Learning quantum systems via non-temporally ordered correlators

Abstract

Methods, systems, and devices for learning quantum systems via non-temporally ordered correlators. In one aspect, a method includes measuring, by a control and measurement system, a non-temporally ordered correlator value of a quantum system including a plurality of qubits, where the plurality of qubits includes a probe qubit and one or more other qubits. To measure non-temporally ordered correlator values, the probe qubit is prepared in an initial state. For time t, forward time evolution is performed on the quantum system. A unitary operator is applied to one or more qubits in the quantum system. For time t, backward time evolution is performed on the quantum system, and the probe qubits are measured to obtain non-temporally ordered correlator values. The classical computing device processes the measured non-temporally ordered correlator values to determine a property of the quantum system.

Description

Technical Field

[0001] The present disclosure relates to quantum computing. Background Art

[0002] Learning properties of quantum systems presents challenges that are not present in their classical counterparts. These challenges often arise from the presence of entanglement - measurements on a quantum system that is highly entangled with another system (or environment) reveal little information from which to learn. In practice, these difficulties are most common in strongly interacting quantum systems. Strong interactions can introduce non-local entanglement throughout the system on very short timescales, and this has been found to inhibit learning system properties (e.g., the Hamiltonian) from physical observables.

[0003] The ubiquity of strong interactions in experimental applications of quantum learning has promoted the emergence of various solutions to this problem. For example, in nuclear magnetic resonance (NMR) spectroscopy, techniques have been developed to controllably suppress unwanted strong interactions between solid-state nuclear spins, which enables the identification of hitherto inaccessible molecular structures. Similarly, in quantum device characterization and quantum sensing, dynamic decoupling control sequences can effectively eliminate unwanted interactions and improve learning of remaining interactions. Other approaches include learning by converting quantum data in the system onto a quantum simulator, or learning from high-precision local measurements at an early stage before entanglement is formed. Despite this, many physical systems remain inaccessible to learning using existing methods due to incomplete control or limited experimental precision. Summary of the invention

[0004] This disclosure describes learning properties of quantum systems via non-time-ordered correlators.

[0005] Generally speaking, one innovative aspect of the subject matter described in this specification can be implemented in a method comprising: measuring, by a measurement and control system, a non-time-ordered correlator value of a quantum system comprising a plurality of qubits, wherein the plurality of qubits comprises a probe qubit and one or more other qubits, the measuring comprising: preparing the probe qubit in an initial state; performing a forward time evolution on the quantum system for a time t; applying a unitary operator to one or more qubits in the quantum system; performing a backward time evolution on the quantum system for a time t; and measuring the probe qubit to obtain a non-time-ordered correlator value; and processing the measured non-time-ordered correlator value by a classical computing device to determine a property of the quantum system.

[0006] Other implementations of these aspects include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the method. A system of one or more classical computers and quantum computers may be configured to perform specific operations or actions by means of software, firmware, hardware, or a combination thereof installed on the system, which software, firmware, hardware, or a combination thereof causes the system to perform actions in operation. One or more computer programs may be configured to perform specific operations or actions by means of including instructions, which, when executed by a data processing device, cause the device to perform actions.

[0007] The foregoing and other implementations can each optionally include one or more of the following features, either alone or in combination. In some implementations, the measured non-time-ordered correlator value indicates whether information encoded at the probe qubit at an initial time is contained in correlations involving other qubits at time t.

[0008] In some implementations, the method further includes, for each of a plurality of values ​​of t and for each of a plurality of unitary operators, repeatedly measuring the non-time ordered correlator value.

[0009] In some implementations, processing the measured non-time-ordered correlator values ​​to determine a property of the quantum system includes using a trained classical learning model to predict the property of the quantum system.

[0010] In some implementations, the method further includes: generating training data by a quantum computer, the generating comprising performing quantum simulations on a Hamiltonian characterizing the quantum system, each quantum simulation corresponding to a corresponding Hamiltonian parameter value; and using the training data to train a classical learning model for predicting properties of the quantum system.

[0011] In some implementations, the method further includes: measuring a non-time ordered correlator value for each of a plurality of values ​​of t and for each of a plurality of unitary operators, wherein the measurements are performed with a first precision; calculating Fisher information for each measured non-time ordered correlator value; and repeating the measurements of the non-time ordered correlator value having the maximum Fisher information, wherein the repeated measurements are performed with a second precision that is higher than the first precision.

[0012] In some implementations, the unitary operator comprises a local unitary operator, optionally a single-qubit Pauli operation.

[0013] In some implementations, the unitary operator includes a global rotation operation.

[0014] In some implementations, the quantum system includes traversing a ID spin chain, and wherein determining a property of the quantum system includes learning a qubit coupling to a probe qubit at a distance d.

[0015] In some implementations, the quantum system includes two spin chains that intersect at a distance d from a probe qubit, and wherein determining a property of the quantum system includes learning a value of d.

[0016] In some implementations, performing the forward time evolution of the quantum system for time t includes applying a second unitary operator e to the quantum system -iHt A quantum circuit of the type t, wherein H denotes a Hamiltonian characterizing the quantum system, and wherein performing a backward time evolution of the quantum system for a time t comprises applying to the quantum system a third unitary operator e iHt quantum circuits.

[0017] In some implementations, performing the backward time evolution of the quantum system for time t is noisy.

[0018] In general, another innovative aspect of the subject matter described in this specification can be implemented in a method comprising: measuring, by a measurement and control system, a non-time-ordered correlator value of a quantum system comprising a plurality of interacting qubits, the measuring comprising: preparing a first qubit and a second qubit in the quantum system in an initial state, wherein the first qubit is adjacent to the second qubit; performing a forward time evolution on the quantum system for a time t; applying a unitary operator to the first qubit; performing a backward time evolution on the quantum system for a time t; and measuring the first qubit and the second qubit to obtain a non-time-ordered correlator value; and processing, by a classical computing device, the measured non-time-ordered correlator value to determine a property of the quantum system.

[0019] Other implementations of these aspects include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the method. A system of one or more classical computers and quantum computers may be configured to perform specific operations or actions by means of software, firmware, hardware, or a combination thereof installed on the system, which software, firmware, hardware, or a combination thereof causes the system to perform actions in operation. One or more computer programs may be configured to perform specific operations or actions by means of including instructions, which, when executed by a data processing device, cause the device to perform actions.

[0020] The foregoing and other implementations can each optionally include one or more of the following features, either alone or in combination. In some implementations, the measured non-time-ordered correlator value indicates whether information encoded at the first qubit at an initial time is contained in correlations involving other qubits at time t.

[0021] In some implementations, the method further includes, for each of a plurality of values ​​of t and for each of a plurality of pairs of qubits in the quantum system, repeatedly measuring the non-time-ordered correlator value.

[0022] In some implementations, processing the measured non-time-ordered correlator values ​​to determine a property of the quantum system includes using a trained classical learning model to predict the property of the quantum system.

[0023] In some implementations, the method further includes: generating training data by a quantum computer, the generating comprising performing quantum simulations on a Hamiltonian characterizing the quantum system, each quantum simulation corresponding to a corresponding Hamiltonian parameter value; and using the training data to train a classical learning model for predicting properties of the quantum system.

