, while eliminating, for purposes of clarity, many other elements that may be well known in the art or not relevant for the understanding of the invention.

[0029] A quantum computing system including a client and quantum-enabled server adapted for delegated quantum blind computing and a method for operating a quantum- enabled server adapted for delegated quantum blind computing are disclosed.

[0030] In embodiments, a non-quantum (i.e. classical) hardware enclave is configured to generate instructions for quantum state transformation and measurement, cause the instructions to be transmitted to a quantum computing means in the quantum- enabled server. Quantum state transformations mean those changes that a quantum state can incur in time due to time evolution as well as the application of any unitary operation. Quantum state measurements mean those operations performed on the quantum state, or on a subsystem as defined above, after which the state is manipulated, and the operation provides a numerical outcome. The classical hardware secure enclave is further configured to receive measurement results in response to the transmission of the instructions, execute a feedforward function for determining next instructions for quantum state transformation and measurement based on the received measurement results, and cause the next instructions to be transmitted to the quantum computing means.

[0031] In quantum computing, a sequence of logical operations defining a quantum algorithm can be converted into a sequence of quantum operations (e.g., quantum state transformation followed by a state measurement) to be performed by quantum computing means. Each quantum operation in the sequence is determined in dependence on the result of the previous quantum operation in the sequence, as a function of the logic underlying the quantum algorithm. For example, a measurement of the state of a qubit is performed, (the qubit collapses into a classical bit, e.g., 0 or 1 ). Depending on the measurement outcome and the logic of the algorithm, a quantum operation may be performed on another qubit.

[0032] In this context, the feedforward function (sometimes referred to as the feedforward operation) refers to a control function used to determine, in an iterative manner, quantum operation by quantum operation, the sequence of quantum operations to be performed for blind computing of the sequence of logical operations. The feedforward function is configured to use the result of a quantum measurement to determine a subsequent quantum operation to be performed on another qubit or quantum system by quantum computing means in order to implement the algorithm. The temporal sequence of quantum operations is typically performed in real time.

[0033] In sum, the feedforward function in quantum computing is a classical conditional function, determined based on the temporal sequence of logical operations defining an algorithm, that determines which quantum operation to perform, based on a prior measurement outcome. The feedforward function corresponds to the algorithm to be implemented and bridges the quantum and classical worlds: quantum states are measured,producing classical data, and then classical logic (i.e. the feedforward function) is used to trigger further quantum operations.

[0034] The feedforward function uniquely defines the quantum computation. In particular, a client can fully hide a computation to a remote quantum server if the client (i) starts by sending random single-qubit quantum sates and (ii) keeps the feedforward functions secret and computes the feedforward based on the outcomes communicated by the server. This is known in the literature as blind quantum computing.

[0035] According to the present disclosure, the feedforward function is kept secret by being executed in a trusted execution environment on server side, not on client side. The feedforward function is configured to determine next instructions for quantum state transformation and measurement on the basis of the received measurement results. The hardware enclave (the feedforward function itself or another function executed in the hardware enclave) may further cause the next instructions to be transmitted to the quantum computing means for execution of the next instructions.

[0036] A classical (i.e., non-quantum) hardware enclave is thus used for implementing a feedforward function in a feedback loop with a quantum computing means for the control and readout of a quantum computing architecture. The generation of the next instructions for quantum state transformation and measurement regulating the feedback mechanism happens in the classical hardware enclave where the information is secured and at all times kept isolated from any unauthorized entity.

[0037] Thanks to the feedback mechanism implemented locally in the hardware enclave, the response time of the feedback loop can be reduced and optimized. The response time of the feedback loop can be less than the coherence time of the quantum computing means. Further the embedding of the feedforward function in the classical hardware secure enclave provides full security of the feedforward configuration data used for configuring the feedforward function.

[0038] The quantum-enabled server allows classical secure and low-latency feedforward control of the quantum computing means, thanks to the presence of a classical (i.e., non-quantum) hardware enclave, where all data are kept isolated and inaccessible by unauthorized users, and of electronic driving interface allowing real-time control of the quantum computing means. The quantum-enabled server provides trustworthiness, by avoiding any private information leakage, and low-latency feedforward control with a fast response time.