[0024] In some implementations, the method further includes: for each of a plurality of values ​​of t and for each of a plurality of pairs of qubits, measuring a non-time ordered correlator value, wherein the measuring is performed with a first precision; calculating Fisher information for each measured non-time ordered correlator value; and repeating the measuring of the non-time ordered correlator value having the maximum Fisher information, wherein the repeated measuring is performed with a second precision that is higher than the first precision.

[0025] In some implementations, the quantum system includes a strongly interacting system.

[0026] In some implementations, the quantum system includes a 1D spin chain, and wherein determining the property of the quantum system includes characterizing weak linking interactions known to exist in the spin chain.

[0027] In some implementations, the method further includes repeatedly measuring the non-time-ordered correlator values ​​for qubit pairs within a predetermined distance from the weak link interaction.

[0028] In some implementations, the method further includes, before processing the measured non-time ordered correlator values: calculating the mutual information between each measured non-time ordered correlator value and the link strength; selecting a predetermined number of measured non-time ordered correlator values ​​having the highest mutual information; and providing the selected predetermined number of measured non-time ordered correlator values ​​for processing by a classical computing device.

[0029] In some implementations, the quantum system includes a 1D spin chain, and wherein determining the property of the quantum system includes predicting whether the spin chain includes or excludes weak link interactions.

[0030] In some implementations, performing the backward time evolution of the quantum system for time t is noisy.

[0031] In some implementations, performing the forward time evolution of the quantum system for time t includes applying a second unitary operator e to the quantum system iIIt A quantum circuit of the type t, wherein H denotes a Hamiltonian characterizing the quantum system, and wherein performing a backward time evolution of the quantum system for a time t comprises applying to the quantum system a third unitary operator e iHt quantum circuits.

[0032] The subject matter described in this specification can be implemented in specific embodiments to realize one or more of the following advantages.

[0033] Learning the properties of dynamical quantum systems is fundamental to applications ranging from nuclear magnetic resonance spectroscopy to quantum device characterization. A central challenge in this pursuit is learning strongly interacting systems, where conventional observables decay rapidly in both time and space, limiting the information that can be learned from their measurements. This disclosure introduces a new class of observables into the context of quantum learning—non-time-ordered correlators—that significantly improve the learnability of strongly interacting systems by virtue of exhibiting information physics over large time and distance.

[0034] The presently described techniques are described in the context of two general scenarios where non-time-ordered correlators offer significant advantages for learning tasks in local Hamiltonian systems. The first scenario is relevant to situations where experimental access to the system is spatially limited, e.g. via a single "probe" degree of freedom (qubit). The second scenario is relevant to detecting weak interactions (in an otherwise strongly interacting system) whose strength is much lower than the typical interaction strength and thus only manifests itself at a late stage. The advantages achieved by the presently described techniques can be characterized using information-theoretic measurements (Fisher information) and performance metrics on a variety of learning problems. Furthermore, these advantages are robust to experimental readout errors and time-reversal defects arising from strong coupling to the environment or decoherence.

[0035] Furthermore, almost all time reversal techniques rely only on the type of interaction being reversed and do not require knowledge of the magnitude of the interaction (i.e., which is what is to be learned). Therefore, learning via non-time-ordered correlators may find applications in different physical contexts. Examples include learning long-range crosstalk in quantum processors and the strongly interacting problem in NMR.

[0036] The details of one or more implementations of the subject matter of this specification are set forth in the accompanying drawings and the following description. Other features, aspects, and advantages of the subject matter will become apparent from the specification, drawings, and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1is a block diagram of an example system for studying quantum systems using non-time-ordered correlators.

[0038] Figure 2 is a flow chart of an example process for learning in a quantum system with restricted access.

[0039] Figure 3 Two diagrams are shown for learning in quantum systems with restricted access using non-time-ordered correlators.

[0040] Figure 4 is a flow chart of an example process for detecting weak interactions in a quantum system.

[0041] Figure 5 Two diagrams used to study weak interactions in quantum systems are shown.

[0042] Figure 6 is a circuit diagram for solving the disjoint unitary problem using non-time ordered correlator measurements.

[0043] Figure 7 An example classical / quantum computer is depicted. DETAILED DESCRIPTION

[0044] This specification describes learning quantum systems and their properties via non-time-ordered correlators. A time-ordered correlator (TOC) is a correlation function that takes the general form given by equation (1) below,

[0045] C TOC =tr(A k (t k )...A1(t1)ρB1(t′1)...B l (t′ L )) (1)

[0046] The operators A, S increase over time from the initial density matrix ρ, i.e., t k >…>t1 and t′ l >…>t′1. This can be achieved by evolving the state ρ forward in time (e.g., via the Hamiltonian evolution O(t)=e iHT Oe -iHT ), and at each time t i , t′ j An intermediate quantum operation is applied to measure the time-ordered correlator. Any correlation function that does not follow this form is called a non-time-ordered correlator. A common example of TOC is the two-point function given by equation (2) below,

[0047] C TOC = <V x (t)W x′(0)>(2)

[0048] where <·>≡tr(·) / 2 L represents the infinite temperature trajectory of L qubits, and V x , W x′ is a local operator at the grid point x, x′. Throughout this disclosure, a time-evolving operator (such as V(t)) is represented by The time evolution is unitary and H(t) is a time-dependent Hamiltonian that characterizes the quantum system. In some implementations, H(t) may be a Floquet Hamiltonian. Such correlators measure the spread of local quantities in space and time, e.g., how many spins prepared at lattice site x′ at time zero have been transferred to lattice site x at time t. It has been shown that the local TOC typically decays rapidly, i.e., in O(1) time, to its thermal value. This rapid decay may inhibit learning tasks, since additional information may not be available from the TOC at times after the decay occurs.

[0049] An example non-time ordered correlator (OTOC) is a four-point correlation function given by equation (3) below,

[0050]

[0051] Where V x , W x′ represents a local operator. Unlike time-ordered measurements, measuring the OTOC typically requires both forward and backward time evolution. That is, for a given evolution of a system "forward" in time, one can also apply an inverted evolution, considered "backward", in order to successfully measure the OTOC. For the applications described in this specification, almost all time-reversal experimental techniques rely solely on the type of interaction that is being inverted and do not require knowledge of the specific Hamiltonian one may want to study. For example, in an NMR experiment, the same pulse sequence will invert an arbitrary dipole-dipole coupling Hamiltonian. In effect, the OTOC probes whether the information encoded at time zero at a lattice site x′ is contained in a correlation involving site x at time t. This is accomplished by comparing the time-evolving operator at x with the local operator at x′ <|[V x (t), W x′ (0)]| 2 >-1-C OTOC In a local strongly interacting system, the precomputed sub-electrons will diffuse in a ballistic manner according to the connectivity of the system. The duration of this diffusion is proportional to the spatial extent of the system ~L, at which point the information is already non-localized in the entire system.

[0052] This phenomenology leads to two core intuitions for learning from the OTOC. First, the dynamics of the OTOC primarily contain information about the connectivity of the system under study. Second, the OTOC continues to reveal such information, up to O(L) time, long after the TOC decays. This timescale increases as the size of the system increases.

[0053] Figure 1 1 is a block diagram of an example system 100 for learning quantum systems using non-time-ordered correlators (OTOCs). The example computing system 100 is an example of a system implemented as classical and quantum computer programs on one or more classical computers and quantum computing devices in one or more locations in which the systems, components, and techniques described herein may be implemented.

[0054] The example computing system 100 includes a quantum computing device 102 and a classical processor 104. For purposes of illustration, Figure 1 The quantum computing device 102 and the classical processor 104 shown in FIG. 1 are shown as separate entities, however, in some implementations, the classical processor 104 may be included in the quantum computing device 102. For example, in some implementations, the quantum computing device 102 may be directly connected to the classical processor 104. In other implementations, the quantum computing system 102 may be connected to the classical processor 104 through a network (e.g., a local area network (LAN), a wide area network (WAN), the Internet, or a combination thereof).

[0055] Quantum computing device 102 includes physical components for performing quantum computing. For example, quantum computing device 102 may include a quantum data plane, which in turn includes a plurality of physical qubits, such as qubit 120; and a control and measurement system 106, which is configured to perform operations and measurements on the physical qubits. Figure 1 Although not shown in the figure, the quantum computing device 102 may also include: a control processor plane configured to determine the sequence of operations and measurements required by the quantum algorithm being executed by the quantum computing system; and a classical computer that communicates data with the control processor and facilitates user interaction and access to a network or storage. The specific type of quantum computing device 102 may depend on the type of qubit used. In some implementations, the qubit may be a superconducting qubit, a semiconductor qubit, a photonic qubit, or an atom-based qubit. For example, the qubit may include an Xmon qubit, a flux qubit, a phase qubit, a CAT qubit, or a qubit with frequency interaction.

[0056] The classical processor 104 includes components for performing classical computations. For example, the classical processor 104 may be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory storage medium for execution by a data processing device or for controlling the operation of a data processing device. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them.

[0057] The example system 100 is configured to perform operations to use OTOC to learn quantum systems and their properties. For example, in some implementations, the system 100 can use OTOC to learn properties of a quantum system with limited access, such as determining the distance d between a probe qubit and the intersection of two spin chains (e.g., Figure 1 122) or determining the strength of the interaction between two qubits that are a distance d from the probe qubit (e.g. Figure 1 In these examples, control and measurement system 106 may be configured to implement a measurement protocol that implements the forward and backward evolution of probe qubits 108 to obtain measurements 112, which when provided to classical processor 104 may be used to compute OTOC 114 and learn properties of quantum system 116 (which may be provided as output). Figure 2 and Figure 3 Example operations performed by quantum computing device 102 and classical processor 104 to learn properties of a quantum system with restricted access are described in further detail.

[0058] As another example, in some implementations, system 100 can use OTOC to study or characterize weak interactions in a quantum system, e.g., to determine whether two qubits in a quantum system interact, such as Figure 1 In these examples, control and measurement system 106 may be configured to implement a measurement protocol that implements forward and backward evolution of qubit pairs 110 to obtain measurement values ​​112, which when provided to classical processor 104 may be used to compute OTOC 114 and learn properties of quantum system 116 (which may be provided as output). Figure 4 and Figure 5 Example operations performed by the quantum computing device 102 and the classical processor 104 to study or characterize weak interactions are described in greater detail.

[0059] Learning with restricted access

[0060] Figure 2is a flow chart of an example process 200 for learning in a quantum system with restricted access. For example, the example process 200 may be applied to a situation where experimental access to a quantum system includes state preparation and readout capabilities, but is spatially restricted to a single probe qubit that interacts with a larger system to be learned (e.g., the experimenter has only local unitary control over the qubit in the quantum system). For convenience, the example process 200 will be described as being performed by a system of one or more classical and quantum computing devices located in one or more locations. For example, a suitably programmed Figure 1 The system 100 may perform the example process 200 .

[0061] The system measures the value of a non-time-ordered correlator of a quantum system including a plurality of qubits by a measurement control system. The quantum system includes a probe qubit (which can be directly accessed) and one or more other qubits. In some implementations, such as in NMR and solid-state defect settings, the quantum system can be initially prepared in an infinite temperature (i.e., maximum mixing) state. The value of the non-time-ordered correlator indicates whether the information encoded at the probe qubit at an initial time is contained in a correlation involving other qubits at a later time t=τ=-τ.

[0062] OTOC can be composed of C OTOC (x, t) = <V p (t)W x (0)V p (t)W x (0)>, where p denotes the probe qubit and <·>≡trr(·) / 2 L represents an infinite temperature trajectory of L qubits. Such OTOCs can be measured using state preparation and readout of the probe qubits, combined with time evolution and a single local unitary operation on the larger quantum system. The operator V,W can iterate over all local operators in the system. For example, the operator can iterate over all local operators with a predefined weight ≤w operator, where w ~ O(1). This can be achieved by random measurement strategies, such as using local Clifford unitary and O(3 w ) measured by shadow tomography. However, in practice, the operators V, W may be restricted to a subset of possible values. For example, in some implementations, for TOC, V = W∈{σ x , σ z}, and for OTOC, V=W∈{σ z It has been observed that OTOC is relatively insensitive to the basis of V and W, so the choice can be restricted to a single Pauli operator, such as σ z (Although it is worth noting that adding additional Pauli operators such as σ x, can only improve the relative advantage of OTOC over TOC). More generally, adding additional {V, W} pairs will likely not change the qualitative behavior of learning via TOC and OTOC. Specifically, the learning advantage of OTOC comes from their ability to detect highly non-local correlations in the system (i.e., the time-evolving operator V p These correlations cannot be detected by any time-ordered correlator involving only few-body operators; indeed, in ergodic systems we generally expect them to be undetectable by any time-ordered measurement.

[0063] To measure a non-time-ordered correlator, the system is prepared to probe qubit p in an initial state (step 202). The initial state may be an eigenstate of the local operator Vp (included in the OTOC), such that the density matrix of the quantum system is given by

[0064]

[0065] in, Denote the identity operator I, V acting on the quantum bit p p represents the operator V acting on the qubit p, L represents the total number of qubits included in the quantum system, and represents the identity operator acting on the entire quantum system

[0066] Then, the system performs forward time evolution on the quantum system for time τ (step 204). For example, the system can apply the unitary operator e to the quantum system. -iHτ A quantum circuit of , where II represents the Hamiltonian that characterizes the quantum system.

[0067] The system then perturbs the quantum system by applying a unitary operator to one or more qubits included in the quantum system (step 206). In some implementations, the unitary operator may be a local unitary operator W applied to qubit x. x , such as a single-qubit Pauli operation. In other implementations, the unitary operator may be a global rotation operation. The type of unitary operator performed in step 106 depends on the type of learning being performed. For example, in some implementations, the quantum system may be an ergodic 1D spin chain. In these implementations, the learning task may be learning the coupling of a qubit at a distance d from a probe qubit. As another example, in some implementations, the quantum system may include two spin chains that intersect at a distance d from the probe qubit (e.g., see Figure 3 302 in the illustration). In these implementations, the learning task can be to learn the value of d (which represents the geometry of the quantum system) from measurements of the correlation function of the quantum system.

[0068] Then, the system performs a backward time evolution on the quantum system for time τ′ (step 208). That is, the system performs a time-reversed evolution on the quantum system compared to the forward time evolution performed in step 204. For example, the system may apply a unitary operator e to the quantum system. iHτ′ In some implementations, the implementation of the backward time evolution may be noisy.