[0039] This architecture can be applied to any quantum computing means and for the implementation of single-party or multi-party delegated quantum computing protocols as will be described in detail below. An example of such protocols is the universal blindquantum computing (UBQC) involving a client and a server including quantum computing means.

[0040] Quantum computation implies transformations on quantum bits or “qubits”. Each qubit represents a unit of quantum information. A qubit may be defined as a two-states (or two-levels) quantum-mechanical system. The quantum state of a qubit may be represented by a linear superposition of its two orthonormal basis states.

[0041] Qubits may be physically implemented by various physical supports including photons, coherent state of light, electrons, nucleus, optical lattices, Josephson junctions for superconducting qubits, etc. A non-exhaustive list may be found, for instance, on Wikipedia: https : / / en.wikipedia.orq / wiki / Qubit.

[0042] In practice, quantum states of qubits can be encoded by using degrees of freedom of the physical support. Degrees of freedom correspond to a physical property of physical systems, which can be described by quantum mechanics. Accordingly, degrees of freedom depend on the physical support and may comprise: phase, phase differences, frequency, polarization, time, localization of photons. Also, spins of electrons, superconducting charge, electron number, etc. may also be used.

[0043] Quantum storage means may be any quantum storage hardware adapted for storing quantum states by means of qubits. Quantum storage means can be implemented with fiber loops, optical cavities, diamond resonators, solid-state quantum memories, etc. The quantum states may for example be stored to build a brickwork state.

[0044] Quantum computing means may be any quantum computing hardware adapted for transformation and measurement of quantum states. Quantum computing means may be implemented, for example, with photonic integrated or bulk circuits, superconducting materials, trapped ions, cold atoms etc.

[0045] The non-quantum hardware enclave is a non-quantum secured hardware enclave, for example secured by a Trusted Execution Environment (TEE). Examples of non- quantum hardware enclaves are the Intel ® SGX (Software Guard Extensions) technology and TrustZone ® from ARM ®.

[0046] A Trusted Execution Environment (TEE) may be defined as a segregated area of a hardware device protected from the rest of the device, for example using encryption, such that any data in the TEE cannot be read or tampered with by any data (e.g., code) outside that environment. A TEE is a secure area of a processor that ensures code and data loaded inside the TEE are protected with respect to confidentiality and integrity. Data can be processed inside the TEE by suitably authorized code. Thus, a TEE is a secure environment for executing software code providing high levels of trust because the TEE can ignore threats from the “unknown” rest of the device. Generally, the rest of thedevice may host a Rich OS (Rich Operating System) and is generically known in this context as the REE (Rich Operating System Execution Environment).

[0047] Embodiments of quantum computing systems including a client 110, a quantum state source 115 and quantum-enabled server 120 (hereafter, the server 120) adapted for delegated quantum blind computing are described by reference to FIGS. 1 to 3.

[0048] In these embodiments, the client 110 may include or be a computer (e.g., a classical computer). In embodiments, the client 110 includes quantum means for operating on quantum states, for example for measuring (e.g., a detector) and / or transforming (e.g., a modulator) quantum states.

[0049] The quantum state source 115 is configured to generate initial quantum states. In embodiments, the initial quantum states are transformed by the client before being sent to the server 120. The server 120 is configured to store the received quantum states in quantum storage means (e.g., a quantum memory) not shown.

[0050] There are several options for preparing the quantum states stored by the server. For example: the client has a source of quantum states, on which the client applies measurements and / or transformations before sending the transformed quantum states to the server; or the server has a source of quantum states, the initial quantum states from the source are sent to the client, which applies measurements and / or transformations on the received quantum states, then the client transmits the transformed quantum states to the server; or a third party has a source of quantum states, the initial quantum states are sent to the client, which applies transformations on the received quantum states, and then the client transmits the transformed quantum states to the server.

[0051] As examples, the following typical implementations may be used:Single photon source 115 connected to a quantum-enabled server 120 implemented as photonic quantum computer, orSingle photon source 115 connected to a quantum-enabled server 120 implemented as superconducting quantum computer through a frequency conversion device, orA single photon detector located in the client and configured to read the quantum states of photons and is connected to an ion trap quantum computer, located in the server and which emits photons entangled with its own quantum storage system.

[0052] The server 120 includes a non-quantum hardware enclave 121 (e.g.,secured by a TEE), quantum storage means and quantum computing means 150. In embodiments, the server 120 may further include a processor 130 (e.g., CPU) and an electronic driving interface 135 for driving the quantum computing means 150. The nonquantum hardware enclave 121 , the processor 130 (e.g., CPU) and the electronic driving interface 135 may be part of a computer (e.g., a classical computer).

[0053] The processor 130 is configured to drive the quantum storage means and quantum computing means 150 through the electronic driving interface 135. The processor 130 may for example configure the quantum storage means and quantum computing means 150 in an initialisation step. For example, the processor 130 could turn on the laser driving a single photon source in an optical quantum computing system, or generate through the electronic driving interface 135 the magnetic field configured to trap ions in an Ion trap system.

[0054] In embodiments, the non-quantum hardware enclave 121 (e.g., a TEE) may include a driving circuitry 122 adapted for driving the quantum computing means 150. The driving circuitry 122 may be adapted for driving the quantum computing means 150 with or without using the electronic driving interface 135, but without the processor 130 (e.g., CPU). The hardware enclave is a secure, isolated area of a processor that protects the confidentiality and integrity of the data and code it handles. The non-quantum hardware enclave 121 or the TEE may be configured with program instructions to implement the functions (e.g., the feedforward function) defined herein for the non-quantum hardware enclave 121 or the TEE.

[0055] The server 120 is configured to operate on the stored quantum states in accordance with instructions, for example by applying measurements and / or transformation to the stored quantum states in accordance with the instructions. For example, the processor 130 may modulate the state of photons an optical quantum computing system, or generate through the electronic driving interface 135 laser pulses configures to change the quantum state of trapped ions. The server 120 is configured to perform measurement on the quantum states according to a measurement basis that can be defined by the instructions.

[0056] A non-quantum hardware enclave 121 is configured to execute a feedforward function for generating instructions for quantum state transformation and measurement. Based on the output of the feedforward function, the non-quantum hardware enclave 121 generates the instructions for quantum state transformation and measurement. The instructions (e.g., including a measurement basis) for quantum state transformation and measurement may be encoded in a digital or analogue signal to be transmitted to the quantum computing means 150.

[0057] In embodiments, the feedforward function may be configured to, based on given measurement results performed on quantum states stored in the server 120, computes instructions indicating the measurement basis for next measurements to be performed on the qubits stored in the server 120. The feedforward function may be configured to generate the instructions for the (n+1 )-th measurement knowing the results of the n first measurements. The feedforward function may be generated according to the standard description of Verifiable Blind Quantum Computing [Ref3].

[0058] Prior to the execution of the protocol, the client 110 establishes a connection with the non-quantum hardware enclave 121 (e.g., a TEE) and uploads there a feedforward function and / or feedforward configuration data for configuring the feedforward function. The client 110 is configured to send, via a classical (i.e. non-quantum) channel, the feedforward configuration data for configuring the feedforward function. Thereby the client 110 drives remotely the computation performed by the server 120, while the server 120 remains blind.

[0059] The non-quantum hardware enclave 121 causes the instructions for quantum state transformation and measurement to be transmitted to the quantum computing means 150 of the server 120: the non-quantum hardware enclave 121 initiates the transmission of the instructions which may then be transmitted successively by one or more components until the instructions are received and executed by the quantum computing means 150.