[0069] The system then measures the probe qubit to obtain the non-time-ordered correlator value (step 210). For example, the system can measure the local operator V p Expected value for the probe qubit. In some implementations, the system can repeat steps 202 to 210 for different values ​​of τ and for different local or global unitary operators (e.g., different rotation angles) to obtain multiple values ​​of the non-time-ordered correlator.

[0070] The system processes the measurements of the non-time-ordered correlator by a classical computing device (such as a classical processor 104) to determine the properties of the quantum system (step 212). In some implementations, the system can use a trained classical learning model to process the measurements of the non-time-ordered correlator and predict the properties of the quantum system. For example, the classical learning model can be a support vector machine (SVM) with a radial basis function that has been trained based on multiple (e.g., 3000) randomly drawn Hamiltonians to predict the distance d (distance detection qubit) where two spin chains intersect (e.g., Figure 3 ). To train the classical learning model, the system can generate training data by a quantum computing device by performing classical or quantum simulations on the Hamiltonian that characterizes the quantum system to calculate the correlation function of the Hamiltonian set for each value of d. Each quantum simulation corresponds to a corresponding Hamiltonian parameter value. The system can then use these sets to train the classical learning model to use the training data to predict the properties of the quantum system, for example, to predict the value of d of an unknown Hamiltonian based on its correlation function.

[0071] In some implementations, before processing the measurements of the non-time ordered correlators to determine the properties of the quantum system, the system can calculate the Fisher information for each measurement of the non-time ordered correlators. The system can then identify one or more correlators that achieve the maximum Fisher information (or correlators having an amount of Fisher information exceeding a predetermined threshold). The system can then repeat the measurements of the non-time ordered correlators corresponding to the maximum Fisher information, wherein the repeated measurements are performed with higher precision.

[0072] Figure 3Two diagrams 300, 350 are shown for learning in a quantum system with restricted access using OTOC. In both diagrams, a spin system with disordered on-site fields and dipolar interactions between neighboring spins is considered. The time evolution of the spin system is simulated using a Krylov subspace method.

[0073] The first figure 300 shows the results of a support vector machine (SVM) regression for learning the distance d in the spin geometry 302, where the TOC or both the TOC and the OTOC are accessed. Specifically, the SVM is trained based on 3000 randomly drawn Hamiltonians (300 for each value of d = 0, ..., 9), and its performance is tested based on 2000 additional Hamiltonians. In order to reduce the sensitivity of learning to the fine-tuning characteristics of the correlation function, all correlation functions use a Gaussian distributed readout error with a mean of zero and a standard deviation equal to 3%. The relationship between the model's prediction and the actual value of d is shown in Figure 300. In Figure 300, the bars represent the 75% (100%) percentile of the prediction on 200 disordered realizations. The step function represents the actual d. As shown in the figure, accessing the OTOC exponentially improves the learnability of long-distance features. Specifically, for all distances explored (up to d-9), learning using the OTOC allows accurate prediction of d, with deviations from its actual value within ±1. In contrast, if only the TOC is accessed, the model performs significantly worse for all d and relies almost entirely on random guessing for d ≥ 3.

[0074] The second graph 350 shows the interaction J with the probe qubit at a distance d. d Fisher information (FI)FI(J d |C), which is maximized across all correlators C in the L-qubit 1D chain 304. FI quantifies the amount of information about an unknown parameter (e.g., coupling strength J) carried by a random variable (e.g., a correlation function C measured within a certain readout error δ), and thereby constrains the ultimate learnability of that parameter. If the readout error is assumed to be normally distributed, then FI is the squared derivative By introducing the factor δ 2 The delta-dependency is eliminated.

[0075] In Figure 350, the FI is numerically computed for a traversal of a 1D spin chain, where the coupling J located at a distance d from the probe qubit is to be learned. d. Consider the same set of correlation functions as those specified for the learning task in Figure 300. The maximum Fisher information among all correlation functions (i.e., all x;t) is plotted, averaged over 200 and 1000 disordered realizations for TOC and OTOC, respectively. As shown, the maximum FI for TOC decays exponentially with the distance d from the probe qubit. In contrast, the maximum FI for OTOC follows a slow algebraic decay of ~1 / d, thereby achieving an advantage of multiple orders of magnitude over TOC even at moderate distances d ≥ 3. This algebraic decay arises from the fact that the OTOC wavefront decays over time. Widen.

[0076] Studying weak interactions

[0077] Figure 4 is a flow chart of an example process 400 for detecting weak interactions in a quantum system. In the present disclosure, a weak interaction in a quantum system is an interaction whose strength is less than the strength of other interactions in the quantum system, for example, a weak interaction in an otherwise strongly interacting system. Unlike the example process 200 described above, in these cases, the experimenter has non-local unitary control over the qubits in the quantum system, for example, being able to measure all local correlation functions of the quantum system of interest. For convenience, process 400 will be described as being performed by a system of one or more classical and quantum computing devices located in one or more locations. For example, a suitably programmed Figure 1 The system 100 may perform the example process 400 .

[0078] The system measures, by a measurement control system, a value of a non-time-ordered correlator of a quantum system including a plurality of interacting qubits. In some implementations, the quantum system may be a strongly interacting system. The value of the non-time-ordered correlator indicates whether information encoded at an initial time at one qubit is contained in correlations involving other qubits at time t.

[0079] The non-time-ordered correlator may take the form given by equation (3) above, where x, x′ traverses all qubits included in the quantum system. Figure 2 As described, operators V, W can be represented by V = W∈{σ x , σ z} is given (for TOC) and by V = W∈{σ z} is given (for OTOC). In some implementations, the indexes x, x' may span all qubits within distance 2 of the link - this consists of 6 possible values ​​for each of x, x', corresponding to distances 0, 1 and 2 to the left and right of the link. In principle, x, x' could traverse the entire lattice, however, in practice it has been observed that correlation functions involving qubits far from the link provide little information and can therefore be safely ignored.

[0080] To measure the non-time-ordered correlator, the system prepares a first qubit and a second qubit in the quantum system in an initial state, wherein the first qubit is adjacent to the second qubit (step 402). For example, the system can prepare the first qubit in an eigenstate of a first operator included in the OTOC and prepare the second qubit in an eigenstate of a second operator included in the OTOC, as described above with reference to Figure 2 described.

[0081] Then, the system performs forward time evolution on the quantum system for time t (step 404). For example, the system can apply the unitary operator e to the quantum system. -iHt A quantum circuit of , where H represents the Hamiltonian that characterizes the quantum system.

[0082] The system then perturbs the quantum system by applying a unitary operator to the first qubit (step 406). The type of unitary operator applied in step 406 depends on the type of learning being performed. For example, in some implementations, the quantum system can be a 1D spin chain. In these implementations, the learning task can be to predict whether the spin chain includes or excludes weak link interactions. As another example, in some implementations, the quantum system can be a 1D spin chain, and the learning task can be a task of characterizing weak link interactions known to exist in the spin chain.

[0083] Then, the system performs a backward time evolution on the quantum system for time t (step 408). That is, the system performs a time-reversed evolution on the quantum system compared to the forward time evolution performed in step 404. For example, the system may apply a unitary operator e to the quantum system. iHt In some implementations, the implementation of the backward time evolution may be noisy.