[0060] The server 120 may include electronic driving interface 135 configured to cause the quantum computing means 150 to perform the requested transformations and measurements. The electronic driving interface 135 may send signals that cause the quantum computing means 150 to be prepared in a given state useful for the computation and / or to perform measurements on the quantum hardware. The electronic driving interface 135 may be implemented by exploiting different platforms, e.g. electro-optical modulators, high-voltage pulses, arbitrary waveform generators, etc. The electronic driving interface 135 may be used under the control of a processor 130 of the server 120.

[0061] In the embodiment of FIG. 1 (embodiment #1), the instructions for quantum state transformation and measurement may be sent by the non-quantum hardware enclave 121 , through the processor 130 (e.g., CPU) and the electronic driving interface 135 of the quantum computing means 150. The measurement results may be transmitted following the same path in inverse: through the electronic driving interface 135 and then through the processor 130 configured to send the measurement results to the non-quantum hardware enclave 121 .

[0062] In the embodiment of FIG. 2 (embodiment #2), the instructions may be sent by a specific driving circuitry 122 of the non-quantum hardware enclave 121 through theelectronic driving interface 135 of the quantum computing means 150, without using the CPU. The measurement results may be transmitted following the same path in inverse: through the electronic driving interface 135 configured to them the measurement results to the non-quantum hardware enclave 121.

[0063] In the embodiment of FIG. 3 (embodiment #3), the instructions may instead be sent by a specific driving circuitry 122 in the non-quantum hardware enclave 121 , directly to the quantum computing means 150, without using the CPU nor the electronic driving interface 135. The measurement results may be transmitted following the same path in inverse and be sent from the quantum computing means 150 directly to the non-quantum hardware enclave 121 .

[0064] In the embodiments #2 and #3, the specific driving circuitry 122 may for example be implemented as an FPGA, suitable for being integrated into a secure non- quantum hardware enclave 121.

[0065] In the embodiment #1 , the server 120 that pilots the operations performed by the quantum computing means 150 may be equipped with a non-quantum hardware enclave 121 communicating with the processor 130 using a dedicated channel, such as a hardware bus or a shared memory.

[0066] During the execution of the protocol, after each measurement, rather than sending the result to the client 110 through a classical communication channel, the measurements results are sent to the non-quantum hardware enclave 121 and the measurement basis for the next measurement is computed inside the non-quantum hardware enclave 121 and sent back to the processor 130 for being forwarded to the electronic driving interface 135 and then to the quantum computing means 150.

[0067] In this configuration, the latency comes from the communication between the CPU and the non-quantum hardware enclave 121. Each measurement requires a round of communication, but the hardware bus inside the server 120 is much faster than a communication over a network.

[0068] In the embodiment #2, the server 120 includes a non-quantum hardware enclave 121 (e.g., TEE) and a driving circuitry 122 (e.g., a FPGA) inside the non-quantum hardware enclave 121. The driving circuitry 122 is configured to generate driving instructions (e.g., driving signals) to pilot the electronic driving interface 135 that is driving the quantum computing means 150.

[0069] The functional properties of the TEE in terms of security are extended to the FPGA using for example the principles described in [Ref1 , Ref2], This may be achieved by encrypting and signing the information flow between the FPGA and the TEE. The feedforward function may be executed directly in the FPGA for generating the instructionsfor the (n+1 )-th measurement knowing the results of the n first measurements.

[0070] Compared to the embodiment #1 , the extension of the non-quantum hardware enclave 121 (e.g., TEE) security to the driving circuitry 122 (e.g., a FPGA) in embodiment #2 reduces the latency further. The communication latency between the internal processor of the non-quantum hardware enclave 121 and the main processor 130 of the server 120 is cancelled by executing the computation directly inside the driving circuitry 122 that is piloting the electronic driving interface 135 to pilot the quantum operations performed by the quantum computing means 150.