[0084] The system then measures the first qubit and the second qubit to obtain a non-time-ordered correlator value (step 410). In some implementations, the system can repeat steps 402 to 410 for different values ​​of t and for each of multiple pairs of qubits in the quantum system (e.g., pairs of qubits within a predetermined distance of a known weak link interaction) to obtain multiple values ​​of the non-time-ordered correlator.

[0085] The system processes the measurements of the non-time-ordered correlator by a classical computing device to determine the properties of the quantum system (step 412). In some implementations, the system can use a trained classical learning model to process the measurements of the non-time-ordered correlator and predict the properties of the quantum system. To train the classical learning model, the system can generate training data by performing quantum simulations on a Hamiltonian that characterizes the quantum system by a quantum computing device. Each quantum simulation corresponds to a corresponding Hamiltonian parameter value. Then, the system can use the training data to train the classical learning model to predict the properties of the quantum system.

[0086] In some implementations, before processing the measurements of the non-time ordered correlators to determine the properties of the quantum system, the system can calculate the Fisher information for each measurement of the non-time ordered correlators. The system can then identify one or more correlators that achieve the maximum Fisher information (or correlators having an amount of Fisher information exceeding a predetermined threshold). The system can then repeat the measurements of the non-time ordered correlators corresponding to the maximum Fisher information, wherein the repeated measurements are performed with higher precision.

[0087] In some implementations, before processing the measured values ​​of the non-time ordered correlators to determine the properties of the quantum system, the system can calculate the mutual information between each measured non-time ordered correlator value and the link strength. The system can then select a predetermined number of measured non-time ordered correlator values ​​with the highest mutual information. The system can then provide the selected predetermined number of measured non-time ordered correlator values ​​for processing by a classical computing device.

[0088] Figure 5 Two diagrams 500, 550 for studying weak interactions in quantum systems are shown. In both diagrams, it is assumed that a spin chain 502 is accessible, which has unknown Hamiltonian parameters and no linking interactions (J l →0) or with a fixed non-zero weak link interaction strength J l In Figure 500, for J l For each fixed value of , a binary SVM classifier was trained based on the correlation function (given by Equations 2 and 3) of 300 unordered samples, including a 3% readout error in each correlator value, as described above in reference Figure 3 The model performance was tested based on 200 additional samples. As shown in Figure 500, the classification accuracy showed the following trends: (i) The accuracy increased with J l (ii) learning via both OTOC and TOC allows detection of ~10 times that of learning via TOC alone l; and (iii) OTOC allows the detection of J that decreases as the chain size L increases l .

[0089] To understand this behavior from an analytical perspective, it is worth noting that the best correlation functions for detecting a link will generally involve operators directly adjacent to (on either side of) the link. These correlators measure the transfer of spin polarization (for TOC) or operator support (for OTOC) across the link and are nontrivial only when the link interaction strength is nonzero. For TOC, spin polarization is expected to transfer at a rate of incoherently passes through the link, where is the typical strong interaction strength. Combined with the overall exponential decay of the spin with time (if the system has no conserved quantities), we would expect For OTOC, the precompute subroutine is supported at a similar rate However, this increase will continue until a very late time t~L / J, when the information propagating in the chain will suddenly cause the OTOC to decay to zero. The best time to detect a link comes when these correlators are maximized, because in the absence of a link, each correlator is zero. The TOC is maximized at the first sequential time t~1 / J, when the correlator magnitudes is suppressed by the square of the weak link interaction strength. In contrast, OTOC is maximized at a much later time t~L / J and thus has magnitude In both cases, it can be seen that as the link strength decreases, the detection of the link becomes more difficult. The detection via OTOC is enhanced by a factor of L, thereby capturing the connectivity changes associated with the link.

[0090] Graph 550 quantitatively confirms these calculations by calculating the Fisher information of the link interaction strengths. In graph 550, the maximum Fisher information is plotted over all local correlation functions. The average was taken over 100 unordered realizations. Here, the logarithm of the link interaction strength is considered in order to appropriately compare the Fisher information over multiple orders of magnitude of the interaction. l The Fisher information of restricts the learnability of interaction strengths to a percentage of their actual values. It is expected that, for TOC, And for OTOC, Figure 550 shows that FI is ~J 4 (For Little J l ) inhibition, and showed a fold advantage for OTOC compared to TOC, which increased with increasing L.

[0091] Disjoint Unitary Problem

[0092] In the disjoint unitary problem, oracle access is given to either (i) a fixed, n-qubit Haar random unitary U, or (ii) two fixed, n / 2-qubit Haar random unitaries The task is to determine which of (i) or (ii) is achieved. Qualitatively, this problem is similar to the Hamiltonian learning scenario identified above. First, the property of the system to be learned - the connectivity of the unitary - directly determines how information diffuses in the system, as measured by the OTOC. Second, Haar random unitaries are inherently strongly interacting, which causes time-ordered measurements to decay and therefore provide little information.

[0093] Figure 6 is a circuit diagram 600 for solving the disjoint unitary problem using OTOC measurement. Next, prepare a register of qubits. Apply unknown unitary 604 (U or ). Next, we apply the operator σ to the first qubit. x 606, followed by the inverse of the unknown unitary 608. Finally, it is determined (via a measurement operation 610) whether the second block of n / 2 qubits is in the all-zero state. If so, then according to case (ii), the hidden unknown unitary is If not, then according to case (i), the unknown unitary is U. As shown in the figure, the disjoint unitary problem can be solved by measuring non-time-ordered observables, using a constant number (in terms of n) of queries to the oracle and its time reversal:

[0094]

[0095] Where V represents the unknown unitary (U or ), represents a constant operator applied to the first block of n / 2 qubits, and represents the Pauli-X operator applied to the first qubit.

[0096] In case (i), the OTOC approaches zero and is likely to approach unity exponentially. In case (ii), the OTOC is unity because the two subsystems are not connected by Therefore, since it is possible to approach unity exponentially, a single query of the unknown unitary and its time reversal can be used to discriminate between the two cases. In contrast, any time-ordered learning protocol requires an exponential number of queries of the unknown unitary to solve the disjoint unitary problem.

[0097] Figure 7An example classical / quantum computer 700 is depicted for performing some or all of the classical and quantum operations described in this specification. The example classical / quantum computer 700 includes an example quantum computing device 702. Quantum computing device 702 is intended to represent various forms of quantum computing devices. The components shown here, their connections and relationships, and their functions are exemplary only and do not limit implementations of the inventions described and / or claimed in this document.

[0098] The example quantum computing device 702 includes a qubit assembly 752 and a control and measurement system 704. The qubit assembly includes a plurality of qubits, such as qubit 706, which are used to perform an algorithmic operation or quantum computation. Figure 7 The qubits are shown arranged in a rectangular array, but this is a schematic depiction and is not intended to be limiting. Qubit assembly 752 also includes adjustable coupling elements, such as couplers 708, which allow for interaction between coupled qubits. Figure 7 In the schematic depiction of , each qubit is adjustably coupled to each of its four neighboring qubits through a corresponding coupling element. However, this is an example arrangement of qubits and couplers, and other arrangements are possible, including non-rectangular arrangements, arrangements that allow coupling between non-adjacent qubits, and arrangements that include adjustable coupling between more than two qubits.

[0099] Each qubit can be a physical two-level quantum system or device with energy levels representing logical values ​​0 and 1. The specific physical implementation of multiple qubits and how they interact with each other depends on various factors, including the type of quantum computing device 702 included in the example computer 700 or the type of quantum computing being performed by the quantum computing device. For example, in an atomic quantum computer, a qubit can be implemented via an atom, a molecule, or a solid-state quantum system (e.g., a hyperfine atomic state). As another example, in a superconducting quantum computer, a qubit can be implemented via a superconducting qubit or a semiconductor qubit (e.g., a superconducting transmon state). As another example, in an NMR quantum computer, a qubit can be implemented via a nuclear spin state.

[0100] In some implementations, quantum computations may proceed by, for example, loading qubits from a quantum memory and applying a sequence of unitary operators to the qubits. In some implementations, the sequence of unitary operators may represent a forward or backward time evolution. Applying a unitary operator to a qubit may include applying a corresponding sequence of quantum logic gates to the qubit, for example, to implement a quantum algorithm, such as a quantum principal component algorithm. Example quantum logic gates include single-qubit gates, such as Pauli-X, Pauli-Y, Pauli-Z (also known as X, Y, Z), Hadamard gates, S gates, rotations; dual-qubit gates, such as controlled X gates, controlled Y gates, controlled Z gates (also known as CX, CY, CZ), controlled NOT gates (also known as CNOTs), controlled exchange gates (also known as CSWAPs); and gates involving three or more qubits, such as Toffoli gates. Quantum logic gates may be implemented by applying control signals 710 generated by a control and measurement system 704 to qubits and couplers.

[0101] For example, in some implementations, the qubits in qubit assembly 752 may be frequency tunable. In these examples, each qubit may have an associated operating frequency that may be adjusted by applying a voltage pulse via one or more drive lines coupled to the qubit. Example operating frequencies include qubit idle frequency, qubit interaction frequency, and qubit readout frequency. Different frequencies correspond to different operations that a qubit may perform. For example, setting the operating frequency to a corresponding idle frequency may place the qubit in a state in which it does not strongly interact with other qubits and it may be used to perform a single qubit gate. As another example, in the case where qubits interact via a coupler with a fixed coupling, the qubits may be configured to interact with each other by setting their respective operating frequencies to a certain gate-related frequency that is detuned from their common interaction frequency. In other cases, for example, when qubits interact via a tunable coupler, the qubits may be configured to interact with each other by setting the parameters of their respective couplers to enable interaction between qubits and then by setting the respective operating frequencies of the qubits to a certain gate-related frequency that is detuned from their common interaction frequency. Such interactions may be performed to perform multi-qubit gates.

[0102] The type of control signal 710 used depends on the physical implementation of the qubit. For example, the control signal may include RF or microwave pulses in NMR or superconducting quantum computer systems, or light pulses in atomic quantum computer systems.

[0103] Quantum computations can be accomplished by measuring the state of a qubit (e.g., using a quantum observable such as X or Z) using a corresponding control signal 710. The measurement results in a readout signal 712 representing the measurement being transmitted back to the control and measurement system 704. Depending on the physical scheme used for the quantum computing device and / or qubit, the readout signal 712 may include an RF, microwave, or optical signal. For convenience, Figure 7 The control signals 710 and readout signals 712 shown are depicted as addressing only selected elements of the qubit assembly (ie, the top and bottom rows), but during operation, the control signals 710 and readout signals 712 may address every element in the qubit assembly 752.

[0104] The control and measurement system 704 is an example of a classical computer system that can be used to perform various operations (as described above) on the quantum assembly 752 as well as other classical subroutines or calculations. The control and measurement system 704 includes one or more classical processors (e.g., the classical processor 414), one or more memories (e.g., the memory 716), and one or more I / O units (e.g., the I / O unit 718) connected via one or more data buses. The control and measurement system 704 can be programmed to send a sequence of control signals 710 to the qubit assembly, for example, to perform a selected series of quantum gate operations, and to receive a sequence of readout signals 712 from the qubit assembly, for example, as part of performing a measurement operation.

[0105] The processor 714 is configured to process instructions for execution within the control and measurement system 704. In some implementations, the processor 714 is a single-threaded processor. In other implementations, the processor 714 is a multi-threaded processor. The processor 714 is capable of processing instructions stored in the memory 716.

[0106] The memory 716 stores information within the control and measurement system 704. In some implementations, the memory 716 includes a computer-readable medium, a volatile memory unit, and / or a non-volatile memory unit. In some cases, the memory 716 may include a storage device capable of providing mass storage for the system 704, such as a hard disk device, an optical disk device, a storage device shared by multiple computing devices over a network (e.g., a cloud storage device), and / or some other mass storage device.

[0107] The input / output device 718 provides input / output operations for the control and measurement system 704. The input / output device 718 may include a D / A converter, an A / D converter, and an RF / microwave / optical signal generator, transmitter, and receiver, whereby control signals 710 are sent to the qubit assembly and readout signals 712 are received from the qubit assembly, as is appropriate for the physical scheme used for the quantum computer. In some implementations, the input / output device 718 may also include one or more network interface devices (e.g., Ethernet cards), serial communication devices (e.g., RS-232 ports), and / or wireless interface devices (e.g., 802.11 cards). In some implementations, the input / output device 718 may include a driver device configured to receive input data and send output data to other external devices (e.g., keyboards, printers, and display devices).

[0108] Although already Figure 7 An example control and measurement system 704 is depicted in the figure, but the subject matter and functional operations described in this specification may be implemented with other types of digital electronic circuit systems or with computer software, firmware or hardware, including the structures disclosed in this specification and their structural equivalents or a combination of one or more of them.

[0109] The example system 700 also includes an example classical processor 750. The classical processor 750 can be used to perform the classical computing operations described in this specification according to some implementations.

[0110] The subject matter and implementation of the operations described in this specification may be implemented with digital electronic circuit systems, analog electronic circuit systems, suitable quantum circuit systems or more generally quantum computing systems, tangibly embodied software or firmware, computer hardware, including the structures disclosed in this specification and their structural equivalents, or a combination of one or more of them. The term "quantum computing system" may include, but is not limited to, a quantum computer, a quantum information processing system, a quantum cryptographic system, or a quantum simulator.

[0111] Implementations of the subject matter described in this specification may be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory storage medium, for execution by a data processing device or for controlling the operation of a data processing device. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubits, or a combination of one or more of them. Alternatively or additionally, the program instructions may be encoded on an artificially generated propagation signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) capable of encoding digital and / or quantum information, the artificially generated propagation signal being generated to encode digital and / or quantum information for transmission to a suitable receiver device for execution by the data processing device.

[0112] The terms quantum information and quantum data refer to information or data carried, held or stored by a quantum system, wherein the smallest non-trivial system is a qubit, i.e., a system defining a unit of quantum information. It should be understood that the term "qubit" encompasses all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems may include multi-level systems, e.g., having two or more energy levels. For example, such systems may include atoms, electrons, photons, ions, or superconducting qubits. In many implementations, the computational ground state is identified with the ground state and the first excited state, however it should be understood that other arrangements in which the computational state is identified with a higher energy level excited state are also possible.