[0071] In this case, the feedforward function is executed directly in the non-quantum hardware enclave 121 , by the driving circuitry 122 (e.g., a FPGA). The input (including the measurement results) of the feedforward function may be acquired by the driving circuitry 122 (e.g., a FPGA) as a digital electric signal, and the output (measurement and / or transformation instructions) of the feedforward function is generated as a function of the input. The output of the feedforward function may be generated by the driving circuitry 122 (e.g., a FPGA) as a digital signal, adapted to pilot the quantum computing means 150. As an example, on an FPGA, the time for such a computation is of the order of nanoseconds. This configuration then reduces the latency to the lowest possible value.

[0072] To summarize, in the embodiment #1 , the feedforward function is executed within the non-quantum hardware enclave 121 . The computation is driven by the processor 130 of the server 120. After each measurement, there is a round of communication between the processor 130 and the non-quantum hardware enclave 121.

[0073] To summarize, in the embodiment #2, the feedforward function is executed within the driving circuitry 122 of the non-quantum hardware enclave 121 , which also benefits from the security features of the non-quantum hardware enclave 121. The non- quantum hardware enclave 121 is driving the computation by piloting the driving circuitry 122. After each measurement, the measurement result is transmitted to the driving circuitry 122 which generates the appropriate instructions to pilot the quantum computing hardware and perform the subsequent measurement on quantum states.

[0074] The embodiment #3 is a variant of embodiment #2, in which the functionalities of the electronic driving interface 135 that are needed for sending instructions and receiving in response measurement results are integrated into the driving circuitry 122 of the non-quantum hardware enclave 121. Thus, the instructions are transmitted by the driving circuitry 122 directly to the quantum computing means 150 and the measurement results follow the inverse path. This allows further reducing the communication latency between the computation of the output of the feedforward function and the receipt of the instructions by the quantum computing hardware.

[0075] An example of protocol that may be applied using one of the embodiments of FIGS. 1 to 3 is the universal blind quantum computing (UBQC) involving a client and a server including quantum computing means.

[0076] Universal blind quantum computing (UBQC) is a protocol that enables a client with limited quantum capabilities to delegate a quantum computation to a powerful but untrusted quantum server, while keeping the client's input, output, and computation private. The client drives the computation executed by a quantum server remotely.

[0077] In this protocol, the quantum computing means for the computation may be a many-particle highly correlated quantum circuit, called a brickwork, and that is configured to perform adaptive single-particle measurements.

[0078] In the context of quantum computing, "brickwork" typically refers to a specific layout or arrangement of qubits (quantum bits) within a quantum processor. In a brickwork layout, qubits are arranged in a grid-like fashion (similar to the layout of bricks in a wall), with neighboring qubits interacting with each other. This arrangement allows for efficient communication and interaction between adjacent qubits, which is adapted for efficient quantum computations. Brickwork layouts may be used in various quantum computing architectures, such as superconducting qubits or trapped ions, to organize and control qubits effectively while minimizing unwanted interactions and errors. Quantum states stored in a brickwork are referred to herein as brickwork states.

[0079] In the preparation stage of the UBQC, the client prepares random singleparticle states and sends them to the server. The server assembles the received states into a brickwork state. The computation stage requires rounds of classical communication between the client and the server: for each particle of the cluster state, the client indicates to the server which measurement to apply. After performing the measurement, the server communicates the measurement result to the client and, according to the measurement result, the client decides the following measurement to be performed.

[0080] FIG. 4 illustrates schematically a multi-client version of the UBQC that may be implemented using any of the embodiments of FIGS. 1 to 3.

[0081] Especially the hardware enclave 421 and quantum means 450 may communicate as disclosed by reference to any of FIGS. 1 to 3.

[0082] Preparation stage

[0083] Alice and Bob want to perform a joint computation (i.e., a computation algorithm) by delegating the computation to a remote quantum server, while keeping the input, algorithm parameters (e.g., the input data of the algorithm and a sequence of logical operations defining the algorithm), and output hidden from any malicious party.