[0113] The term "data processing device" refers to digital and / or quantum data processing hardware, and covers all kinds of devices, apparatuses and machines for processing digital and / or quantum data, including, for example, programmable digital processors, programmable quantum processors, digital computers, quantum computers, multiple digital and quantum processors or computers, and combinations thereof. The device may also be or also include a dedicated logic circuit system, such as an FPGA (field programmable gate array), an ASIC (application-specific integrated circuit), or a quantum simulator, i.e., a quantum data processing device designed to simulate or generate information about a specific quantum system. Specifically, a quantum simulator is a dedicated quantum computer that does not have the ability to perform general quantum computations. In addition to the hardware, the device may optionally include code that creates an execution environment for a digital and / or quantum computer program, for example, code that constitutes a processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0114] A digital computer program, which may also be referred to or described as a program, software, software application, module, software module, script or code, may be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it may be deployed in any form, including as a stand-alone program or as a module, component, subroutine or other unit suitable for use in a digital computing environment. A quantum computer program, which may also be referred to or described as a program, software, software application, module, software module, script or code, may be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or may be written in a quantum programming language such as QCL or Quipper.

[0115] A computer program may, but need not, correspond to a file in a file system. A program may be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, subroutines, or code portions). A computer program may be deployed to execute on one computer or on multiple computers located at one site or distributed across multiple sites and interconnected by a digital and / or quantum data communication network. A quantum data communication network is understood to be a network that can send quantum data using quantum systems (e.g., qubits). In general, digital data communication networks cannot send quantum data, however, quantum data communication networks can send both quantum data and digital data.

[0116] The processes and logic flows described in this specification can be performed by one or more programmable computers (operating using one or more processors, as appropriate) executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by a dedicated logic circuit system, and the device can also be implemented as a dedicated logic circuit system, such as an FPGA or ASIC or a quantum simulator, or by a combination of a dedicated logic circuit system or a quantum simulator and one or more programmed digital and / or quantum computers.

[0117] For a system of one or more computers "configured to" perform a particular operation or action, it is meant that the system has installed thereon software, firmware, hardware, or a combination thereof that, in operation, causes the system to perform the operation or action. For one or more computer programs configured to perform a particular operation or action, it is meant that the one or more programs include instructions that, when executed by a data processing device, cause the device to perform the operation or action. For example, a quantum computer may receive instructions from a digital computer that, when executed by a quantum computing device, cause the device to perform an operation or action.

[0118] Computers suitable for executing computer programs may be based on general or special purpose processors or any other kind of central processing unit. In general, the central processing unit will receive instructions and data from a read-only memory, a random access memory, or a quantum system suitable for sending quantum data (e.g. photons), or a combination thereof.

[0119] Elements of a computer include a central processing unit for executing or performing instructions and one or more memory devices for storing instructions and digital, analog and / or quantum data. The central processing unit and the memory may be supplemented by or incorporated into a dedicated logic circuit system or a quantum simulator. In general, a computer will also include one or more mass storage devices for storing data, such as magnetic disks, magneto-optical disks, optical disks, or quantum systems suitable for storing quantum information, or be operatively coupled to receive data from or transmit data to or both of the one or more mass storage devices. However, a computer need not have such devices.

[0120] Quantum circuit elements (also called quantum computing circuit elements) include circuit elements for performing quantum processing operations. That is, quantum circuit elements are configured to utilize quantum mechanical phenomena such as superposition and entanglement to perform operations on data in a non-deterministic manner. Certain quantum circuit elements such as qubits can be configured to simultaneously represent information in more than one state and operate on the information. Examples of superconducting quantum circuit elements include circuit elements such as quantum LC oscillators, qubits (e.g., flux qubits, phase qubits, or charge qubits), and superconducting quantum interference devices (SQUIDs) (e.g., RF-SQUIDs or DC-SQUIDs), etc.

[0121] In contrast, classical circuit elements typically process data in a deterministic manner. Classical circuit elements can be configured to collectively execute instructions of a computer program by performing basic arithmetic, logic, and / or input / output operations on data, where the data is represented in analog or digital form. In some implementations, classical circuit elements can be used to send data to and / or receive data from quantum circuit elements via electrical or electromagnetic connections. Examples of classical circuit elements include circuit elements based on CMOS circuit systems, fast single flux quantum (RSFQ) devices, reciprocal quantum logic (RQL) devices, and ERSFQ devices, where ERSFQ devices are energy-saving versions of RSFQ that do not use bias resistors.

[0122] In some cases, some or all of the quantum and / or classical circuit elements may be implemented using, for example, superconducting quantum and / or classical circuit elements. The manufacture of superconducting circuit elements may require the deposition of one or more materials, such as superconductors, dielectrics and / or metals. Depending on the selected material, deposition processes such as chemical vapor deposition, physical vapor deposition (e.g., evaporation or sputtering) or epitaxial techniques and other deposition processes may be used to deposit these materials. The process for manufacturing circuit elements described herein may require the removal of one or more materials from the device during manufacture. Depending on the material to be removed, the removal process may include, for example, wet etching techniques, dry etching techniques or stripping processes. The materials forming the circuit elements described herein may be patterned using known photolithography techniques (e.g., photolithography or electron beam lithography).

[0123] During operation of a quantum computing system using superconducting quantum circuit elements and / or superconducting classical circuit elements (such as the circuit elements described herein), the superconducting circuit elements are cooled in a cryostat to a temperature that allows the superconducting material to exhibit superconducting properties. Superconductor (or superconducting) materials can be understood as materials that exhibit superconducting properties at or below the superconducting critical temperature. Examples of superconducting materials include aluminum (superconducting critical temperature is 1.2 Kelvin) and niobium (superconducting critical temperature is 9.3 Kelvin). Therefore, superconducting structures such as superconducting traces and superconducting ground planes are formed of materials that exhibit superconducting properties at or below the superconducting critical temperature.

[0124] In certain implementations, classical circuit elements electrically and / or electromagnetically coupled to quantum circuit elements (e.g., qubits and qubit couplers) may be used to provide control signals for these quantum circuit elements. The control signals may be provided in digital and / or analog form.

[0125] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile digital and / or quantum memory, media and memory devices, including, for example, semiconductor memory devices, such as EPROM, EEPROM and flash memory devices; magnetic disks, such as internal hard disks or removable disks; magneto-optical disks; CD-ROM and DVD-ROM disks; and quantum systems, such as trapped atoms or electrons. It should be understood that quantum memory is a device capable of storing quantum data with high fidelity and efficiency for a long time, such as a light-matter interface that uses light for transmission and uses matter for storage and preservation of quantum characteristics of quantum data (such as superposition or quantum coherence).

[0126] The control of the various systems or parts thereof described in this specification may be implemented with a computer program product, which includes instructions stored on one or more non-transitory machine-readable storage media and executable on one or more processing devices. The systems or parts thereof described in this specification may each be implemented as an apparatus, method, or system, which may include one or more processing devices and a memory for storing executable instructions to perform the operations described in this specification.

[0127] Although this specification contains many specific implementation details, these details should not be interpreted as limitations on the scope of the content that may be claimed, but should be interpreted as descriptions of features that may be peculiar to a particular implementation. Certain features described in this specification in the context of separate implementations may also be implemented in a single implementation in combination. Conversely, the individual features described in the context of a single implementation may also be implemented in multiple implementations individually or in any suitable sub-combination. In addition, although the features are described above as working in certain combinations and even initially claimed, one or more features from the claimed combination may be removed from the combination in some cases, and the claimed combination may be a variation on a sub-combination or a sub-combination.