[0084] A quantum source 415 provides Alice 41 A with initial quantum states. Alice encodes her private data PA into the received initial quantum states by applying transformations corresponding to her private data PA to generate first quantum states. Then Alice applies, to the first quantum states, random rotations, corresponding to a random key KA (e.g., a single-use key) to generate second quantum states. The random key KA encodes for example a list of angles of rotations to be performed on the quantum states and a basis for the angle values. To guarantee blindness according to UBQC, the rotation angles are randomly selected such that the quantum states are prepared in a random state. Alice sends her random key KA and her private data PA to a non-quantum hardware enclave 421 through a non-quantum channel.

[0085] Then, Alice sends the second quantum states to Bob, who also encodes its private data PB over the second quantum states, e.g., by applying transformations corresponding to his private data PB to generate third quantum states. To ensure blindness, Bob also applies, to the third quantum states, random rotations, corresponding to his random key KB (e.g., a single-use key) to generate fourth quantum states. The random key KB encodes for example a list of angles of rotations to be performed on the quantum states and a basis for the angle values. Bob sends his random key KB and his private data PB to the non-quantum hardware enclave 421 .

[0086] Bob sends to the non-quantum hardware enclave 421 either all or a part of the algorithm parameters (e.g., the input data of the algorithm and a sequence of logical operations defining the algorithm). Alice may send the other part of the algorithm parameters if Bob does not send all the algorithm parameters.

[0087] The quantum computing hardware 450 stores the fourth quantum states received from Bob. The quantum states may be stored in a quantum circuit, for example in a brickwork state.

[0088] Computation stage

[0089] A feedforward function is determined or configured by the non-quantum hardware enclave 421 on the basis of the algorithm parameters (i.e., feedforward configuration data) received from Alice and / or Bob. The feedforward function is determined or configured on the basis of the private data PA, PB and the random keys KA, KB received respectively from Alice and Bob. The feedforward function is used to generate the instructions for quantum operations (measurement and / or transformation) to be performed (using a quantum circuit, e.g., a brickwork) on the quantum states stored in the quantum computing hardware 450. The feedforward function may be the same as the one defined in the UBQC protocol.

[0090] The non-quantum hardware enclave 421 computes first instructions MBA foroperations (e.g., measurements and / or transformations) to be performed on the quantum states stored in the quantum circuit. The quantum computing hardware 450 generates a first measurement result MRA by operating on the quantum states in accordance with the instructions and gives back the first measurement result MRA to the non-quantum hardware enclave 421 .

[0091] The non-quantum hardware enclave 421 computes, using the feedforward function FF taking as input the first measurement result MRA, the second instructions MBB for operations (e.g., measurements and / or transformations) to be performed on the quantum states stored in the quantum circuit. The quantum computing hardware 450 generates a second measurement result MRB by operating on the quantum states in accordance with the instructions and gives back the second measurement result MRB to the non-quantum hardware enclave 421 .

[0092] The computation of instructions based on at least one of the measurement results and the operations (e.g., measurements and / or transformations) performed on the quantum states based on the instructions to generate a new measurement result are repeated iteratively until the whole computation algorithm is executed.

[0093] The computations of the first instructions MBA and second instructions MBB are performed in an iterative manner. Finally, the non-quantum hardware enclave sends back a final result to the clients, Alice and Bob. The whole algorithm has been performed on randomly rotated states such that from the server’s point of view, it is indistinguishable from a random computation. The feedforward function used to compute the instructions ensures that the computation’s result remains decodable for the client.

[0094] FIG. 5 shows a flowchart of a method for operating a quantum-enabled server adapted for delegated quantum blind computing of a computation algorithm defined by a sequence of logical operations according to one or more example embodiments.

[0095] The steps of the method may be implemented by a quantum enabled server according to any example described herein. While the steps are described in a sequential manner, the person skilled in the art will appreciate that some steps may be omitted, combined, performed in different order and I or in parallel.

[0096] In step 520, a non-quantum hardware enclave generates instructions for quantum state transformation and measurement. The instructions are generated by a feedforward function executed by the non-quantum hardware enclave. The non-quantum hardware enclave may be secured by a trusted execution environment adapted to run software code configured to execute the feedforward function.

[0097] In step 530, the non-quantum hardware enclave causes transmission of theinstructions to quantum computing means.