[0128] Similarly, although operations are depicted in a particular order in the accompanying drawings, this should not be construed as requiring that such operations be performed in the particular order shown or in a sequential order, or that all of the illustrated operations be performed, in order to achieve a desired result. In certain contexts, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the implementations described above should not be construed as requiring such separation in all implementations, and it should be understood that the described program components and systems may generally be integrated together in a single software product or packaged in multiple software products.

[0129] Specific implementations of the subject matter have been described. Other implementations are within the scope of the appended claims. For example, the actions recited in the claims can be performed in a different order and still achieve the desired results. As an example, the processes depicted in the accompanying drawings do not necessarily require the specific order shown or sequential order to achieve the desired results. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. A method comprising: Measuring, by a control and measurement system, a non-time-ordered correlator value of a quantum system comprising a plurality of qubits, wherein the plurality of qubits comprises a probe qubit and one or more other qubits, the measuring comprising: preparing the probe qubit in an initial state, For time t, the forward time evolution of the quantum system is performed, applying a unitary operator to one or more qubits in the quantum system, For said time t, performing a backward time evolution of said quantum system, and measuring the probe qubit to obtain the non-time-ordered correlator value; and The measured non-time-ordered correlator values ​​are processed by a classical computing device to determine properties of the quantum system.

2. The method of claim 1 , wherein the measured non-time-ordered correlator value indicates whether information encoded at the probe qubit at an initial time is contained in correlations involving the other qubits at time t.

3. The method of claim 1 or claim 2, further comprising repeatedly measuring the non-time ordered correlator value for each of a plurality of values ​​of t and for each of a plurality of unitary operators.

4. The method of claim 3, wherein processing the measured non-time-ordered correlator values ​​to determine a property of the quantum system comprises using a trained classical learning model to predict the property of the quantum system.

5. The method of claim 4, further comprising: Generating training data by a quantum computer, the generating comprising performing quantum simulations on a Hamiltonian characterizing the quantum system, each quantum simulation corresponding to a corresponding Hamiltonian parameter value; as well as The classical learning model for predicting properties of the quantum system is trained using the training data.

6. The method according to any one of claims 3 to 5, further comprising: for each of a plurality of values ​​of t and for each of a plurality of unitary operators, measuring the non-time ordered correlator value, wherein the measuring is performed with a first precision; calculating the Fisher information for each measured non-time-ordered correlator value; as well as Repeating the measurement of the non-time ordered correlator value having the maximum Fisher information, wherein the repeated measurement is performed with a second precision higher than the first precision.

7. A method as claimed in any preceding claim, wherein the unitary operator comprises a local unitary operator, optionally a single-qubit Pauli operation.

8. A method as claimed in any preceding claim, wherein the unitary operator comprises a global rotation operation.

9. The method of any one of the preceding claims, wherein the quantum system comprises a traversing ID spin chain, and wherein determining a property of the quantum system comprises learning a qubit coupling to the probe qubit at a distance d.

10. A method as claimed in any preceding claim, wherein the quantum system comprises two spin chains intersecting at a distance d from the probe qubit, and wherein determining a property of the quantum system comprises learning a value of d.

11. The method of any one of the preceding claims, wherein performing a forward time evolution of the quantum system for time t comprises applying to the quantum system a second unitary operator e -iHt wherein H represents a Hamiltonian characterizing the quantum system, and wherein performing a backward time evolution on the quantum system for the time t comprises applying a third unitary operator e to the quantum system. iHt quantum circuits.

12. A method as claimed in any preceding claim, wherein performing the backward time evolution of the quantum system for the time t is noisy.

13. A method comprising: A non-time-ordered correlator value of a quantum system including a plurality of interacting qubits is measured by a control and measurement system, the measurement comprising: preparing a first qubit and a second qubit in the quantum system in an initial state, wherein the first qubit is adjacent to the second qubit, For time t, the forward time evolution of the quantum system is performed, Applying a unitary operator to the first qubit, For said time t, performing a backward time evolution of said quantum system, and measuring the first qubit and the second qubit to obtain the non-time-ordered correlator value; and The measured non-time-ordered correlator values ​​are processed by a classical computing device to determine properties of the quantum system.

14. The method of claim 13, wherein the measured non-time-ordered correlator value indicates whether information encoded at the first qubit at an initial time is contained in correlations involving other qubits at time t.

15. The method of claim 13 or claim 14, further comprising repeatedly measuring the non-time ordered correlator value for each of a plurality of values ​​of t and for each of a plurality of pairs of qubits in the quantum system.

16. The method of claim 15, wherein processing the measured non-time-ordered correlator values ​​to determine a property of the quantum system comprises using a trained classical learning model to predict the property of the quantum system.

17. The method of claim 16, further comprising: Generating training data by a quantum computer, the generating comprising performing quantum simulations on a Hamiltonian characterizing the quantum system, each quantum simulation corresponding to a corresponding Hamiltonian parameter value; as well as The classical learning model for predicting properties of the quantum system is trained using the training data.

18. The method of any one of claims 15 to 17, further comprising: for each of a plurality of values ​​of t and for each of a plurality of pairs of qubits, measuring the non-time-ordered correlator value, wherein the measuring is performed with a first precision; calculating the Fisher information for each measured non-time-ordered correlator value; as well as Repeating the measurement of the non-time ordered correlator value having the maximum Fisher information, wherein the repeated measurement is performed with a second precision higher than the first precision.

19. The method of any one of claims 13 to 18, wherein the quantum system comprises a strongly interacting system.

20. The method of claim 19, wherein the quantum system comprises a ID spin chain, and wherein determining a property of the quantum system comprises characterizing weak linking interactions known to exist in the spin chain.

21. The method of claim 20, further comprising repeatedly measuring the non-time-ordered correlator values ​​for qubit pairs within a predetermined distance from the weak link interaction.

22. The method of claim 20 or claim 21 further comprising, prior to processing the measured non-time ordered correlator values: calculating the mutual information between each measured non-time-ordered correlator value and the link strength; selecting a predetermined number of the measured non-time ordered correlator values ​​having the highest mutual information; and The predetermined number of measured non-time ordered correlator values ​​is provided for processing by the classical computing device.

23. The method of any one of claims 13 to 22, wherein the quantum system comprises a ID spin chain, and wherein determining a property of the quantum system comprises predicting whether the spin chain includes or excludes weak link interactions.

24. The method of any one of claims 13 to 23, wherein performing the backward time evolution of the quantum system for the time t is noisy.

25. The method of any one of claims 13 to 24, wherein performing a forward time evolution of the quantum system for time t comprises applying to the quantum system a second unitary operator e -iHt wherein H represents a Hamiltonian characterizing the quantum system, and wherein performing a backward time evolution on the quantum system for the time t comprises applying a third unitary operator e to the quantum system. iHt quantum circuits.

26. A system comprising: Control and measurement systems; as well as A classical computing device coupled to the control and measurement system, wherein the classical computing device includes a computer-readable medium having instructions stored thereon, the instructions, when executed by the classical computing device, causing the control and measurement system and the classical computing device to perform operations according to the method of any one of claims 1 to 25.

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