[0098] For example, as in embodiment #1 , the quantum-enabled server may comprise an electronic driving interface for driving the quantum computing means and a processor configured to control the electronic driving interface. To cause the instructions to be transmitted to the quantum computing means, the non-quantum hardware enclave is configured to transmit the instructions to the processor, then the processor is configured to cause the instructions to be transmitted to the quantum computing means via the electronic driving interface.

[0099] For example, as in embodiments #2 and #3, the non-quantum hardware enclave may include driving circuitry (e.g., FPGA). The driving circuitry may be a FPGA coupled or interfaced with a trusted execution environment of the non-quantum hardware enclave. To cause the instructions to be transmitted to the quantum computing means, the non-quantum hardware enclave may be configured to transmit the instructions to the quantum computing means via the driving circuitry and the driving circuitry unit may be configured to cause the instructions to be transmitted to the quantum computing means by the driving circuitry, either directly (embodiment #3) or via the electronic driving interface (embodiment #2). The non-quantum hardware enclave may comprise a digital-to-analogue converter for converting the instructions into one or more analogue control signals carrying the instructions and adapted to be transmitted to the quantum computing means by the driving circuitry, either directly (embodiment #3) or via the electronic driving interface (embodiment #2). In step 540, the quantum computing means generates measurement results by operating (e.g., performing transformations and / or measurements) on one or more quantum states stored in the quantum storage means in accordance with the received instructions. The stored quantum states may be quantum states transformed by a client from quantum states generated by a quantum source.

[0100] In step 550, the quantum computing means may cause the measurement results to be transmitted to the non-quantum hardware enclave and the non-quantum hardware enclave receives the measurement results.

[0101] The quantum computing means may cause the measurement results to be transmitted to the non-quantum hardware enclave via the electronic driving interface (embodiment #1). The quantum computing means may cause the measurement results to be transmitted to the non-quantum hardware enclave to the driving circuitry, either directly (embodiment #3) or via the electronic driving interface (embodiment #2).

[0102] In step 560, the non-quantum hardware enclave executes a feedforward function. The feedforward function may be adapted to control the execution of a sequence of quantum operations corresponding to the sequence of logical operations. The control ofthis execution is done at each iteration by determining next instructions for quantum state transformation and measurement on the basis of the received measurement results. The feedforward function is determined based on a computation algorithm to be executed by the quantum computing means, where the computation algorithm is defined by the sequence of logical operations. The non-quantum hardware enclave may receive, from the client, via a classical communication channel, feedforward configuration data for configuring the feedforward function.

[0103] In step 570, the non-quantum hardware enclave causes the next instructions to be transmitted to the quantum computing means.

[0104] After step 570, steps 540 to 560 may be repeated. Generally steps 530 to 560 (or 540 to 570) may be performed in an iterative manner with the new instructions generated from measurements results until a computation algorithm is fully executed based on the feedforward function.

[0105] LIST OF CITE REFERENCES

[0106] [Ref1] Anati, Ittai, et al. "Innovative technology for CPU based attestation and sealing." Proceedings of the 2nd international workshop on hardware and architectural support for security and privacy. Vol. 13. No. 7. New York, USA: ACM, 2013

[0107] [Ref2] Xia, Ke, et al. "Sgx-fpga: Trusted execution environment for cpu-fpga heterogeneous architecture." 2021 58th ACM / IEEE Design Automation Conference (DAC). IEEE, 2021

[0108] [Ref3] Fitzsimons, Joseph F., and Elham Kashefi. "Unconditionally verifiable blind quantum computation." Physical Review A 96.1 (2017): 012303

[0109] LIST OF MAIN ABBREVIATIONS

[0110] FPGA field-programmable gate array

[0111] SMPC Secure Multi-Party Computation

[0112] TEE Trusted Execution Environment

[0113] UBQC universal blind quantum computing

Claims

CLAIMS1. A quantum-enabled server adapted for delegated quantum blind computing of a sequence of logical operations, the quantum-enabled server comprising- quantum storage means configured to store quantum states;- quantum computing means comprising quantum state transformation and measurement hardware;- a classical hardware enclave configured to generate instructions for quantum state transformation and measurement and cause the instructions to be transmitted to the quantum computing means, wherein the quantum computing means are configured to generate measurement results by operating on one or more quantum states stored in the quantum storage means in accordance with the instructions and to provide measurement results to the classical hardware enclave in response to the instructions; wherein the classical hardware enclave is configured to execute a feedforward function configured to control an execution of a sequence of quantum operations corresponding to the sequence of logical operations by determining next instructions for quantum state transformation and measurement on the basis of the received measurement results and cause the next instructions to be transmitted to the quantum computing means.

2. Quantum-enabled server according to claim 1 , wherein the classical hardware enclave is configured to receive, from a client, via a classical communication channel, feedforward configuration data for configuring the feedforward function, wherein the classical hardware enclave is configured to configure the feedforward function based on the feedforward configuration data.

3. Quantum-enabled server according to claim 1 or 2, wherein the quantum-enabled server comprises an electronic driving interface for driving the quantum computing means and a processor configured to control the electronic driving interface, wherein to cause the instructions to be transmitted to the quantum computing means, the classical hardware enclave is configured to transmit the instructions to the processor, wherein the processor is configured to cause the instructions to be transmitted to the quantum computing means via the electronic driving interface.

4. Quantum-enabled server according to claim 1 or 2, wherein the classical hardware enclave includes driving circuitry, wherein to cause the instructions to be transmitted to the quantum computing means, the classical hardware enclave is configured to transmit the instructions to the quantum computing means via the driving circuitry; wherein the driving circuitry unit is configured to cause the instructions to be transmitted the quantum computing means.

5. Quantum-enabled server according to claim 4, wherein the quantum computing means is configured to cause the measurement results to be transmitted to the classical hardware enclave via the driving circuitry.

6. Quantum-enabled server according to claim 4 or 5, wherein the driving circuitry is a FPGA coupled with a trusted execution environment of the classical hardware enclave.

7. Quantum-enabled server according to claim 4, wherein the quantum-enabled server comprises electronic driving interface adapted for driving the quantum computing means and a processor configured to control the electronic driving interface, wherein the quantum computing means are configured to cause the measurement results to be transmitted to the classical hardware enclave via the electronic driving interface.

8. Quantum-enabled server according to any of the previous claims, wherein the classical hardware enclave is secured by a trusted execution environment adapted to run software code configured to execute the feedforward function to generate the instructions.

9. Quantum-enabled server according to claims 4 and 7, wherein the classical hardware enclave comprises a digital-to-analogue converter for converting the instructions into one or more analogue control signals carrying the instructions and adapted to be transmitted to the quantum computing means by the driving circuitry directly or via the electronic driving interface.

10. Quantum-enabled server according to any of the previous claims, wherein the quantum states are quantum states transformed by a client from quantum states generated by a quantum source.11 . A method for operating a quantum-enabled server adapted for delegated quantum blind computing of a sequence of logical operations, the method comprising- generating, by a classical hardware enclave of the quantum-enabled server, instructions for quantum state transformation and measurement;- causing, by the classical hardware enclave, transmission of the instructions to quantum computing means of the quantum-enabled server via electronic driving interface;- generating, by the quantum computing means, measurement results by operating on quantum states stored in quantum storage means of the quantum-enabled server in accordance with the instructions;- receiving, by the classical hardware enclave, the measurement results;- executing, by the classical hardware enclave, a feedforward function configured to control an execution of a sequence of quantum operations corresponding to the sequence of logical operations by determining next instructions for quantum state transformation and measurement on the basis of the received measurement results;- causing, by the classical hardware enclave, the next instructions to be transmitted to the quantum computing means.

12. The method according to claim 11 , comprising receiving from a client, via a classical communication channel, feedforward configuration data for configuring the feedforward function,- configuring, by the classical hardware enclave the feedforward function based on the received feedforward configuration data.

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